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<!--Modified on: 8/22/2026 1:45:25 AM-->
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CashAndCashEquivalentsAtCarryingValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash and Cash Equivalents, at Carrying Value</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CashAndCashEquivalentsAtCarryingValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash and cash equivalents</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountsReceivableNetCurrent" xlink:label="us-gaap_AccountsReceivableNetCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccountsReceivableNetCurrent" xlink:to="us-gaap_AccountsReceivableNetCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AccountsReceivableNetCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts Receivable, after Allowance for Credit Loss, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AccountsReceivableNetCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts receivable - net of allowance for credit loss</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_AccountsReceivableNetCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of standard support services owed from related party</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherReceivablesNetCurrent" xlink:label="us-gaap_OtherReceivablesNetCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OtherReceivablesNetCurrent" xlink:to="us-gaap_OtherReceivablesNetCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OtherReceivablesNetCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other Receivables, Net, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_OtherReceivablesNetCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Related party receivables</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherReceivableAfterAllowanceForCreditLossCurrentRelatedPartyTypeExtensibleEnumeration" xlink:label="us-gaap_OtherReceivableAfterAllowanceForCreditLossCurrentRelatedPartyTypeExtensibleEnumeration" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OtherReceivableAfterAllowanceForCreditLossCurrentRelatedPartyTypeExtensibleEnumeration" xlink:to="us-gaap_OtherReceivableAfterAllowanceForCreditLossCurrentRelatedPartyTypeExtensibleEnumeration_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OtherReceivableAfterAllowanceForCreditLossCurrentRelatedPartyTypeExtensibleEnumeration_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other Receivable, after Allowance for Credit Loss, Current, Related Party [Extensible Enumeration]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ContractWithCustomerAssetNetCurrent" xlink:label="us-gaap_ContractWithCustomerAssetNetCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ContractWithCustomerAssetNetCurrent" xlink:to="us-gaap_ContractWithCustomerAssetNetCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ContractWithCustomerAssetNetCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contract with Customer, Asset, after Allowance for Credit Loss, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ContractWithCustomerAssetNetCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contract asset</label>
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    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InventoryNet" xlink:to="us-gaap_InventoryNet_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_InventoryNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Inventories, net</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PrepaidExpenseAndOtherAssetsCurrent" xlink:label="us-gaap_PrepaidExpenseAndOtherAssetsCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PrepaidExpenseAndOtherAssetsCurrent" xlink:to="us-gaap_PrepaidExpenseAndOtherAssetsCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PrepaidExpenseAndOtherAssetsCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Prepaid Expense and Other Assets, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PrepaidExpenseAndOtherAssetsCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Prepaid expenses and other current assets</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationCurrent" xlink:label="us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationCurrent" xlink:to="us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Including Discontinued Operation, Assets, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Current assets from discontinued operations</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Current assets from discontinued operations</label>
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    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetsCurrent" xlink:to="us-gaap_AssetsCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AssetsCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Assets, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_AssetsCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total current assets</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseRightOfUseAsset" xlink:label="us-gaap_OperatingLeaseRightOfUseAsset" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OperatingLeaseRightOfUseAsset" xlink:to="us-gaap_OperatingLeaseRightOfUseAsset_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OperatingLeaseRightOfUseAsset_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating Lease, Right-of-Use Asset</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OperatingLeaseRightOfUseAsset_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Right-of-use asset - operating lease</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinanceLeaseRightOfUseAsset" xlink:label="us-gaap_FinanceLeaseRightOfUseAsset" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FinanceLeaseRightOfUseAsset" xlink:to="us-gaap_FinanceLeaseRightOfUseAsset_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FinanceLeaseRightOfUseAsset_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finance Lease, Right-of-Use Asset, after Accumulated Amortization</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FinanceLeaseRightOfUseAsset_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Right-of-use asset - finance lease</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PropertyPlantAndEquipmentNet" xlink:label="us-gaap_PropertyPlantAndEquipmentNet" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PropertyPlantAndEquipmentNet" xlink:to="us-gaap_PropertyPlantAndEquipmentNet_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PropertyPlantAndEquipmentNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Property, Plant and Equipment, Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PropertyPlantAndEquipmentNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Property and equipment, net</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Goodwill" xlink:label="us-gaap_Goodwill" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_Goodwill" xlink:to="us-gaap_Goodwill_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_Goodwill_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Goodwill</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_Goodwill_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Goodwill</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_Goodwill_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Goodwill</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IntangibleAssetsNetExcludingGoodwill" xlink:label="us-gaap_IntangibleAssetsNetExcludingGoodwill" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IntangibleAssetsNetExcludingGoodwill" xlink:to="us-gaap_IntangibleAssetsNetExcludingGoodwill_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IntangibleAssetsNetExcludingGoodwill_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Intangible Assets, Net (Excluding Goodwill)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IntangibleAssetsNetExcludingGoodwill_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Intangible assets, net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_IntangibleAssetsNetExcludingGoodwill_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquityMethodInvestments" xlink:label="us-gaap_EquityMethodInvestments" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EquityMethodInvestments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity Method Investments</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_EquityMethodInvestments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Investment in equity method investee</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_EquityMethodInvestments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Investment in Sun Solar</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquitySecuritiesFVNINoncurrent" xlink:label="us-gaap_EquitySecuritiesFVNINoncurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EquitySecuritiesFVNINoncurrent" xlink:to="us-gaap_EquitySecuritiesFVNINoncurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EquitySecuritiesFVNINoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity Securities, FV-NI, Noncurrent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_EquitySecuritiesFVNINoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Investment in equity securities receivable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_EquitySecuritiesFVNINoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Investment in equity securities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisposalGroupIncludingDiscontinuedOperationAssetsNoncurrent" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationAssetsNoncurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DisposalGroupIncludingDiscontinuedOperationAssetsNoncurrent" xlink:to="us-gaap_DisposalGroupIncludingDiscontinuedOperationAssetsNoncurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationAssetsNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Including Discontinued Operation, Assets, Noncurrent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationAssetsNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Non - current assets from discontinued operations</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationAssetsNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Non-current assets from discontinued operations</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Assets" xlink:label="us-gaap_Assets" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_Assets" xlink:to="us-gaap_Assets_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_Assets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Assets</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_Assets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total assets</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_Assets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total Assets</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:label="us-gaap_LiabilitiesAndStockholdersEquityAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:to="us-gaap_LiabilitiesAndStockholdersEquityAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LiabilitiesAndStockholdersEquityAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Liabilities and Equity [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LiabilitiesAndStockholdersEquityAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Liabilities and Stockholders' Deficit</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesCurrentAbstract" xlink:label="us-gaap_LiabilitiesCurrentAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LiabilitiesCurrentAbstract" xlink:to="us-gaap_LiabilitiesCurrentAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LiabilitiesCurrentAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Liabilities, Current [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LiabilitiesCurrentAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Current liabilities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountsPayableCurrent" xlink:label="us-gaap_AccountsPayableCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccountsPayableCurrent" xlink:to="us-gaap_AccountsPayableCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AccountsPayableCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts Payable, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AccountsPayableCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts payable</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccruedLiabilitiesAndOtherLiabilities" xlink:label="us-gaap_AccruedLiabilitiesAndOtherLiabilities" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccruedLiabilitiesAndOtherLiabilities" xlink:to="us-gaap_AccruedLiabilitiesAndOtherLiabilities_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AccruedLiabilitiesAndOtherLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accrued Liabilities and Other Liabilities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AccruedLiabilitiesAndOtherLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accrued expenses and other current liabilities</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_LiabilityForContingentConsiderationCurrent" xlink:label="cntm_LiabilityForContingentConsiderationCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_LiabilityForContingentConsiderationCurrent" xlink:to="cntm_LiabilityForContingentConsiderationCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_LiabilityForContingentConsiderationCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of liability recognized arising from contingent consideration within one year.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_LiabilityForContingentConsiderationCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Liability For Contingent Consideration Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_LiabilityForContingentConsiderationCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contingent consideration liability</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LoansPayableCurrent" xlink:label="us-gaap_LoansPayableCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LoansPayableCurrent" xlink:to="us-gaap_LoansPayableCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LoansPayableCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loans Payable, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LoansPayableCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt, net of debt discount</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConvertibleNotesPayableCurrent" xlink:label="us-gaap_ConvertibleNotesPayableCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ConvertibleNotesPayableCurrent" xlink:to="us-gaap_ConvertibleNotesPayableCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ConvertibleNotesPayableCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Notes Payable, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ConvertibleNotesPayableCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible debt, at fair value</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_ConvertibleNotesPayableCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible notes payable</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeLiabilitiesCurrent" xlink:label="us-gaap_DerivativeLiabilitiesCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DerivativeLiabilitiesCurrent" xlink:to="us-gaap_DerivativeLiabilitiesCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DerivativeLiabilitiesCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative Liability, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DerivativeLiabilitiesCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of derivative liabilities associated with share reset adjustment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_DerivativeLiabilitiesCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative liabilities</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DeferredConsiderationCurrent" xlink:label="cntm_DeferredConsiderationCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DeferredConsiderationCurrent" xlink:to="cntm_DeferredConsiderationCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DeferredConsiderationCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The amount of deferred consideration,  expected to be settled within one year or normal operating cycle.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DeferredConsiderationCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Deferred Consideration, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DeferredConsiderationCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Deferred consideration</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseLiabilityCurrent" xlink:label="us-gaap_OperatingLeaseLiabilityCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OperatingLeaseLiabilityCurrent" xlink:to="us-gaap_OperatingLeaseLiabilityCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OperatingLeaseLiabilityCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating Lease, Liability, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OperatingLeaseLiabilityCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating lease liability</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinanceLeaseLiabilityCurrent" xlink:label="us-gaap_FinanceLeaseLiabilityCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FinanceLeaseLiabilityCurrent" xlink:to="us-gaap_FinanceLeaseLiabilityCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FinanceLeaseLiabilityCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finance Lease, Liability, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FinanceLeaseLiabilityCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finance lease liability</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ContractWithCustomerLiabilityCurrent" xlink:label="us-gaap_ContractWithCustomerLiabilityCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ContractWithCustomerLiabilityCurrent" xlink:to="us-gaap_ContractWithCustomerLiabilityCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ContractWithCustomerLiabilityCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contract with Customer, Liability, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:label="us-gaap_ContractWithCustomerLiabilityCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Ending balance</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:label="us-gaap_ContractWithCustomerLiabilityCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Beginning balance</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ContractWithCustomerLiabilityCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contract liabilities</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_SettlementAgreementFairValueDisclosure" xlink:label="cntm_SettlementAgreementFairValueDisclosure" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_SettlementAgreementFairValueDisclosure" xlink:to="cntm_SettlementAgreementFairValueDisclosure_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_SettlementAgreementFairValueDisclosure_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair value portion of settlement agreement for shares issued under Section 3(a)(10) of the Securities Act.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_SettlementAgreementFairValueDisclosure_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Settlement Agreement, Fair Value Disclosure</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_SettlementAgreementFairValueDisclosure_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">3(a)(10) Settlement Agreement</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_SettlementAgreementFairValueDisclosure_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">3(a)(10) Settlement Agreement, at fair value</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherLiabilitiesCurrent" xlink:label="us-gaap_OtherLiabilitiesCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OtherLiabilitiesCurrent" xlink:to="us-gaap_OtherLiabilitiesCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OtherLiabilitiesCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other Liabilities, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OtherLiabilitiesCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other payable</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationCurrent" xlink:label="us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationCurrent" xlink:to="us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Including Discontinued Operation, Liabilities, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Current liabilities from discontinued operations</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Current liabilities from discontinued operations</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesCurrent" xlink:label="us-gaap_LiabilitiesCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LiabilitiesCurrent" xlink:to="us-gaap_LiabilitiesCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LiabilitiesCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Liabilities, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_LiabilitiesCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total current liabilities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongTermNotesPayable" xlink:label="us-gaap_LongTermNotesPayable" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LongTermNotesPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Notes Payable, Noncurrent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LongTermNotesPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt, net of current portion</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseLiabilityNoncurrent" xlink:label="us-gaap_OperatingLeaseLiabilityNoncurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OperatingLeaseLiabilityNoncurrent" xlink:to="us-gaap_OperatingLeaseLiabilityNoncurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OperatingLeaseLiabilityNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating Lease, Liability, Noncurrent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OperatingLeaseLiabilityNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating lease liabilities, net of current portion</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinanceLeaseLiabilityNoncurrent" xlink:label="us-gaap_FinanceLeaseLiabilityNoncurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FinanceLeaseLiabilityNoncurrent" xlink:to="us-gaap_FinanceLeaseLiabilityNoncurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FinanceLeaseLiabilityNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finance Lease, Liability, Noncurrent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FinanceLeaseLiabilityNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finance lease liabilities, net of current portion</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessCombinationContingentConsiderationLiabilityNoncurrent" xlink:label="us-gaap_BusinessCombinationContingentConsiderationLiabilityNoncurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessCombinationContingentConsiderationLiabilityNoncurrent" xlink:to="us-gaap_BusinessCombinationContingentConsiderationLiabilityNoncurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessCombinationContingentConsiderationLiabilityNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Contingent Consideration, Liability, Noncurrent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_BusinessCombinationContingentConsiderationLiabilityNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contingent consideration liability, net of current portion</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationNoncurrent" xlink:label="us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationNoncurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationNoncurrent" xlink:to="us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationNoncurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Including Discontinued Operation, Liabilities, Noncurrent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Non-current liabilities from discontinued operations</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Non-current liabilities from discontinued operations</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Liabilities" xlink:label="us-gaap_Liabilities" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_Liabilities" xlink:to="us-gaap_Liabilities_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_Liabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Liabilities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_Liabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total liabilities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommitmentsAndContingencies" xlink:label="us-gaap_CommitmentsAndContingencies" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommitmentsAndContingencies" xlink:to="us-gaap_CommitmentsAndContingencies_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CommitmentsAndContingencies_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Commitments and Contingencies.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CommitmentsAndContingencies_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Commitments and Contingencies (Note 11)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockholdersEquityAbstract" xlink:label="us-gaap_StockholdersEquityAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockholdersEquityAbstract" xlink:to="us-gaap_StockholdersEquityAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockholdersEquityAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity, Attributable to Parent [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_StockholdersEquityAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stockholders' Equity:</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PreferredStockValue" xlink:label="us-gaap_PreferredStockValue" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PreferredStockValue" xlink:to="us-gaap_PreferredStockValue_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PreferredStockValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Preferred Stock, Value, Issued</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_PreferredStockValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Preferred stock Series A, $0.0001 par value, 10,000,000 shares authorized as of June 30, 2026 and December 31, 2025 no shares issued or outstanding as of June 30, 2026 and December 31, 2025</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockValue" xlink:label="us-gaap_CommonStockValue" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommonStockValue" xlink:to="us-gaap_CommonStockValue_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CommonStockValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common Stock, Value, Issued</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CommonStockValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common stock, $0.0001 par value, 250,000,000 shares authorized as of June 30, 2026 and December 31, 2025, 656,163 and 4,789,230 issued and outstanding as of June 30, 2026 and December 31, 2025 respectively</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AdditionalPaidInCapital" xlink:label="us-gaap_AdditionalPaidInCapital" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AdditionalPaidInCapital" xlink:to="us-gaap_AdditionalPaidInCapital_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AdditionalPaidInCapital_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Additional Paid in Capital</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AdditionalPaidInCapital_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Additional paid-in-capital</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RetainedEarningsAccumulatedDeficit" xlink:label="us-gaap_RetainedEarningsAccumulatedDeficit" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RetainedEarningsAccumulatedDeficit" xlink:to="us-gaap_RetainedEarningsAccumulatedDeficit_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RetainedEarningsAccumulatedDeficit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Retained Earnings (Accumulated Deficit)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RetainedEarningsAccumulatedDeficit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accumulated deficit</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_AccumulatedOtherComprehensiveIncomeLossNetOfTaxDiscontinuedOperations" xlink:label="cntm_AccumulatedOtherComprehensiveIncomeLossNetOfTaxDiscontinuedOperations" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_AccumulatedOtherComprehensiveIncomeLossNetOfTaxDiscontinuedOperations" xlink:to="cntm_AccumulatedOtherComprehensiveIncomeLossNetOfTaxDiscontinuedOperations_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_AccumulatedOtherComprehensiveIncomeLossNetOfTaxDiscontinuedOperations_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount, after tax, of accumulated increase (decrease) in equity from transaction and other event and circumstance from non-owner source attributable to discontinued operations.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_AccumulatedOtherComprehensiveIncomeLossNetOfTaxDiscontinuedOperations_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accumulated Other Comprehensive Income (Loss), Net of Tax, Discontinued Operations</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_AccumulatedOtherComprehensiveIncomeLossNetOfTaxDiscontinuedOperations_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accumulated other comprehensive loss from discontinuing operations</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockholdersEquity" xlink:label="us-gaap_StockholdersEquity" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockholdersEquity" xlink:to="us-gaap_StockholdersEquity_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockholdersEquity_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity, Attributable to Parent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_StockholdersEquity_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total ConnectM Technology Solutions, Inc.'s stockholders' equity/(deficit)</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_EquityAttributableToNoncontrollingInterestContinuingOperations" xlink:label="cntm_EquityAttributableToNoncontrollingInterestContinuingOperations" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_EquityAttributableToNoncontrollingInterestContinuingOperations" xlink:to="cntm_EquityAttributableToNoncontrollingInterestContinuingOperations_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_EquityAttributableToNoncontrollingInterestContinuingOperations_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of equity (deficit) attributable to non controlling interest. Excludes temporary equity attributable to continuing operations.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_EquityAttributableToNoncontrollingInterestContinuingOperations_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity, Attributable to Noncontrolling Interest, Continuing Operations</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_EquityAttributableToNoncontrollingInterestContinuingOperations_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Noncontrolling interest from continuing operations</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_EquityAttributableToNoncontrollingInterestDiscontinuedOperations" xlink:label="cntm_EquityAttributableToNoncontrollingInterestDiscontinuedOperations" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_EquityAttributableToNoncontrollingInterestDiscontinuedOperations" xlink:to="cntm_EquityAttributableToNoncontrollingInterestDiscontinuedOperations_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_EquityAttributableToNoncontrollingInterestDiscontinuedOperations_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of equity (deficit) attributable to non controlling interest. Excludes temporary equity attributable to continuing operations.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_EquityAttributableToNoncontrollingInterestDiscontinuedOperations_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity, Attributable to Noncontrolling Interest, Discontinued Operations</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_EquityAttributableToNoncontrollingInterestDiscontinuedOperations_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Noncontrolling interest from discontinuing operations</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:label="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:to="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity, Including Portion Attributable to Noncontrolling Interest</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:label="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Ending balance</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:label="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Beginning balance</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total stockholders' equity</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesAndStockholdersEquity" xlink:label="us-gaap_LiabilitiesAndStockholdersEquity" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LiabilitiesAndStockholdersEquity" xlink:to="us-gaap_LiabilitiesAndStockholdersEquity_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LiabilitiesAndStockholdersEquity_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Liabilities and Equity</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_LiabilitiesAndStockholdersEquity_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total liabilities and stockholders' equity</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementClassOfStockAxis" xlink:label="us-gaap_StatementClassOfStockAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StatementClassOfStockAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Class of Stock [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ClassOfStockDomain" xlink:label="us-gaap_ClassOfStockDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ClassOfStockDomain" xlink:to="us-gaap_ClassOfStockDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SeriesAPreferredStockMember" xlink:to="us-gaap_SeriesAPreferredStockMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PreferredStockParOrStatedValuePerShare" xlink:to="us-gaap_PreferredStockParOrStatedValuePerShare_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PreferredStockParOrStatedValuePerShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Preferred Stock, Par or Stated Value Per Share</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_PreferredStockParOrStatedValuePerShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Preferred stock, par value (in dollars per share)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PreferredStockSharesAuthorized" xlink:label="us-gaap_PreferredStockSharesAuthorized" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PreferredStockSharesAuthorized" xlink:to="us-gaap_PreferredStockSharesAuthorized_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PreferredStockSharesAuthorized_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Preferred Stock, Shares Authorized</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_PreferredStockSharesAuthorized_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Preferred stock, shares authorized (in shares)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PreferredStockSharesIssued" xlink:label="us-gaap_PreferredStockSharesIssued" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PreferredStockSharesIssued" xlink:to="us-gaap_PreferredStockSharesIssued_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PreferredStockSharesIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Preferred Stock, Shares Issued</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_PreferredStockSharesIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Preferred stock, shares issued (in shares)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PreferredStockSharesOutstanding" xlink:label="us-gaap_PreferredStockSharesOutstanding" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PreferredStockSharesOutstanding" xlink:to="us-gaap_PreferredStockSharesOutstanding_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PreferredStockSharesOutstanding_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Preferred Stock, Shares Outstanding</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_PreferredStockSharesOutstanding_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Preferred stock, shares outstanding (in shares)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockParOrStatedValuePerShare" xlink:label="us-gaap_CommonStockParOrStatedValuePerShare" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommonStockParOrStatedValuePerShare" xlink:to="us-gaap_CommonStockParOrStatedValuePerShare_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CommonStockParOrStatedValuePerShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common Stock, Par or Stated Value Per Share</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CommonStockParOrStatedValuePerShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common stock, par value (in dollars per share)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockSharesAuthorized" xlink:label="us-gaap_CommonStockSharesAuthorized" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommonStockSharesAuthorized" xlink:to="us-gaap_CommonStockSharesAuthorized_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CommonStockSharesAuthorized_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common Stock, Shares Authorized</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_CommonStockSharesAuthorized_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common stock, shares authorized (in shares)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockSharesIssued" xlink:label="us-gaap_CommonStockSharesIssued" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommonStockSharesIssued" xlink:to="us-gaap_CommonStockSharesIssued_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CommonStockSharesIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common Stock, Shares, Issued</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_CommonStockSharesIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common stock, shares issued (in shares)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockSharesOutstanding" xlink:label="us-gaap_CommonStockSharesOutstanding" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommonStockSharesOutstanding" xlink:to="us-gaap_CommonStockSharesOutstanding_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CommonStockSharesOutstanding_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common Stock, Shares, Outstanding</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CommonStockSharesOutstanding_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common stock, stock outstanding (in shares)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_CommonStockSharesOutstanding_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common Stock, Outstanding</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockholdersEquityNoteStockSplitConversionRatio1" xlink:label="us-gaap_StockholdersEquityNoteStockSplitConversionRatio1" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockholdersEquityNoteStockSplitConversionRatio1" xlink:to="us-gaap_StockholdersEquityNoteStockSplitConversionRatio1_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockholdersEquityNoteStockSplitConversionRatio1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stockholders' Equity Note, Stock Split, Conversion Ratio</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_StockholdersEquityNoteStockSplitConversionRatio1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Reverse stock split</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeStatementAbstract" xlink:label="us-gaap_IncomeStatementAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncomeStatementAbstract" xlink:to="us-gaap_IncomeStatementAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncomeStatementAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">CONDENSED CONSOLIDATED STATEMENTS OF OPERATIONS AND COMPREHENSIVE LOSS</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:label="us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:to="us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Revenue from Contract with Customer, Excluding Assessed Tax</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Revenues</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CostOfRevenue" xlink:label="us-gaap_CostOfRevenue" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CostOfRevenue" xlink:to="us-gaap_CostOfRevenue_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CostOfRevenue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cost of Revenue</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CostOfRevenue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cost of revenues</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GrossProfit" xlink:label="us-gaap_GrossProfit" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_GrossProfit" xlink:to="us-gaap_GrossProfit_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_GrossProfit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gross Profit</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_GrossProfit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gross profit</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SellingGeneralAndAdministrativeExpense" xlink:label="us-gaap_SellingGeneralAndAdministrativeExpense" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SellingGeneralAndAdministrativeExpense" xlink:to="us-gaap_SellingGeneralAndAdministrativeExpense_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SellingGeneralAndAdministrativeExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Selling, General and Administrative Expense</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SellingGeneralAndAdministrativeExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Selling, general and administrative expenses</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_SellingGeneralAndAdministrativeExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total selling, general and administrative expenses</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ImpairmentOfIntangibleAssetsExcludingGoodwill" xlink:label="us-gaap_ImpairmentOfIntangibleAssetsExcludingGoodwill" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ImpairmentOfIntangibleAssetsExcludingGoodwill" xlink:to="us-gaap_ImpairmentOfIntangibleAssetsExcludingGoodwill_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ImpairmentOfIntangibleAssetsExcludingGoodwill_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Impairment of Intangible Assets (Excluding Goodwill)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_ImpairmentOfIntangibleAssetsExcludingGoodwill_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loss on impairment of intangible assets</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ImpairmentOfIntangibleAssetsExcludingGoodwill_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loss on impairment of intangible assets</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_ImpairmentOfIntangibleAssetsExcludingGoodwill_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loss on impairment of intangible assets</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingIncomeLoss" xlink:label="us-gaap_OperatingIncomeLoss" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OperatingIncomeLoss" xlink:to="us-gaap_OperatingIncomeLoss_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OperatingIncomeLoss_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating Income (Loss)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_OperatingIncomeLoss_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loss from operations</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_OperatingIncomeLoss_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">(Loss) income from operations</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NonoperatingIncomeExpenseAbstract" xlink:label="us-gaap_NonoperatingIncomeExpenseAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NonoperatingIncomeExpenseAbstract" xlink:to="us-gaap_NonoperatingIncomeExpenseAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NonoperatingIncomeExpenseAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Nonoperating Income (Expense) [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NonoperatingIncomeExpenseAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other income (expense):</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestExpenseNonoperating" xlink:label="us-gaap_InterestExpenseNonoperating" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InterestExpenseNonoperating" xlink:to="us-gaap_InterestExpenseNonoperating_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_InterestExpenseNonoperating_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest Expense, Nonoperating</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_InterestExpenseNonoperating_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest expense</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_InterestExpenseNonoperating_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest expense</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_LossOnIssuanceOfFinancialInstruments" xlink:label="cntm_LossOnIssuanceOfFinancialInstruments" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_LossOnIssuanceOfFinancialInstruments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of discount or loss on issuance of financial instruments.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_LossOnIssuanceOfFinancialInstruments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loss On Issuance Of Financial Instruments</label>
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    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_GainLossOnExtinguishmentOfDebtAndVendorPayable" xlink:label="cntm_GainLossOnExtinguishmentOfDebtAndVendorPayable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_GainLossOnExtinguishmentOfDebtAndVendorPayable" xlink:to="cntm_GainLossOnExtinguishmentOfDebtAndVendorPayable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_GainLossOnExtinguishmentOfDebtAndVendorPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The amount of gain or loss from difference between the fair value of payments made and the carrying amount of debt and vendor payable which is extinguished prior to maturity during the reporting period.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_GainLossOnExtinguishmentOfDebtAndVendorPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gain (Loss) On Extinguishment Of Debt And Vendor Payable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="cntm_GainLossOnExtinguishmentOfDebtAndVendorPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loss on extinguishment of debt and vendor payable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_GainLossOnExtinguishmentOfDebtAndVendorPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loss on extinguishment of debt and vendor payable</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_GainOnExtinguishmentOfDebt" xlink:label="cntm_GainOnExtinguishmentOfDebt" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_GainOnExtinguishmentOfDebt" xlink:to="cntm_GainOnExtinguishmentOfDebt_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_GainOnExtinguishmentOfDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of gain recognized during the period upon extinguishment of debt.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_GainOnExtinguishmentOfDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gain On Extinguishment of Debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_GainOnExtinguishmentOfDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gain on extinguishment of debt</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_FairValueMeasurementOfDebtUnrealizedGainLoss" xlink:label="cntm_FairValueMeasurementOfDebtUnrealizedGainLoss" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FairValueMeasurementOfDebtUnrealizedGainLoss" xlink:to="cntm_FairValueMeasurementOfDebtUnrealizedGainLoss_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FairValueMeasurementOfDebtUnrealizedGainLoss_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of unrealized gain (loss) on fair value measurement of debt.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FairValueMeasurementOfDebtUnrealizedGainLoss_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value Measurement of Debt, Unrealized Gain (Loss)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FairValueMeasurementOfDebtUnrealizedGainLoss_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Change in fair value of convertible debt</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_UnrealizedGainLossOnDerivatives" xlink:label="us-gaap_UnrealizedGainLossOnDerivatives" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_UnrealizedGainLossOnDerivatives" xlink:to="us-gaap_UnrealizedGainLossOnDerivatives_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_UnrealizedGainLossOnDerivatives_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Unrealized Gain (Loss) on Derivatives</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="us-gaap_UnrealizedGainLossOnDerivatives_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Change in fair value of derivative liabilities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_UnrealizedGainLossOnDerivatives_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair value gain/(loss)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_UnrealizedGainLossOnDerivatives_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Change in fair value of derivative liabilities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentConsiderationLiability1" xlink:label="us-gaap_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentConsiderationLiability1" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentConsiderationLiability1" xlink:to="us-gaap_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentConsiderationLiability1_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentConsiderationLiability1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Contingent Consideration Arrangements, Change in Amount of Contingent Consideration, Liability</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentConsiderationLiability1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gain on settlement of contingent consideration</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentConsiderationLiability1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gain on settlement of contingent consideration</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_UnrealizedGainLossOnDerivativesLiabilitiesForwardPurchaseAgreement" xlink:label="cntm_UnrealizedGainLossOnDerivativesLiabilitiesForwardPurchaseAgreement" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_UnrealizedGainLossOnDerivativesLiabilitiesForwardPurchaseAgreement" xlink:to="cntm_UnrealizedGainLossOnDerivativesLiabilitiesForwardPurchaseAgreement_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_UnrealizedGainLossOnDerivativesLiabilitiesForwardPurchaseAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The net change in the difference between the fair value and the carrying value, or in the comparative fair values, of forward purchase agreement put option liabilities, held at each balance sheet date, that was included in earnings for the period.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_UnrealizedGainLossOnDerivativesLiabilitiesForwardPurchaseAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Unrealized Gain (Loss) on Derivatives, Liabilities, Forward Purchase Agreement</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_UnrealizedGainLossOnDerivativesLiabilitiesForwardPurchaseAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Change in fair value of forward purchase agreement</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_FairValueAdjustmentOfOtherPayablesSettlementAgreement" xlink:label="cntm_FairValueAdjustmentOfOtherPayablesSettlementAgreement" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FairValueAdjustmentOfOtherPayablesSettlementAgreement" xlink:to="cntm_FairValueAdjustmentOfOtherPayablesSettlementAgreement_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FairValueAdjustmentOfOtherPayablesSettlementAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of expense (income) related to adjustment to fair value of shares settled liability under settlement agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FairValueAdjustmentOfOtherPayablesSettlementAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value Adjustment of Other Payables, Settlement Agreement</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="cntm_FairValueAdjustmentOfOtherPayablesSettlementAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Change in fair value on Section 3(a)(10) Settlement Agreement (Note 9)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="cntm_FairValueAdjustmentOfOtherPayablesSettlementAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Change in fair value on 3(a)(10) Settlement Agreement (Note 6)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisposalGroupNotDiscontinuedOperationGainLossOnDisposal" xlink:label="us-gaap_DisposalGroupNotDiscontinuedOperationGainLossOnDisposal" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DisposalGroupNotDiscontinuedOperationGainLossOnDisposal" xlink:to="us-gaap_DisposalGroupNotDiscontinuedOperationGainLossOnDisposal_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DisposalGroupNotDiscontinuedOperationGainLossOnDisposal_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Not Discontinued Operation, Gain (Loss) on Disposal</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_DisposalGroupNotDiscontinuedOperationGainLossOnDisposal_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loss on disposal of business</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DisposalGroupNotDiscontinuedOperationGainLossOnDisposal_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gain (loss) on disposal of business</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeLossFromEquityMethodInvestments" xlink:label="us-gaap_IncomeLossFromEquityMethodInvestments" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncomeLossFromEquityMethodInvestments" xlink:to="us-gaap_IncomeLossFromEquityMethodInvestments_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncomeLossFromEquityMethodInvestments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Income (Loss) from Equity Method Investments</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_IncomeLossFromEquityMethodInvestments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity in earnings of equity method investee</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IncomeLossFromEquityMethodInvestments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity in earnings of equity method investee</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquitySecuritiesFvNiGainLoss" xlink:label="us-gaap_EquitySecuritiesFvNiGainLoss" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EquitySecuritiesFvNiGainLoss" xlink:to="us-gaap_EquitySecuritiesFvNiGainLoss_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EquitySecuritiesFvNiGainLoss_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity Securities, FV-NI, Gain (Loss)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="us-gaap_EquitySecuritiesFvNiGainLoss_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Change in fair value of investment in equity securities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_EquitySecuritiesFvNiGainLoss_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Change in fair value of investment in equity securities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_EquitySecuritiesFvNiGainLoss_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Unrealized gain on investment</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherNonoperatingIncomeExpense" xlink:label="us-gaap_OtherNonoperatingIncomeExpense" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OtherNonoperatingIncomeExpense" xlink:to="us-gaap_OtherNonoperatingIncomeExpense_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OtherNonoperatingIncomeExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other Nonoperating Income (Expense)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OtherNonoperatingIncomeExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other income (expense), net</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NonoperatingIncomeExpense" xlink:label="us-gaap_NonoperatingIncomeExpense" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NonoperatingIncomeExpense" xlink:to="us-gaap_NonoperatingIncomeExpense_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NonoperatingIncomeExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Nonoperating Income (Expense)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NonoperatingIncomeExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other (expense) income, net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_NonoperatingIncomeExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total other income (expense), net</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:label="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:to="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Income (Loss) from Continuing Operations before Income Taxes, Noncontrolling Interest</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loss from operations before income taxes</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeLossFromContinuingOperationsIncludingPortionAttributableToNoncontrollingInterest" xlink:label="us-gaap_IncomeLossFromContinuingOperationsIncludingPortionAttributableToNoncontrollingInterest" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncomeLossFromContinuingOperationsIncludingPortionAttributableToNoncontrollingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Income (Loss) from Continuing Operations, Net of Tax, Including Portion Attributable to Noncontrolling Interest</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IncomeLossFromContinuingOperationsIncludingPortionAttributableToNoncontrollingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loss from continuing operations</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_IncomeLossFromContinuingOperationsIncludingPortionAttributableToNoncontrollingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net loss from continuing operations</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncomeLossFromContinuingOperationsPerBasicShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Income (Loss) from Continuing Operations, Per Basic Share</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IncomeLossFromContinuingOperationsPerBasicShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Basic net loss per share, common stock for continuing operations ( in dollars per share)</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IncomeLossFromContinuingOperationsPerDilutedShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Diluted net loss per share, common stock for continuing operations ( in dollars per share)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxPerBasicShare" xlink:label="us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxPerBasicShare" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxPerBasicShare" xlink:to="us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxPerBasicShare_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxPerBasicShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Income (Loss) from Discontinued Operations and Disposal of Discontinued Operations, Net of Tax, Per Basic Share</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxPerBasicShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Basic net loss per share, common stock for discontinued operations (in dollars per share)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxPerDilutedShare" xlink:label="us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxPerDilutedShare" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxPerDilutedShare" xlink:to="us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxPerDilutedShare_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxPerDilutedShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Income (Loss) from Discontinued Operations and Disposal of Discontinued Operations, Net of Tax, Per Diluted Share</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxPerDilutedShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Diluted net loss per share, common stock for discontinued operations (in dollars per share)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementOfStockholdersEquityAbstract" xlink:label="us-gaap_StatementOfStockholdersEquityAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StatementOfStockholdersEquityAbstract" xlink:to="us-gaap_StatementOfStockholdersEquityAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StatementOfStockholdersEquityAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">CONDENSED CONSOLIDATED STATEMENTS OF STOCKHOLDERS' EQUITY</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementEquityComponentsAxis" xlink:label="us-gaap_StatementEquityComponentsAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StatementEquityComponentsAxis" xlink:to="us-gaap_StatementEquityComponentsAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StatementEquityComponentsAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity Components [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquityComponentDomain" xlink:label="us-gaap_EquityComponentDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EquityComponentDomain" xlink:to="us-gaap_EquityComponentDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EquityComponentDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity Component [Domain]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ParentMember" xlink:label="us-gaap_ParentMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ParentMember" xlink:to="us-gaap_ParentMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ParentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Parent [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ParentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stockholders' Equity/(Deficit)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockMember" xlink:label="us-gaap_CommonStockMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommonStockMember" xlink:to="us-gaap_CommonStockMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CommonStockMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common Stock [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CommonStockMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common Stock</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AdditionalPaidInCapitalMember" xlink:label="us-gaap_AdditionalPaidInCapitalMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AdditionalPaidInCapitalMember" xlink:to="us-gaap_AdditionalPaidInCapitalMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AdditionalPaidInCapitalMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Additional Paid-in Capital [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AdditionalPaidInCapitalMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Additional Paid-In Capital</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RetainedEarningsMember" xlink:label="us-gaap_RetainedEarningsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RetainedEarningsMember" xlink:to="us-gaap_RetainedEarningsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RetainedEarningsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Retained Earnings [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RetainedEarningsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accumulated Deficit</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeMember" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">AOCI Attributable to Parent [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accumulated Other Comprehensive Income (Loss)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NoncontrollingInterestMember" xlink:label="us-gaap_NoncontrollingInterestMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NoncontrollingInterestMember" xlink:to="us-gaap_NoncontrollingInterestMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NoncontrollingInterestMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Noncontrolling Interest [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NoncontrollingInterestMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Noncontrolling interest</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:label="us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:to="us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Increase (Decrease) in Stockholders' Equity [Roll Forward]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Increase (Decrease) in Stockholders' Equity</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SharesOutstanding" xlink:label="us-gaap_SharesOutstanding" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SharesOutstanding" xlink:to="us-gaap_SharesOutstanding_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SharesOutstanding_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Shares, Outstanding</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:label="us-gaap_SharesOutstanding_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Ending balance (in shares)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:label="us-gaap_SharesOutstanding_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Beginning balance (in shares)</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_StockIssuedDuringPeriodValueStandbyEquityPurchaseAgreement" xlink:label="cntm_StockIssuedDuringPeriodValueStandbyEquityPurchaseAgreement" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_StockIssuedDuringPeriodValueStandbyEquityPurchaseAgreement" xlink:to="cntm_StockIssuedDuringPeriodValueStandbyEquityPurchaseAgreement_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_StockIssuedDuringPeriodValueStandbyEquityPurchaseAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity impact of the value of new stock issued during the period pursuant to standby equity purchase agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_StockIssuedDuringPeriodValueStandbyEquityPurchaseAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period, Value, Standby Equity Purchase Agreement</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_StockIssuedDuringPeriodValueStandbyEquityPurchaseAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of common stock in connection with the conversion of SEPA convertible debt</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_StockIssuedDuringPeriodSharesStandbyEquityPurchaseAgreement" xlink:label="cntm_StockIssuedDuringPeriodSharesStandbyEquityPurchaseAgreement" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_StockIssuedDuringPeriodSharesStandbyEquityPurchaseAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of new stock issued during the period pursuant to standby equity purchase agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_StockIssuedDuringPeriodSharesStandbyEquityPurchaseAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period, Shares, Standby Equity Purchase Agreement</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_StockIssuedDuringPeriodSharesStandbyEquityPurchaseAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of common stock in connection with the conversion of SEPA convertible debt (in shares)</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_StockIssuedDuringPeriodValueCommitmentSharesUponAcquisitionOfConvertibleDebt" xlink:label="cntm_StockIssuedDuringPeriodValueCommitmentSharesUponAcquisitionOfConvertibleDebt" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_StockIssuedDuringPeriodValueCommitmentSharesUponAcquisitionOfConvertibleDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of commitment shares issued in connection with the acquisition of convertible debt.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_StockIssuedDuringPeriodValueCommitmentSharesUponAcquisitionOfConvertibleDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period, Value, Commitment Shares, Upon Acquisition Of Convertible Debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_StockIssuedDuringPeriodValueCommitmentSharesUponAcquisitionOfConvertibleDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of commitment shares in connection with convertible debt</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_StockIssuedDuringPeriodSharesCommitmentSharesUponAcquisitionOfConvertibleDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of commitment shares issued in connection with the acquisition of convertible debt.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_StockIssuedDuringPeriodSharesCommitmentSharesUponAcquisitionOfConvertibleDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period, Shares, Commitment Shares, Upon Acquisition Of Convertible Debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_StockIssuedDuringPeriodSharesCommitmentSharesUponAcquisitionOfConvertibleDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of commitment shares in connection with convertible debt (in shares)</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_StockIssuedDuringPeriodValueSettlementAgreement" xlink:label="cntm_StockIssuedDuringPeriodValueSettlementAgreement" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_StockIssuedDuringPeriodValueSettlementAgreement" xlink:to="cntm_StockIssuedDuringPeriodValueSettlementAgreement_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_StockIssuedDuringPeriodValueSettlementAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Value of stock issued during the period as part of settlement agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_StockIssuedDuringPeriodValueSettlementAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period, Value, Settlement Agreement</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_StockIssuedDuringPeriodValueSettlementAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of common stock to settle claim under Section 3(a)10 Settlement Agreement (see Note 9)</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_StockIssuedDuringPeriodSharesSettlementAgreement" xlink:label="cntm_StockIssuedDuringPeriodSharesSettlementAgreement" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_StockIssuedDuringPeriodSharesSettlementAgreement" xlink:to="cntm_StockIssuedDuringPeriodSharesSettlementAgreement_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_StockIssuedDuringPeriodSharesSettlementAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of shares of stock issued during the period as part of settlement agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_StockIssuedDuringPeriodSharesSettlementAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period, Shares, Settlement Agreement</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_StockIssuedDuringPeriodSharesSettlementAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of common stock to settle claim under Section 3(a)10 Settlement Agreement (see Note 9) (in shares)</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_StockIssuedDuringPeriodValueIssuedForShareResetDerivativeLiabilities" xlink:label="cntm_StockIssuedDuringPeriodValueIssuedForShareResetDerivativeLiabilities" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_StockIssuedDuringPeriodValueIssuedForShareResetDerivativeLiabilities" xlink:to="cntm_StockIssuedDuringPeriodValueIssuedForShareResetDerivativeLiabilities_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_StockIssuedDuringPeriodValueIssuedForShareResetDerivativeLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Value of stock issued to settle share reset derivative liabilities.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_StockIssuedDuringPeriodValueIssuedForShareResetDerivativeLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period, Value, Issued for Share Reset Derivative Liabilities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_StockIssuedDuringPeriodValueIssuedForShareResetDerivativeLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of common stock to settle share reset derivative liabilities (see Note 9)</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_StockIssuedDuringPeriodSharesIssuedForShareResetDerivativeLiabilities" xlink:label="cntm_StockIssuedDuringPeriodSharesIssuedForShareResetDerivativeLiabilities" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_StockIssuedDuringPeriodSharesIssuedForShareResetDerivativeLiabilities" xlink:to="cntm_StockIssuedDuringPeriodSharesIssuedForShareResetDerivativeLiabilities_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_StockIssuedDuringPeriodSharesIssuedForShareResetDerivativeLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of shares issued to settle share reset derivative liabilities.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_StockIssuedDuringPeriodSharesIssuedForShareResetDerivativeLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period, Shares, Issued for Share Reset Derivative Liabilities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_StockIssuedDuringPeriodSharesIssuedForShareResetDerivativeLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of common stock to settle share reset derivative liabilities (see Note 9) (in shares)</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_StockIssuedDuringPeriodValueIssuedForExtinguishObligationsToVendorsAndLender" xlink:label="cntm_StockIssuedDuringPeriodValueIssuedForExtinguishObligationsToVendorsAndLender" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_StockIssuedDuringPeriodValueIssuedForExtinguishObligationsToVendorsAndLender" xlink:to="cntm_StockIssuedDuringPeriodValueIssuedForExtinguishObligationsToVendorsAndLender_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_StockIssuedDuringPeriodValueIssuedForExtinguishObligationsToVendorsAndLender_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity impact of the value of new stock issued during the period in connection with extinguish obligations to vendors and lenders.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_StockIssuedDuringPeriodValueIssuedForExtinguishObligationsToVendorsAndLender_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period, Value, Issued For Extinguish Obligations To Vendors And Lender</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_StockIssuedDuringPeriodValueIssuedForExtinguishObligationsToVendorsAndLender_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of common stock to extinguish obligations to vendors and lenders under 3a10 plan</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_StockIssuedDuringPeriodSharesIssuedForExtinguishObligationsToVendorsAndLenders" xlink:label="cntm_StockIssuedDuringPeriodSharesIssuedForExtinguishObligationsToVendorsAndLenders" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_StockIssuedDuringPeriodSharesIssuedForExtinguishObligationsToVendorsAndLenders" xlink:to="cntm_StockIssuedDuringPeriodSharesIssuedForExtinguishObligationsToVendorsAndLenders_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_StockIssuedDuringPeriodSharesIssuedForExtinguishObligationsToVendorsAndLenders_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of new stock issued during the period in connection with extinguish obligations to vendors and lenders.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_StockIssuedDuringPeriodSharesIssuedForExtinguishObligationsToVendorsAndLenders_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period, Shares, Issued For Extinguish Obligations To Vendors And Lenders</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_StockIssuedDuringPeriodSharesIssuedForExtinguishObligationsToVendorsAndLenders_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of common stock to extinguish obligations to vendors and lenders under 3a10 plan (in shares)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssuedDuringPeriodValueConversionOfConvertibleSecurities" xlink:label="us-gaap_StockIssuedDuringPeriodValueConversionOfConvertibleSecurities" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockIssuedDuringPeriodValueConversionOfConvertibleSecurities" xlink:to="us-gaap_StockIssuedDuringPeriodValueConversionOfConvertibleSecurities_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockIssuedDuringPeriodValueConversionOfConvertibleSecurities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period, Value, Conversion of Convertible Securities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_StockIssuedDuringPeriodValueConversionOfConvertibleSecurities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of common stock in connection with the conversion of convertible debt and accrued interest 3a9</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities" xlink:label="us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities" xlink:to="us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period, Shares, Conversion of Convertible Securities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of common stock in connection with the conversion of convertible debt and accrued interest 3a9 (in shares)</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_StockIssuedDuringPeriodValueSettlementOfAccountsPayableVendors" xlink:label="cntm_StockIssuedDuringPeriodValueSettlementOfAccountsPayableVendors" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_StockIssuedDuringPeriodValueSettlementOfAccountsPayableVendors" xlink:to="cntm_StockIssuedDuringPeriodValueSettlementOfAccountsPayableVendors_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_StockIssuedDuringPeriodValueSettlementOfAccountsPayableVendors_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Value of shares issued for settlement of vendors obligation classified in accounts payable.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_StockIssuedDuringPeriodValueSettlementOfAccountsPayableVendors_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period, Value, Settlement Of Accounts Payable Vendors</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_StockIssuedDuringPeriodValueSettlementOfAccountsPayableVendors_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of common stock in connection with share exchange agreement to settled accounts payable vendors</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_StockIssuedDuringPeriodSharesSettlementOfAccountsPayableVendors" xlink:label="cntm_StockIssuedDuringPeriodSharesSettlementOfAccountsPayableVendors" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_StockIssuedDuringPeriodSharesSettlementOfAccountsPayableVendors" xlink:to="cntm_StockIssuedDuringPeriodSharesSettlementOfAccountsPayableVendors_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_StockIssuedDuringPeriodSharesSettlementOfAccountsPayableVendors_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of shares issued for settlement of vendors obligation classified in accounts payable.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_StockIssuedDuringPeriodSharesSettlementOfAccountsPayableVendors_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period, Shares, Settlement Of Accounts Payable Vendors</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_StockIssuedDuringPeriodSharesSettlementOfAccountsPayableVendors_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of common stock in connection with share exchange agreement to settled accounts payable vendors (in shares)</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_StockIssuedDuringPeriodValueIssuedToBoardOfDirectorsAndEmployees" xlink:label="cntm_StockIssuedDuringPeriodValueIssuedToBoardOfDirectorsAndEmployees" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_StockIssuedDuringPeriodValueIssuedToBoardOfDirectorsAndEmployees" xlink:to="cntm_StockIssuedDuringPeriodValueIssuedToBoardOfDirectorsAndEmployees_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_StockIssuedDuringPeriodValueIssuedToBoardOfDirectorsAndEmployees_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity impact of the value of new stock issued during the period to board of directors and employees.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_StockIssuedDuringPeriodValueIssuedToBoardOfDirectorsAndEmployees_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period, Value, Issued To Board Of Directors And Employees</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_StockIssuedDuringPeriodValueIssuedToBoardOfDirectorsAndEmployees_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of common stock to BOD and employees</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_StockIssuedDuringPeriodSharesIssuedToBoardOfDirectorsAndEmployees" xlink:label="cntm_StockIssuedDuringPeriodSharesIssuedToBoardOfDirectorsAndEmployees" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_StockIssuedDuringPeriodSharesIssuedToBoardOfDirectorsAndEmployees" xlink:to="cntm_StockIssuedDuringPeriodSharesIssuedToBoardOfDirectorsAndEmployees_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_StockIssuedDuringPeriodSharesIssuedToBoardOfDirectorsAndEmployees_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of new stock issued during the period to board of directors and employees.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_StockIssuedDuringPeriodSharesIssuedToBoardOfDirectorsAndEmployees_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period, Shares, Issued To Board Of Directors And Employees</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_StockIssuedDuringPeriodSharesIssuedToBoardOfDirectorsAndEmployees_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of common stock to BOD and employees (in shares)</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_StockIssuedDuringPeriodValueEquityMethodInvestment" xlink:label="cntm_StockIssuedDuringPeriodValueEquityMethodInvestment" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_StockIssuedDuringPeriodValueEquityMethodInvestment" xlink:to="cntm_StockIssuedDuringPeriodValueEquityMethodInvestment_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_StockIssuedDuringPeriodValueEquityMethodInvestment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Value of stock issued pursuant to an equity method investment entered during the period.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_StockIssuedDuringPeriodValueEquityMethodInvestment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period, Value, Equity Method Investment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_StockIssuedDuringPeriodValueEquityMethodInvestment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of common stock in connection with equity method investment in Sun Solar</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_IssuanceOfCommonStockInConnectionWithEquityMethodInvestmentInSunSolar" xlink:label="cntm_IssuanceOfCommonStockInConnectionWithEquityMethodInvestmentInSunSolar" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_IssuanceOfCommonStockInConnectionWithEquityMethodInvestmentInSunSolar" xlink:to="cntm_IssuanceOfCommonStockInConnectionWithEquityMethodInvestmentInSunSolar_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_IssuanceOfCommonStockInConnectionWithEquityMethodInvestmentInSunSolar_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of shares of stock issued during the period pursuant to an equity method investment.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_IssuanceOfCommonStockInConnectionWithEquityMethodInvestmentInSunSolar_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of common stock in connection with equity method investment in Sun Solar</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_IssuanceOfCommonStockInConnectionWithEquityMethodInvestmentInSunSolar_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of common stock in connection with equity method investment in Sun Solar (in shares)</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_StockIssuedDuringPeriodValueIssuedForStockSubscription" xlink:label="cntm_StockIssuedDuringPeriodValueIssuedForStockSubscription" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_StockIssuedDuringPeriodValueIssuedForStockSubscription" xlink:to="cntm_StockIssuedDuringPeriodValueIssuedForStockSubscription_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_StockIssuedDuringPeriodValueIssuedForStockSubscription_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity impact of the value of new stock issued during the period in connection with stock subscription.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_StockIssuedDuringPeriodValueIssuedForStockSubscription_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period, Value, Issued For Stock Subscription</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_StockIssuedDuringPeriodValueIssuedForStockSubscription_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of common stock in connection with stock subscription</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_StockIssuedDuringPeriodSharesIssuedForStockSubscription" xlink:label="cntm_StockIssuedDuringPeriodSharesIssuedForStockSubscription" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_StockIssuedDuringPeriodSharesIssuedForStockSubscription" xlink:to="cntm_StockIssuedDuringPeriodSharesIssuedForStockSubscription_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_StockIssuedDuringPeriodSharesIssuedForStockSubscription_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of new stock issued during the period in connection with stock subscription.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_StockIssuedDuringPeriodSharesIssuedForStockSubscription_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period, Shares, Issued For Stock Subscription</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_StockIssuedDuringPeriodSharesIssuedForStockSubscription_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of common stock in connection with stock subscription (in shares)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NoncontrollingInterestDecreaseFromDeconsolidation" xlink:label="us-gaap_NoncontrollingInterestDecreaseFromDeconsolidation" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockIssuedDuringPeriodSharesNewIssues_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period, Shares, New Issues</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_StockIssuedDuringPeriodSharesNewIssues_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common Share Issuable (in shares)</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockIssuedDuringPeriodValueAcquisitions_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period, Value, Acquisitions</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_StockIssuedDuringPeriodValueAcquisitions_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of common stock in connection with acquisition</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssuedDuringPeriodSharesAcquisitions" xlink:label="us-gaap_StockIssuedDuringPeriodSharesAcquisitions" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockIssuedDuringPeriodSharesAcquisitions" xlink:to="us-gaap_StockIssuedDuringPeriodSharesAcquisitions_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockIssuedDuringPeriodSharesAcquisitions_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period, Shares, Acquisitions</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_StockIssuedDuringPeriodSharesAcquisitions_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of common stock in connection with acquisition (in shares)</label>
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    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_StockIssuedDuringPeriodSharesAdjustmentsDueToReverseStockSplits" xlink:to="cntm_StockIssuedDuringPeriodSharesAdjustmentsDueToReverseStockSplits_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_StockIssuedDuringPeriodSharesAdjustmentsDueToReverseStockSplits_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Adjustments to the number of shares during the period as a result of a reverse stock split.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_StockIssuedDuringPeriodSharesAdjustmentsDueToReverseStockSplits_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period, Shares, Adjustments Due to Reverse Stock Splits</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_StockIssuedDuringPeriodSharesAdjustmentsDueToReverseStockSplits_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fractional share adjustment due to reverse stock split (in shares)</label>
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    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_NoncontrollingInterestIncreaseDecreaseFromBusinessCombination" xlink:to="cntm_NoncontrollingInterestIncreaseDecreaseFromBusinessCombination_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockIssuedDuringPeriodValueIssuedForServices" xlink:to="us-gaap_StockIssuedDuringPeriodValueIssuedForServices_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockIssuedDuringPeriodValueIssuedForServices_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period, Value, Issued for Services</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_StockIssuedDuringPeriodValueIssuedForServices_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of common stock to vendors</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssuedDuringPeriodSharesIssuedForServices" xlink:label="us-gaap_StockIssuedDuringPeriodSharesIssuedForServices" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockIssuedDuringPeriodSharesIssuedForServices" xlink:to="us-gaap_StockIssuedDuringPeriodSharesIssuedForServices_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockIssuedDuringPeriodSharesIssuedForServices_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period, Shares, Issued for Services</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_StockIssuedDuringPeriodSharesIssuedForServices_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of common stock to vendors (in shares)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationReclassificationAdjustmentFromAOCIRealizedUponSaleOrLiquidationNetOfTax" xlink:label="us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationReclassificationAdjustmentFromAOCIRealizedUponSaleOrLiquidationNetOfTax" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationReclassificationAdjustmentFromAOCIRealizedUponSaleOrLiquidationNetOfTax" xlink:to="us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationReclassificationAdjustmentFromAOCIRealizedUponSaleOrLiquidationNetOfTax_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationReclassificationAdjustmentFromAOCIRealizedUponSaleOrLiquidationNetOfTax_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other Comprehensive Income (Loss), Foreign Currency Transaction and Translation Reclassification Adjustment from AOCI, Realized upon Sale or Liquidation, Net of Tax</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationReclassificationAdjustmentFromAOCIRealizedUponSaleOrLiquidationNetOfTax_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Release of cumulative translation adjustment on deconsolidation of GIX</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationReclassificationAdjustmentFromAOCIRealizedUponSaleOrLiquidationNetOfTax_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cumulative translation adjustments reclassified from accumulated other comprehensive loss</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax" xlink:label="us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other Comprehensive Income (Loss), Foreign Currency Transaction and Translation Adjustment, Net of Tax</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other comprehensive income</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_OtherComprehensiveIncomeLossFromDiscontinuingOperationsNetOfTax" xlink:label="cntm_OtherComprehensiveIncomeLossFromDiscontinuingOperationsNetOfTax" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_OtherComprehensiveIncomeLossFromDiscontinuingOperationsNetOfTax" xlink:to="cntm_OtherComprehensiveIncomeLossFromDiscontinuingOperationsNetOfTax_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_OtherComprehensiveIncomeLossFromDiscontinuingOperationsNetOfTax_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount after tax of other comprehensive income (loss) from discontinuing operations.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_OtherComprehensiveIncomeLossFromDiscontinuingOperationsNetOfTax_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other Comprehensive Income (Loss), from Discontinuing Operations, Net of Tax</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_OtherComprehensiveIncomeLossFromDiscontinuingOperationsNetOfTax_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other comprehensive income from discontinuing operations</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetIncomeLossIncludingPortionAttributableToNonredeemableNoncontrollingInterest" xlink:label="us-gaap_NetIncomeLossIncludingPortionAttributableToNonredeemableNoncontrollingInterest" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetIncomeLossIncludingPortionAttributableToNonredeemableNoncontrollingInterest" xlink:to="us-gaap_NetIncomeLossIncludingPortionAttributableToNonredeemableNoncontrollingInterest_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NetIncomeLossIncludingPortionAttributableToNonredeemableNoncontrollingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net Income (Loss), Including Portion Attributable to Nonredeemable Noncontrolling Interest</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NetIncomeLossIncludingPortionAttributableToNonredeemableNoncontrollingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net loss from continuing and discontinued operations</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementOfCashFlowsAbstract" xlink:label="us-gaap_StatementOfCashFlowsAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StatementOfCashFlowsAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">CONDENSED CONSOLIDATED STATEMENTS OF CASH FLOWS</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsAxis" xlink:label="us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group Name [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisposalGroupsIncludingDiscontinuedOperationsNameDomain" xlink:label="us-gaap_DisposalGroupsIncludingDiscontinuedOperationsNameDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_GreenEnergyGainsMember" xlink:label="cntm_GreenEnergyGainsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_GreenEnergyGainsMember" xlink:to="cntm_GreenEnergyGainsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_GreenEnergyGainsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to Green Energy Gains ("GEG").</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_GreenEnergyGainsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Green Energy Gains [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_GreenEnergyGainsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Green Energy Gains</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_HvacBusinessAssetsAndOperationsMember" xlink:label="cntm_HvacBusinessAssetsAndOperationsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_HvacBusinessAssetsAndOperationsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to HVAC business assets and operations.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_HvacBusinessAssetsAndOperationsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">HVAC Business Assets And Operations [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_HvacBusinessAssetsAndOperationsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">HVAC business assets and operations</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:to="us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net Cash Provided by (Used in) Operating Activities [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">CASH FLOWS FROM OPERATING ACTIVITIES:</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:label="us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Adjustments to Reconcile Net Income (Loss) to Cash Provided by (Used in) Operating Activities [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Adjustments to reconcile net loss to net cash used in operating activities:</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DepreciationDepletionAndAmortization" xlink:label="us-gaap_DepreciationDepletionAndAmortization" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DepreciationDepletionAndAmortization" xlink:to="us-gaap_DepreciationDepletionAndAmortization_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DepreciationDepletionAndAmortization_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Depreciation, Depletion and Amortization</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DepreciationDepletionAndAmortization_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Depreciation and amortization expense</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AmortizationOfDebtDiscountPremium" xlink:label="us-gaap_AmortizationOfDebtDiscountPremium" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AmortizationOfDebtDiscountPremium" xlink:to="us-gaap_AmortizationOfDebtDiscountPremium_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AmortizationOfDebtDiscountPremium_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amortization of Debt Discount (Premium)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AmortizationOfDebtDiscountPremium_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amortization of debt discount</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensation" xlink:label="us-gaap_ShareBasedCompensation" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensation" xlink:to="us-gaap_ShareBasedCompensation_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ShareBasedCompensation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Payment Arrangement, Noncash Expense</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ShareBasedCompensation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock-based compensation expense</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinanceLeaseRightOfUseAssetAmortization" xlink:label="us-gaap_FinanceLeaseRightOfUseAssetAmortization" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FinanceLeaseRightOfUseAssetAmortization" xlink:to="us-gaap_FinanceLeaseRightOfUseAssetAmortization_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FinanceLeaseRightOfUseAssetAmortization_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finance Lease, Right-of-Use Asset, Amortization</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FinanceLeaseRightOfUseAssetAmortization_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Right-of-use asset - amortization on finance leases</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense" xlink:label="us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense" xlink:to="us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating Lease, Right-of-Use Asset, Periodic Reduction</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Right-of-use asset - amortization on operating leases</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProvisionForDoubtfulAccounts" xlink:label="us-gaap_ProvisionForDoubtfulAccounts" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ProvisionForDoubtfulAccounts" xlink:to="us-gaap_ProvisionForDoubtfulAccounts_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ProvisionForDoubtfulAccounts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts Receivable, Credit Loss Expense (Reversal)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_ProvisionForDoubtfulAccounts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Provision for expected credit loss</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GainsLossesOnExtinguishmentOfDebt" xlink:label="us-gaap_GainsLossesOnExtinguishmentOfDebt" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_GainsLossesOnExtinguishmentOfDebt" xlink:to="us-gaap_GainsLossesOnExtinguishmentOfDebt_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_GainsLossesOnExtinguishmentOfDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gain (Loss) on Extinguishment of Debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="us-gaap_GainsLossesOnExtinguishmentOfDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gain on extinguishment of debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_GainsLossesOnExtinguishmentOfDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Impact of extinguishment of debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_GainsLossesOnExtinguishmentOfDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gain on extinguishment of debt</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GainLossOnSaleOfPropertyPlantEquipment" xlink:label="us-gaap_GainLossOnSaleOfPropertyPlantEquipment" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_GainLossOnSaleOfPropertyPlantEquipment" xlink:to="us-gaap_GainLossOnSaleOfPropertyPlantEquipment_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_GainLossOnSaleOfPropertyPlantEquipment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gain (Loss) on Disposition of Property Plant Equipment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_GainLossOnSaleOfPropertyPlantEquipment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gain on disposal of property and equipment</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_LossOfAcquisitionOfSubsidiary" xlink:label="cntm_LossOfAcquisitionOfSubsidiary" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_LossOfAcquisitionOfSubsidiary" xlink:to="cntm_LossOfAcquisitionOfSubsidiary_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_LossOfAcquisitionOfSubsidiary_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of loss incurred on acquisition of subsidiary during the period.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_LossOfAcquisitionOfSubsidiary_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loss Of Acquisition Of Subsidiary</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_LossOfAcquisitionOfSubsidiary_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loss on reposessed vehicle</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_ChangeInFairValueOfSettlementAgreementOperatingActivities" xlink:label="cntm_ChangeInFairValueOfSettlementAgreementOperatingActivities" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ChangeInFairValueOfSettlementAgreementOperatingActivities" xlink:to="cntm_ChangeInFairValueOfSettlementAgreementOperatingActivities_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ChangeInFairValueOfSettlementAgreementOperatingActivities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of expense (income) related to adjustment to fair value of shares settled liability under settlement agreement in operating activities.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ChangeInFairValueOfSettlementAgreementOperatingActivities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Change In Fair Value Of Settlement Agreement Operating Activities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ChangeInFairValueOfSettlementAgreementOperatingActivities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Change in fair value of 3(a)(10) Settlement Agreement</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_IncreaseDecreaseInGainLossOnFairValueMeasurementOfConvertibleDebt" xlink:label="cntm_IncreaseDecreaseInGainLossOnFairValueMeasurementOfConvertibleDebt" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_IncreaseDecreaseInGainLossOnFairValueMeasurementOfConvertibleDebt" xlink:to="cntm_IncreaseDecreaseInGainLossOnFairValueMeasurementOfConvertibleDebt_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_IncreaseDecreaseInGainLossOnFairValueMeasurementOfConvertibleDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of gain (loss) increase (decrease) on change in fair value of convertible debt during the reporting period.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_IncreaseDecreaseInGainLossOnFairValueMeasurementOfConvertibleDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Increase Decrease In Gain (Loss) On Fair Value Measurement Of Convertible Debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="cntm_IncreaseDecreaseInGainLossOnFairValueMeasurementOfConvertibleDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Change in fair value of convertible debt</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInOtherCurrentLiabilities" xlink:label="us-gaap_IncreaseDecreaseInOtherCurrentLiabilities" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncreaseDecreaseInOtherCurrentLiabilities" xlink:to="us-gaap_IncreaseDecreaseInOtherCurrentLiabilities_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncreaseDecreaseInOtherCurrentLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Increase (Decrease) in Other Current Liabilities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IncreaseDecreaseInOtherCurrentLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other payable</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GainLossOnTerminationOfLease" xlink:label="us-gaap_GainLossOnTerminationOfLease" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_GainLossOnTerminationOfLease" xlink:to="us-gaap_GainLossOnTerminationOfLease_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_GainLossOnTerminationOfLease_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gain (Loss) on Termination of Lease</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_GainLossOnTerminationOfLease_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loss on termination of lease</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_LossOnForwardPurchaseAgreementModification" xlink:label="cntm_LossOnForwardPurchaseAgreementModification" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_LossOnForwardPurchaseAgreementModification" xlink:to="cntm_LossOnForwardPurchaseAgreementModification_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_LossOnForwardPurchaseAgreementModification_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of recycled shares released as consideration related to modification on forward purchase agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_LossOnForwardPurchaseAgreementModification_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loss On Forward Purchase Agreement Modification</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_LossOnForwardPurchaseAgreementModification_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Change in fair value of forward purchase agreement</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:label="us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:to="us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Increase (Decrease) in Operating Capital [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Changes in operating assets and liabilities:</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInAccountsReceivable" xlink:label="us-gaap_IncreaseDecreaseInAccountsReceivable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncreaseDecreaseInAccountsReceivable" xlink:to="us-gaap_IncreaseDecreaseInAccountsReceivable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncreaseDecreaseInAccountsReceivable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Increase (Decrease) in Accounts Receivable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_IncreaseDecreaseInAccountsReceivable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts receivable</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInContractWithCustomerAsset" xlink:label="us-gaap_IncreaseDecreaseInContractWithCustomerAsset" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncreaseDecreaseInContractWithCustomerAsset" xlink:to="us-gaap_IncreaseDecreaseInContractWithCustomerAsset_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncreaseDecreaseInContractWithCustomerAsset_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Increase (Decrease) in Contract with Customer, Asset</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_IncreaseDecreaseInContractWithCustomerAsset_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contract asset</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInInventories" xlink:label="us-gaap_IncreaseDecreaseInInventories" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncreaseDecreaseInInventories" xlink:to="us-gaap_IncreaseDecreaseInInventories_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncreaseDecreaseInInventories_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Increase (Decrease) in Inventories</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_IncreaseDecreaseInInventories_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Inventory</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Increase (Decrease) in Prepaid Expense and Other Assets</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Prepaid expenses and other current assets</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInAccountsPayable" xlink:label="us-gaap_IncreaseDecreaseInAccountsPayable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncreaseDecreaseInAccountsPayable" xlink:to="us-gaap_IncreaseDecreaseInAccountsPayable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IncreaseDecreaseInAccountsPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts payable</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInAccruedLiabilitiesAndOtherOperatingLiabilities" xlink:label="us-gaap_IncreaseDecreaseInAccruedLiabilitiesAndOtherOperatingLiabilities" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncreaseDecreaseInAccruedLiabilitiesAndOtherOperatingLiabilities" xlink:to="us-gaap_IncreaseDecreaseInAccruedLiabilitiesAndOtherOperatingLiabilities_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncreaseDecreaseInAccruedLiabilitiesAndOtherOperatingLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Increase (Decrease) in Accrued Liabilities and Other Operating Liabilities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IncreaseDecreaseInAccruedLiabilitiesAndOtherOperatingLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accrued expenses and other current liabilities</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_ChangeInFairValueOfContingentConsideration" xlink:label="cntm_ChangeInFairValueOfContingentConsideration" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ChangeInFairValueOfContingentConsideration_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of increase (decrease) in value of liability in contingent consideration arrangement in business combination, including, but not limited to, difference arising upon settlement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ChangeInFairValueOfContingentConsideration_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Change in Fair Value of Contingent Consideration</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_ChangeInFairValueOfContingentConsideration_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contingent consideration liability</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInOperatingLeaseLiability" xlink:label="us-gaap_IncreaseDecreaseInOperatingLeaseLiability" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncreaseDecreaseInOperatingLeaseLiability" xlink:to="us-gaap_IncreaseDecreaseInOperatingLeaseLiability_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncreaseDecreaseInOperatingLeaseLiability_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Increase (Decrease) in Operating Lease Liability</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IncreaseDecreaseInOperatingLeaseLiability_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating lease liabilities</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_IncreaseDecreaseWorkingCapitalAdvance" xlink:label="cntm_IncreaseDecreaseWorkingCapitalAdvance" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_IncreaseDecreaseWorkingCapitalAdvance" xlink:to="cntm_IncreaseDecreaseWorkingCapitalAdvance_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_IncreaseDecreaseWorkingCapitalAdvance_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of increase (decrease) working capital advance.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_IncreaseDecreaseWorkingCapitalAdvance_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Increase (Decrease) Working Capital Advance</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="cntm_IncreaseDecreaseWorkingCapitalAdvance_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Working capital advances</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInContractWithCustomerLiability" xlink:label="us-gaap_IncreaseDecreaseInContractWithCustomerLiability" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncreaseDecreaseInContractWithCustomerLiability" xlink:to="us-gaap_IncreaseDecreaseInContractWithCustomerLiability_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncreaseDecreaseInContractWithCustomerLiability_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Increase (Decrease) in Contract with Customer, Liability</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IncreaseDecreaseInContractWithCustomerLiability_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contract liabilities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivitiesContinuingOperations" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivitiesContinuingOperations" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivitiesContinuingOperations" xlink:to="us-gaap_NetCashProvidedByUsedInOperatingActivitiesContinuingOperations_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivitiesContinuingOperations_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash Provided by (Used in) Operating Activity, Continuing Operation</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivitiesContinuingOperations_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net cash used in operating activities - continuing operations</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivitiesContinuingOperations_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net loss from operating activities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashProvidedByUsedInOperatingActivitiesDiscontinuedOperations" xlink:label="us-gaap_CashProvidedByUsedInOperatingActivitiesDiscontinuedOperations" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CashProvidedByUsedInOperatingActivitiesDiscontinuedOperations" xlink:to="us-gaap_CashProvidedByUsedInOperatingActivitiesDiscontinuedOperations_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CashProvidedByUsedInOperatingActivitiesDiscontinuedOperations_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash Provided by (Used in) Operating Activity, Discontinued Operation</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CashProvidedByUsedInOperatingActivitiesDiscontinuedOperations_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net cash used in operating activities - discontinuing operations</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInInvestingActivitiesContinuingOperationsAbstract" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivitiesContinuingOperationsAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetCashProvidedByUsedInInvestingActivitiesContinuingOperationsAbstract" xlink:to="us-gaap_NetCashProvidedByUsedInInvestingActivitiesContinuingOperationsAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivitiesContinuingOperationsAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash Provided by (Used in) Investing Activity, Continuing Operation [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivitiesContinuingOperationsAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">CASH FLOWS FROM INVESTING ACTIVITIES - CONTINUING OPERATIONS</label>
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    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_PaymentsForProceedsFromAcquirePropertyPlantAndEquipment" xlink:to="cntm_PaymentsForProceedsFromAcquirePropertyPlantAndEquipment_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_PaymentsForProceedsFromAcquirePropertyPlantAndEquipment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The cash outflow or inflow associated with the acquisition of long-lived, physical assets that are used in the normal conduct of business to produce goods and services and not intended for resale; includes cash outflows to pay for construction of self-constructed assets.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_PaymentsForProceedsFromAcquirePropertyPlantAndEquipment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments For (Proceeds From) Acquire Property Plant And Equipment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="cntm_PaymentsForProceedsFromAcquirePropertyPlantAndEquipment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Purchase of property and equipment</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromDivestitureOfBusinesses" xlink:label="us-gaap_ProceedsFromDivestitureOfBusinesses" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ProceedsFromDivestitureOfBusinesses" xlink:to="us-gaap_ProceedsFromDivestitureOfBusinesses_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ProceedsFromDivestitureOfBusinesses_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from Divestiture of Businesses</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ProceedsFromDivestitureOfBusinesses_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from disposal of GEG</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashAcquiredFromAcquisition" xlink:label="us-gaap_CashAcquiredFromAcquisition" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CashAcquiredFromAcquisition" xlink:to="us-gaap_CashAcquiredFromAcquisition_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CashAcquiredFromAcquisition_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash Acquired from Acquisition</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CashAcquiredFromAcquisition_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Purchase consideration paid for acquisition of HKA, net of cash acquired</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsToDevelopSoftware" xlink:label="us-gaap_PaymentsToDevelopSoftware" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PaymentsToDevelopSoftware" xlink:to="us-gaap_PaymentsToDevelopSoftware_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PaymentsToDevelopSoftware_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments to Develop Software</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_PaymentsToDevelopSoftware_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash paid for capitalized software development costs</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromSaleOfPropertyPlantAndEquipment" xlink:label="us-gaap_ProceedsFromSaleOfPropertyPlantAndEquipment" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ProceedsFromSaleOfPropertyPlantAndEquipment" xlink:to="us-gaap_ProceedsFromSaleOfPropertyPlantAndEquipment_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ProceedsFromSaleOfPropertyPlantAndEquipment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from Sale of Property, Plant, and Equipment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ProceedsFromSaleOfPropertyPlantAndEquipment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from the sale of property and equipment</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInInvestingActivitiesContinuingOperations" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivitiesContinuingOperations" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetCashProvidedByUsedInInvestingActivitiesContinuingOperations" xlink:to="us-gaap_NetCashProvidedByUsedInInvestingActivitiesContinuingOperations_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivitiesContinuingOperations_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash Provided by (Used in) Investing Activity, Continuing Operation</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivitiesContinuingOperations_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net cash used in investing activities - continuing operations</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashProvidedByUsedInInvestingActivitiesDiscontinuedOperations" xlink:label="us-gaap_CashProvidedByUsedInInvestingActivitiesDiscontinuedOperations" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CashProvidedByUsedInInvestingActivitiesDiscontinuedOperations" xlink:to="us-gaap_CashProvidedByUsedInInvestingActivitiesDiscontinuedOperations_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CashProvidedByUsedInInvestingActivitiesDiscontinuedOperations_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash Provided by (Used in) Investing Activity, Discontinued Operation</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CashProvidedByUsedInInvestingActivitiesDiscontinuedOperations_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net cash provided by (used in) investing activities - discontinuing operations</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:to="us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net Cash Provided by (Used in) Financing Activities [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">CASH FLOWS FROM FINANCING ACTIVITIES:</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromIssuanceOfDebt" xlink:label="us-gaap_ProceedsFromIssuanceOfDebt" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ProceedsFromIssuanceOfDebt" xlink:to="us-gaap_ProceedsFromIssuanceOfDebt_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ProceedsFromIssuanceOfDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from Issuance of Debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ProceedsFromIssuanceOfDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds form the issuance of debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_ProceedsFromIssuanceOfDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from the issuance of debt</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_ProceedsFromFactoringReceivableArrangements" xlink:label="cntm_ProceedsFromFactoringReceivableArrangements" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ProceedsFromFactoringReceivableArrangements" xlink:to="cntm_ProceedsFromFactoringReceivableArrangements_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ProceedsFromFactoringReceivableArrangements_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The amount of cash inflows from factoring receivable arrangements.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ProceedsFromFactoringReceivableArrangements_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds From Factoring Receivable Arrangements</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ProceedsFromFactoringReceivableArrangements_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from factoring receivable arrangements</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromConvertibleDebt" xlink:label="us-gaap_ProceedsFromConvertibleDebt" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ProceedsFromConvertibleDebt" xlink:to="us-gaap_ProceedsFromConvertibleDebt_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ProceedsFromConvertibleDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from Convertible Debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ProceedsFromConvertibleDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from convertible debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_ProceedsFromConvertibleDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from the issuance of convertible notes</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RepaymentsOfNotesPayable" xlink:label="us-gaap_RepaymentsOfNotesPayable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RepaymentsOfNotesPayable" xlink:to="us-gaap_RepaymentsOfNotesPayable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RepaymentsOfNotesPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Repayments of Notes Payable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_RepaymentsOfNotesPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Repayments on convertible notes</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RepaymentsOfNotesPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Repayments of convertible debt</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsOfDebtIssuanceCosts" xlink:label="us-gaap_PaymentsOfDebtIssuanceCosts" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PaymentsOfDebtIssuanceCosts" xlink:to="us-gaap_PaymentsOfDebtIssuanceCosts_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PaymentsOfDebtIssuanceCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments of Debt Issuance Costs</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_PaymentsOfDebtIssuanceCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash paid for debt issuance costs</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RepaymentsOfDebt" xlink:label="us-gaap_RepaymentsOfDebt" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RepaymentsOfDebt" xlink:to="us-gaap_RepaymentsOfDebt_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RepaymentsOfDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Repayments of Debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_RepaymentsOfDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Repayments of debt</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinanceLeasePrincipalPayments" xlink:label="us-gaap_FinanceLeasePrincipalPayments" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FinanceLeasePrincipalPayments" xlink:to="us-gaap_FinanceLeasePrincipalPayments_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FinanceLeasePrincipalPayments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finance Lease, Principal Payments</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_FinanceLeasePrincipalPayments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payment on finance leases</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_PurchaseFromStockSubscriptionAgreement" xlink:label="cntm_PurchaseFromStockSubscriptionAgreement" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_PurchaseFromStockSubscriptionAgreement" xlink:to="cntm_PurchaseFromStockSubscriptionAgreement_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_PurchaseFromStockSubscriptionAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The cash inflow from stock subscription agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_PurchaseFromStockSubscriptionAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Purchase From Stock Subscription Agreement</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_PurchaseFromStockSubscriptionAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from Stock Subscription agreement</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_RepaymentOfFunds" xlink:label="cntm_RepaymentOfFunds" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_RepaymentOfFunds" xlink:to="cntm_RepaymentOfFunds_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_RepaymentOfFunds_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The amount of cash outflow from funds.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_RepaymentOfFunds_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Repayment of Funds</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="cntm_RepaymentOfFunds_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Repayment of premium financing obligations</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_ProceedsFromTerminationOfDerivativeInstrument" xlink:label="cntm_ProceedsFromTerminationOfDerivativeInstrument" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ProceedsFromTerminationOfDerivativeInstrument" xlink:to="cntm_ProceedsFromTerminationOfDerivativeInstrument_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ProceedsFromTerminationOfDerivativeInstrument_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The cash inflow from the termination of derivative instrument during the period.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ProceedsFromTerminationOfDerivativeInstrument_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds From Termination Of Derivative Instrument</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ProceedsFromTerminationOfDerivativeInstrument_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from Forward Purchase agreement</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivitiesContinuingOperations" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivitiesContinuingOperations" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetCashProvidedByUsedInFinancingActivitiesContinuingOperations" xlink:to="us-gaap_NetCashProvidedByUsedInFinancingActivitiesContinuingOperations_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivitiesContinuingOperations_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash Provided by (Used in) Financing Activity, Continuing Operation</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivitiesContinuingOperations_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net cash provided by financing activities - continuing operations</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashProvidedByUsedInFinancingActivitiesDiscontinuedOperations" xlink:label="us-gaap_CashProvidedByUsedInFinancingActivitiesDiscontinuedOperations" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CashProvidedByUsedInFinancingActivitiesDiscontinuedOperations" xlink:to="us-gaap_CashProvidedByUsedInFinancingActivitiesDiscontinuedOperations_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CashProvidedByUsedInFinancingActivitiesDiscontinuedOperations_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash Provided by (Used in) Financing Activity, Discontinued Operation</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CashProvidedByUsedInFinancingActivitiesDiscontinuedOperations_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net cash provided by (used in) financing activities - discontinuing operations</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:label="us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:to="us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Effect of Exchange Rate on Cash, Cash Equivalents, Restricted Cash, and Restricted Cash Equivalents, Continuing Operations</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Effect of exchange rate changes on cash</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:to="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash, Cash Equivalents, Restricted Cash, and Restricted Cash Equivalents, Period Increase (Decrease), Including Exchange Rate Effect</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Increase (decrease) in cash and cash equivalents</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:to="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash, Cash Equivalents, Restricted Cash, and Restricted Cash Equivalents</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash and cash equivalents, end of the period</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash and cash equivalents, beginning of the period</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SupplementalCashFlowInformationAbstract" xlink:label="us-gaap_SupplementalCashFlowInformationAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SupplementalCashFlowInformationAbstract" xlink:to="us-gaap_SupplementalCashFlowInformationAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SupplementalCashFlowInformationAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Supplemental Cash Flow Information [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SupplementalCashFlowInformationAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Supplemental disclosures of cash flow information:</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestPaidNet" xlink:label="us-gaap_InterestPaidNet" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InterestPaidNet" xlink:to="us-gaap_InterestPaidNet_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_InterestPaidNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest Paid, Excluding Capitalized Interest, Operating Activities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_InterestPaidNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash paid for interest</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract" xlink:label="us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract" xlink:to="us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash Flow, Noncash Investing and Financing Activities Disclosure [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Supplemental disclosures of noncash investing and financing information:</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssued1" xlink:label="us-gaap_StockIssued1" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockIssued1" xlink:to="us-gaap_StockIssued1_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockIssued1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_StockIssued1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of shares for equity method investment</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_IssuanceOfCommitmentSharesInConnectionWithConvertibleDebt" xlink:label="cntm_IssuanceOfCommitmentSharesInConnectionWithConvertibleDebt" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_IssuanceOfCommitmentSharesInConnectionWithConvertibleDebt" xlink:to="cntm_IssuanceOfCommitmentSharesInConnectionWithConvertibleDebt_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_IssuanceOfCommitmentSharesInConnectionWithConvertibleDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The value of commitment shares issued in connection with convertible debt.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_IssuanceOfCommitmentSharesInConnectionWithConvertibleDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance Of Commitment Shares In Connection With Convertible Debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_IssuanceOfCommitmentSharesInConnectionWithConvertibleDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of commitment shares in connection with convertible debt</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_IssuanceOfCommonStockInConnectionWithConversionOfSepaConvertibleDebt" xlink:label="cntm_IssuanceOfCommonStockInConnectionWithConversionOfSepaConvertibleDebt" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_IssuanceOfCommonStockInConnectionWithConversionOfSepaConvertibleDebt" xlink:to="cntm_IssuanceOfCommonStockInConnectionWithConversionOfSepaConvertibleDebt_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_IssuanceOfCommonStockInConnectionWithConversionOfSepaConvertibleDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The value of common stock in connection with the conversion of SEPA convertible debt.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_IssuanceOfCommonStockInConnectionWithConversionOfSepaConvertibleDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of common stock in Connection with the Conversion of SEPA Convertible Debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_IssuanceOfCommonStockInConnectionWithConversionOfSepaConvertibleDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of common stock in connection with the conversion of SEPA conversion debt</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_FairValueOfSharesIssuedToSettleOtherPayablesSettlementAgreement" xlink:label="cntm_FairValueOfSharesIssuedToSettleOtherPayablesSettlementAgreement" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FairValueOfSharesIssuedToSettleOtherPayablesSettlementAgreement" xlink:to="cntm_FairValueOfSharesIssuedToSettleOtherPayablesSettlementAgreement_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FairValueOfSharesIssuedToSettleOtherPayablesSettlementAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair value of shares issued to settle other payables under 3(a)(9) settlement agreement in non-cash financing activities.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FairValueOfSharesIssuedToSettleOtherPayablesSettlementAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value of Shares Issued To Settle Other Payables Settlement Agreement</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FairValueOfSharesIssuedToSettleOtherPayablesSettlementAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair value of shares issued to settle Claim under Section 3(a)(9) Settlement Agreement</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_SettlementOfAccountsPayableThroughIssuanceOfShares" xlink:label="cntm_SettlementOfAccountsPayableThroughIssuanceOfShares" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_SettlementOfAccountsPayableThroughIssuanceOfShares" xlink:to="cntm_SettlementOfAccountsPayableThroughIssuanceOfShares_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_SettlementOfAccountsPayableThroughIssuanceOfShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The amount of accounts payable settled through issuance of shares in non-cash financing activities.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_SettlementOfAccountsPayableThroughIssuanceOfShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Settlement Of Accounts Payable Through Issuance Of Shares</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_SettlementOfAccountsPayableThroughIssuanceOfShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Settlement of accounts payable through issuance of shares</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DisposalGroupIncludingDiscontinuedOperationNonCashInvestingItemsHoldback" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationNonCashInvestingItemsHoldback" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DisposalGroupIncludingDiscontinuedOperationNonCashInvestingItemsHoldback" xlink:to="cntm_DisposalGroupIncludingDiscontinuedOperationNonCashInvestingItemsHoldback_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationNonCashInvestingItemsHoldback_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of holdback consideration recorded as non-cash investing item.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationNonCashInvestingItemsHoldback_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group Including Discontinued Operation, Non-cash Investing items, Holdback</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationNonCashInvestingItemsHoldback_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Holdback recorded as non-cash investing item</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationNonCashInvestingItemsHoldback_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Consideration receivable from disposal of GEG</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_SharesIssuedToAcquireNewSubsidiaries" xlink:label="cntm_SharesIssuedToAcquireNewSubsidiaries" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_SharesIssuedToAcquireNewSubsidiaries" xlink:to="cntm_SharesIssuedToAcquireNewSubsidiaries_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_SharesIssuedToAcquireNewSubsidiaries_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of shares issued to acquire new subsidiaries (HKA).</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_SharesIssuedToAcquireNewSubsidiaries_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Shares Issued to Acquire New Subsidiaries</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_SharesIssuedToAcquireNewSubsidiaries_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Shares issued to acquire new subsidiaries (HKA)</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DisposalGroupIncludingDiscontinuedOperationNonCashConsideration" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationNonCashConsideration" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DisposalGroupIncludingDiscontinuedOperationNonCashConsideration" xlink:to="cntm_DisposalGroupIncludingDiscontinuedOperationNonCashConsideration_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationNonCashConsideration_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The fair value of shares received for the disposal of assets and liabilities, including discontinued operation in a non-cash activity.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationNonCashConsideration_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Including Discontinued Operation, Non Cash Consideration</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationNonCashConsideration_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Non-cash investment for shares received from Blue Cloud</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DiscontinuedOperationGainLossOnDisposalOfDiscontinuedOperationNetOfTax" xlink:label="us-gaap_DiscontinuedOperationGainLossOnDisposalOfDiscontinuedOperationNetOfTax" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DiscontinuedOperationGainLossOnDisposalOfDiscontinuedOperationNetOfTax" xlink:to="us-gaap_DiscontinuedOperationGainLossOnDisposalOfDiscontinuedOperationNetOfTax_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DiscontinuedOperationGainLossOnDisposalOfDiscontinuedOperationNetOfTax_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Discontinued Operation, Gain (Loss) on Disposal of Discontinued Operation, Net of Tax</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DiscontinuedOperationGainLossOnDisposalOfDiscontinuedOperationNetOfTax_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gain on deconsolidation of discontinuing operations (net of tax)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredRevenue" xlink:label="us-gaap_DeferredRevenue" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DeferredRevenue" xlink:to="us-gaap_DeferredRevenue_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DeferredRevenue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Deferred Revenue</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_DeferredRevenue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Deferred consideration payable</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_FairValueOfSharesIssuedToSettleOtherPayablesUnderSettlementAgreement" xlink:label="cntm_FairValueOfSharesIssuedToSettleOtherPayablesUnderSettlementAgreement" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FairValueOfSharesIssuedToSettleOtherPayablesUnderSettlementAgreement" xlink:to="cntm_FairValueOfSharesIssuedToSettleOtherPayablesUnderSettlementAgreement_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FairValueOfSharesIssuedToSettleOtherPayablesUnderSettlementAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The amount of fair value of shares issued to settle other payables under settlement agreement in non-cash financing activities.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FairValueOfSharesIssuedToSettleOtherPayablesUnderSettlementAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value of Shares Issued To Settle Other Payables Under Settlement Agreement</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FairValueOfSharesIssuedToSettleOtherPayablesUnderSettlementAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair value of shares issued to settle Claim under 3(a)(10) Settlement Agreement</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_CarryingValueOfAccountsPayableExtinguishedWithSettlementAgreement" xlink:label="cntm_CarryingValueOfAccountsPayableExtinguishedWithSettlementAgreement" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_CarryingValueOfAccountsPayableExtinguishedWithSettlementAgreement" xlink:to="cntm_CarryingValueOfAccountsPayableExtinguishedWithSettlementAgreement_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_CarryingValueOfAccountsPayableExtinguishedWithSettlementAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The carrying value of accounts payable extinguished with settlement agreement  in non-cash financing activities.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_CarryingValueOfAccountsPayableExtinguishedWithSettlementAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Carrying Value of Accounts Payable Extinguished With Settlement Agreement</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_CarryingValueOfAccountsPayableExtinguishedWithSettlementAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Carrying value of accounts payable extinguished with 3(a)(10) Settlement Agreement</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_CarryingValueOfDebtExtinguished" xlink:label="cntm_CarryingValueOfDebtExtinguished" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_CarryingValueOfDebtExtinguished" xlink:to="cntm_CarryingValueOfDebtExtinguished_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_CarryingValueOfDebtExtinguished_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The carrying value of debt extinguished in non-cash financing activities.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_CarryingValueOfDebtExtinguished_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Carrying Value Of Debt Extinguished</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_CarryingValueOfDebtExtinguished_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Carrying value of debt extinguished with 3(a)(10) Settlement Agreement</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_FairValueOfSharesIssuedToSettleShareResetDerivativeLiabilities" xlink:label="cntm_FairValueOfSharesIssuedToSettleShareResetDerivativeLiabilities" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FairValueOfSharesIssuedToSettleShareResetDerivativeLiabilities" xlink:to="cntm_FairValueOfSharesIssuedToSettleShareResetDerivativeLiabilities_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FairValueOfSharesIssuedToSettleShareResetDerivativeLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The amount of fair value of shares issued to settle share reset derivative liability in non-cash financing activities.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FairValueOfSharesIssuedToSettleShareResetDerivativeLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value of Shares Issued To Settle Share Reset Derivative Liabilities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FairValueOfSharesIssuedToSettleShareResetDerivativeLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair value of shares issued to settle the share reset derivative liabilities</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_ExtinguishmentOfAccountsPayableThroughIssuanceOfDebt" xlink:label="cntm_ExtinguishmentOfAccountsPayableThroughIssuanceOfDebt" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ExtinguishmentOfAccountsPayableThroughIssuanceOfDebt" xlink:to="cntm_ExtinguishmentOfAccountsPayableThroughIssuanceOfDebt_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ExtinguishmentOfAccountsPayableThroughIssuanceOfDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The amount of extinguishment of accounts payable through issuance of debt in non-cash financing activities.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ExtinguishmentOfAccountsPayableThroughIssuanceOfDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Extinguishment of Accounts Payable Through Issuance of Debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ExtinguishmentOfAccountsPayableThroughIssuanceOfDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Extinguishment of accounts payable through issuance of debt</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_ReposesedVehicle" xlink:label="cntm_ReposesedVehicle" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ReposesedVehicle" xlink:to="cntm_ReposesedVehicle_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ReposesedVehicle_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents amount of reposesed vehicle.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ReposesedVehicle_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Reposesed vehicle</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ReposesedVehicle_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Reposesed vehicle</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DeRecognitionOfRightOfUseAssetAndLeaseLiability" xlink:label="cntm_DeRecognitionOfRightOfUseAssetAndLeaseLiability" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DeRecognitionOfRightOfUseAssetAndLeaseLiability" xlink:to="cntm_DeRecognitionOfRightOfUseAssetAndLeaseLiability_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DeRecognitionOfRightOfUseAssetAndLeaseLiability_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">De-recognition of ROU asset and lease liability on termination of lease.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DeRecognitionOfRightOfUseAssetAndLeaseLiability_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">De-Recognition Of Right-Of-Use Asset And Lease Liability</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DeRecognitionOfRightOfUseAssetAndLeaseLiability_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Removal of ROU asset and lease liability at lease termination</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_ReclassificationOfRemainingObligationUnderTerminatedLease" xlink:label="cntm_ReclassificationOfRemainingObligationUnderTerminatedLease" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ReclassificationOfRemainingObligationUnderTerminatedLease" xlink:to="cntm_ReclassificationOfRemainingObligationUnderTerminatedLease_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ReclassificationOfRemainingObligationUnderTerminatedLease_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Reclassification adjustment of remaining obligation under terminated lease.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ReclassificationOfRemainingObligationUnderTerminatedLease_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Reclassification Of Remaining Obligation Under Terminated Lease</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ReclassificationOfRemainingObligationUnderTerminatedLease_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Reclassification of remaining obligation under terminated lease</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_AcquisitionOfNonControllingInterest" xlink:label="cntm_AcquisitionOfNonControllingInterest" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_AcquisitionOfNonControllingInterest" xlink:to="cntm_AcquisitionOfNonControllingInterest_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_AcquisitionOfNonControllingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Increase in non-controlling interest during the period.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_AcquisitionOfNonControllingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Acquisition Of Non-Controlling Interest</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_AcquisitionOfNonControllingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Acquisition of non-controlling interest</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_BusinessOnStockIssued" xlink:label="cntm_BusinessOnStockIssued" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_BusinessOnStockIssued" xlink:to="cntm_BusinessOnStockIssued_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_BusinessOnStockIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The stock issued in noncash financing activities.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_BusinessOnStockIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business on stock issued</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_BusinessOnStockIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Shares issued to acquire new subsidiaries</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_NonCashInvestingAndFinancingActivitiesFinancedInsurancePremium" xlink:label="cntm_NonCashInvestingAndFinancingActivitiesFinancedInsurancePremium" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_NonCashInvestingAndFinancingActivitiesFinancedInsurancePremium" xlink:to="cntm_NonCashInvestingAndFinancingActivitiesFinancedInsurancePremium_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_NonCashInvestingAndFinancingActivitiesFinancedInsurancePremium_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of non cash investing and financing activities financed insurance premium.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_NonCashInvestingAndFinancingActivitiesFinancedInsurancePremium_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Non Cash Investing And Financing Activities Financed Insurance Premium</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_NonCashInvestingAndFinancingActivitiesFinancedInsurancePremium_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Financed insurance premium</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:label="us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:to="us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">ORGANIZATION AND OPERATIONS</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NatureOfOperations" xlink:label="us-gaap_NatureOfOperations" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NatureOfOperations" xlink:to="us-gaap_NatureOfOperations_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NatureOfOperations_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Nature of Operations [Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NatureOfOperations_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">ORGANIZATION AND OPERATIONS</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountingPoliciesAbstract" xlink:label="us-gaap_AccountingPoliciesAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccountingPoliciesAbstract" xlink:to="us-gaap_AccountingPoliciesAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AccountingPoliciesAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">BASIS OF PRESENTATION AND SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SignificantAccountingPoliciesTextBlock" xlink:label="us-gaap_SignificantAccountingPoliciesTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SignificantAccountingPoliciesTextBlock" xlink:to="us-gaap_SignificantAccountingPoliciesTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SignificantAccountingPoliciesTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Significant Accounting Policies [Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SignificantAccountingPoliciesTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">BASIS OF PRESENTATION AND SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_GoingConcernAbstract" xlink:label="cntm_GoingConcernAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_GoingConcernAbstract" xlink:to="cntm_GoingConcernAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_GoingConcernAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">No definition available.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_GoingConcernAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">GOING CONCERN</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubstantialDoubtAboutGoingConcernTextBlock" xlink:label="us-gaap_SubstantialDoubtAboutGoingConcernTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SubstantialDoubtAboutGoingConcernTextBlock" xlink:to="us-gaap_SubstantialDoubtAboutGoingConcernTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SubstantialDoubtAboutGoingConcernTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Substantial Doubt about Going Concern [Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SubstantialDoubtAboutGoingConcernTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">GOING CONCERN</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DiscontinuedOperationsAndDisposalGroupsAbstract" xlink:label="us-gaap_DiscontinuedOperationsAndDisposalGroupsAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DiscontinuedOperationsAndDisposalGroupsAbstract" xlink:to="us-gaap_DiscontinuedOperationsAndDisposalGroupsAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DiscontinuedOperationsAndDisposalGroupsAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">DISPOSALS AND DISCONTINUED OPERATIONS</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock" xlink:label="us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock" xlink:to="us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Groups, Including Discontinued Operations, Disclosure [Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">DISPOSALS AND DISCONTINUED OPERATIONS</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquityMethodInvestmentsAndJointVenturesAbstract" xlink:label="us-gaap_EquityMethodInvestmentsAndJointVenturesAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EquityMethodInvestmentsAndJointVenturesAbstract" xlink:to="us-gaap_EquityMethodInvestmentsAndJointVenturesAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EquityMethodInvestmentsAndJointVenturesAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">EQUITY METHOD INVESTMENT</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquityMethodInvestmentsDisclosureTextBlock" xlink:label="us-gaap_EquityMethodInvestmentsDisclosureTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EquityMethodInvestmentsDisclosureTextBlock" xlink:to="us-gaap_EquityMethodInvestmentsDisclosureTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EquityMethodInvestmentsDisclosureTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity Method Investments and Joint Ventures Disclosure [Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_EquityMethodInvestmentsDisclosureTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">EQUITY METHOD INVESTMENT</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract" xlink:label="us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract" xlink:to="us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">INTANGIBLE ASSETS, NET</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IntangibleAssetsDisclosureTextBlock" xlink:label="us-gaap_IntangibleAssetsDisclosureTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IntangibleAssetsDisclosureTextBlock" xlink:to="us-gaap_IntangibleAssetsDisclosureTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IntangibleAssetsDisclosureTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Intangible Assets Disclosure [Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IntangibleAssetsDisclosureTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">INTANGIBLE ASSETS, NET</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongtermConvertibleDebtCurrentAndNoncurrentAbstract" xlink:label="us-gaap_LongtermConvertibleDebtCurrentAndNoncurrentAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LongtermConvertibleDebtCurrentAndNoncurrentAbstract" xlink:to="us-gaap_LongtermConvertibleDebtCurrentAndNoncurrentAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LongtermConvertibleDebtCurrentAndNoncurrentAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">CONVERTIBLE DEBT</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_ConvertibleDebtTextBlock" xlink:label="cntm_ConvertibleDebtTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertibleDebtTextBlock" xlink:to="cntm_ConvertibleDebtTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertibleDebtTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The entire disclosure of the entity's convertible debt.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertibleDebtTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Debt [Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertibleDebtTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">CONVERTIBLE DEBT</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtDisclosureAbstract" xlink:label="us-gaap_DebtDisclosureAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtDisclosureAbstract" xlink:to="us-gaap_DebtDisclosureAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtDisclosureAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">DEBT</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtDisclosureTextBlock" xlink:label="us-gaap_DebtDisclosureTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtDisclosureTextBlock" xlink:to="us-gaap_DebtDisclosureTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtDisclosureTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Disclosure [Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DebtDisclosureTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">DEBT</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueDisclosuresAbstract" xlink:label="us-gaap_FairValueDisclosuresAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueDisclosuresAbstract" xlink:to="us-gaap_FairValueDisclosuresAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueDisclosuresTextBlock" xlink:label="us-gaap_FairValueDisclosuresTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxDisclosureAbstract" xlink:label="us-gaap_IncomeTaxDisclosureAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxDisclosureTextBlock" xlink:label="us-gaap_IncomeTaxDisclosureTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IncomeTaxDisclosureTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">INCOME TAXES</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SegmentReportingAbstract" xlink:label="us-gaap_SegmentReportingAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SegmentReportingAbstract" xlink:to="us-gaap_SegmentReportingAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SegmentReportingAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">REPORTABLE SEGMENTS</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SegmentReportingDisclosureTextBlock" xlink:label="us-gaap_SegmentReportingDisclosureTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SegmentReportingDisclosureTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Segment Reporting Disclosure [Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SegmentReportingDisclosureTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">REPORTABLE SEGMENTS</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessCombinationsAbstract" xlink:label="us-gaap_BusinessCombinationsAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessCombinationsAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">ACQUISITION</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessCombinationDisclosureTextBlock" xlink:label="us-gaap_BusinessCombinationDisclosureTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsequentEventsAbstract" xlink:label="us-gaap_SubsequentEventsAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SubsequentEventsAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">SUBSEQUENT EVENTS</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SubsequentEventsTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Subsequent Events [Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SubsequentEventsTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">SUBSEQUENT EVENTS</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BasisOfPresentationAndSignificantAccountingPoliciesTextBlock" xlink:label="us-gaap_BasisOfPresentationAndSignificantAccountingPoliciesTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_InvestmentPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Investments in Equity Securities</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_BusinessCombinationAndAssetAcquisitionPolicyPolicyTextBlock" xlink:label="cntm_BusinessCombinationAndAssetAcquisitionPolicyPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy" xlink:label="us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DiscontinuedOperationsPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Discontinued Operations, Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DiscontinuedOperationsPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Held for Sale and Discontinued operations</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EarningsPerSharePolicyTextBlock" xlink:label="us-gaap_EarningsPerSharePolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EarningsPerSharePolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Earnings Per Share, Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_EarningsPerSharePolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net income (loss) per share</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_ConvertibleNotesPayablePolicyTextBlock" xlink:label="cntm_ConvertibleNotesPayablePolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertibleNotesPayablePolicyTextBlock" xlink:to="cntm_ConvertibleNotesPayablePolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertibleNotesPayablePolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disclosure of accounting policy for convertible notes payable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertibleNotesPayablePolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Notes Payable [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertibleNotesPayablePolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible notes payable</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockholdersEquityPolicyTextBlock" xlink:label="us-gaap_StockholdersEquityPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockholdersEquityPolicyTextBlock" xlink:to="us-gaap_StockholdersEquityPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockholdersEquityPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stockholders' Equity, Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_StockholdersEquityPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Reverse Stock Split</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ComparabilityOfPriorYearFinancialData" xlink:label="us-gaap_ComparabilityOfPriorYearFinancialData" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ComparabilityOfPriorYearFinancialData_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Comparability of Prior Year Financial Data, Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ComparabilityOfPriorYearFinancialData_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounting Treatment and Retroactive Restatement</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:label="us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:to="us-gaap_BasisOfAccountingPolicyPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BasisOfAccountingPolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Basis of Accounting, Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_BasisOfAccountingPolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Significant Accounting Policies</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:label="us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:to="us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">New Accounting Pronouncements, Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Recently issued accounting pronouncements, not yet adopted</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfErrorCorrectionsAndPriorPeriodAdjustmentsTextBlock" xlink:label="us-gaap_ScheduleOfErrorCorrectionsAndPriorPeriodAdjustmentsTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfErrorCorrectionsAndPriorPeriodAdjustmentsTextBlock" xlink:to="us-gaap_ScheduleOfErrorCorrectionsAndPriorPeriodAdjustmentsTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfErrorCorrectionsAndPriorPeriodAdjustmentsTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of Error Corrections and Prior Period Adjustments [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ScheduleOfErrorCorrectionsAndPriorPeriodAdjustmentsTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of the effect of the correction on each financial statement line item</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTextBlock" xlink:label="us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTextBlock" xlink:to="us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of Antidilutive Securities Excluded from Computation of Earnings Per Share [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of outstanding shares of common stock equivalents</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_ScheduleOfEffectOfReverseStockSplitOnSharesOutstandingTableTextBlock" xlink:label="cntm_ScheduleOfEffectOfReverseStockSplitOnSharesOutstandingTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ScheduleOfEffectOfReverseStockSplitOnSharesOutstandingTableTextBlock" xlink:to="cntm_ScheduleOfEffectOfReverseStockSplitOnSharesOutstandingTableTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ScheduleOfEffectOfReverseStockSplitOnSharesOutstandingTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Tabular disclosure of effect of reverse stock split on shares outstanding.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ScheduleOfEffectOfReverseStockSplitOnSharesOutstandingTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule Of Effect Of Reverse Stock Split On Shares Outstanding [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ScheduleOfEffectOfReverseStockSplitOnSharesOutstandingTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of reverse stock split</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfDisposalGroupsIncludingDiscontinuedOperationsIncomeStatementBalanceSheetAndAdditionalDisclosuresTextBlock" xlink:label="us-gaap_ScheduleOfDisposalGroupsIncludingDiscontinuedOperationsIncomeStatementBalanceSheetAndAdditionalDisclosuresTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ScheduleOfDisposalGroupsIncludingDiscontinuedOperationsIncomeStatementBalanceSheetAndAdditionalDisclosuresTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of financial statements of discontinued operation</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock" xlink:label="us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock" xlink:to="us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of Finite-Lived Intangible Assets [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of identifiable intangible assets</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock" xlink:label="us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock" xlink:to="us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of Finite-Lived Intangible Assets, Future Amortization Expense [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of amortization expense</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentTable" xlink:label="us-gaap_DebtInstrumentTable" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of Long-Term Debt Instruments [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentAxis" xlink:label="us-gaap_DebtInstrumentAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentNameDomain" xlink:label="us-gaap_DebtInstrumentNameDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentNameDomain" xlink:to="us-gaap_DebtInstrumentNameDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentNameDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Name [Domain]</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_ConvertibleNotes2026Member" xlink:label="cntm_ConvertibleNotes2026Member" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertibleNotes2026Member" xlink:to="cntm_ConvertibleNotes2026Member_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertibleNotes2026Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the member information pertaining to 2026 Convertible Notes.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertibleNotes2026Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Notes, 2026 [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertibleNotes2026Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2026 Convertible Notes</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentLineItems" xlink:label="us-gaap_DebtInstrumentLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DebtInstrumentLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">DEBT</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_DebtInstrumentLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">CONVERTIBLE DEBT</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConvertibleDebtTableTextBlock" xlink:label="us-gaap_ConvertibleDebtTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ConvertibleDebtTableTextBlock" xlink:to="us-gaap_ConvertibleDebtTableTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ConvertibleDebtTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Debt [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ConvertibleDebtTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of convertible debt</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfDebtInstrumentsTextBlock" xlink:label="us-gaap_ScheduleOfDebtInstrumentsTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfDebtInstrumentsTextBlock" xlink:to="us-gaap_ScheduleOfDebtInstrumentsTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfDebtInstrumentsTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of Long-Term Debt Instruments [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ScheduleOfDebtInstrumentsTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Summary of the individual convertible notes</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_ScheduleOfDebtInstrumentsTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of debt</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:label="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:to="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Related and Nonrelated Parties [Axis]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Related and Nonrelated Parties [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyDomain" xlink:label="us-gaap_RelatedPartyDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RelatedPartyDomain" xlink:to="us-gaap_RelatedPartyDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RelatedPartyDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Related and Nonrelated Parties [Domain]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NonrelatedPartyMember" xlink:label="us-gaap_NonrelatedPartyMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NonrelatedPartyMember" xlink:to="us-gaap_NonrelatedPartyMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NonrelatedPartyMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Nonrelated Party [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NonrelatedPartyMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Non-related party</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable" xlink:label="us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable" xlink:to="us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueByLiabilityClassAxis" xlink:label="us-gaap_FairValueByLiabilityClassAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueByLiabilityClassAxis" xlink:to="us-gaap_FairValueByLiabilityClassAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueByLiabilityClassAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Liability Class [Axis]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FairValueByLiabilityClassAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Liability Class [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain" xlink:label="us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain" xlink:to="us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value by Liability Class [Domain]</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_ConvertibleNotes2026And2025Member" xlink:label="cntm_ConvertibleNotes2026And2025Member" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertibleNotes2026And2025Member" xlink:to="cntm_ConvertibleNotes2026And2025Member_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertibleNotes2026And2025Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the member information pertaining to 2026 and 2025 Convertible Notes.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertibleNotes2026And2025Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Notes 2026 and 2025 [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertibleNotes2026And2025Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Notes 2026 and 2025</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_StandbyEquityPurchaseAgreementConvertibleNoteMember" xlink:label="cntm_StandbyEquityPurchaseAgreementConvertibleNoteMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_StandbyEquityPurchaseAgreementConvertibleNoteMember" xlink:to="cntm_StandbyEquityPurchaseAgreementConvertibleNoteMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_StandbyEquityPurchaseAgreementConvertibleNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to standby equity purchase agreement convertible notes.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_StandbyEquityPurchaseAgreementConvertibleNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Standby Equity Purchase Agreement Convertible Note [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_StandbyEquityPurchaseAgreementConvertibleNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">SEPA Convertible Note</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_SettlementAgreementMember" xlink:label="cntm_SettlementAgreementMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_SettlementAgreementMember" xlink:to="cntm_SettlementAgreementMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_SettlementAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the member information pertaining to settlement agreement for shares issued under Section 3(a)(10) of the Securities Act.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_SettlementAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Settlement Agreement [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_SettlementAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">3(a)(10) Settlement Agreement</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems" xlink:label="us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems" xlink:to="us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">FAIR VALUE MEASUREMENTS</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTableTextBlock" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTableTextBlock" xlink:to="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTableTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value Measurements, Recurring and Nonrecurring [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of assets and liabilities measured and recorded at fair value on a recurring basis</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:label="us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:to="us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of reconciliation of assets and liabilities measured at fair value using Level 3 inputs</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfCarryingValuesAndEstimatedFairValuesOfDebtInstrumentsTableTextBlock" xlink:label="us-gaap_ScheduleOfCarryingValuesAndEstimatedFairValuesOfDebtInstrumentsTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfCarryingValuesAndEstimatedFairValuesOfDebtInstrumentsTableTextBlock" xlink:to="us-gaap_ScheduleOfCarryingValuesAndEstimatedFairValuesOfDebtInstrumentsTableTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfCarryingValuesAndEstimatedFairValuesOfDebtInstrumentsTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of Carrying Values and Estimated Fair Values of Debt Instruments [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ScheduleOfCarryingValuesAndEstimatedFairValuesOfDebtInstrumentsTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of carrying value and fair value for the convertible notes payable for which the Company elected the fair value option</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value Measurement Inputs and Valuation Techniques [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of fair value measurements</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RevenueFromExternalCustomersByGeographicAreasTableTextBlock" xlink:label="us-gaap_RevenueFromExternalCustomersByGeographicAreasTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RevenueFromExternalCustomersByGeographicAreasTableTextBlock" xlink:to="us-gaap_RevenueFromExternalCustomersByGeographicAreasTableTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RevenueFromExternalCustomersByGeographicAreasTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Revenue from External Customers by Geographic Areas [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RevenueFromExternalCustomersByGeographicAreasTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of disaggregated revenue information from continuing operations by geographic area based upon customer's country of domicile</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ContractWithCustomerAssetAndLiabilityTableTextBlock" xlink:label="us-gaap_ContractWithCustomerAssetAndLiabilityTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ContractWithCustomerAssetAndLiabilityTableTextBlock" xlink:to="us-gaap_ContractWithCustomerAssetAndLiabilityTableTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ContractWithCustomerAssetAndLiabilityTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contract with Customer, Contract Asset, Contract Liability, and Receivable [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ContractWithCustomerAssetAndLiabilityTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of contract assets and liability activity</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:label="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:to="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of Segment Reporting Information, by Segment [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of principal business segments</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisaggregationOfRevenueTableTextBlock" xlink:label="us-gaap_DisaggregationOfRevenueTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DisaggregationOfRevenueTableTextBlock" xlink:to="us-gaap_DisaggregationOfRevenueTableTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DisaggregationOfRevenueTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disaggregation of Revenue [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DisaggregationOfRevenueTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of disaggregated revenue information by geographic area</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfRecognizedIdentifiedAssetsAcquiredAndLiabilitiesAssumedTableTextBlock" xlink:label="us-gaap_ScheduleOfRecognizedIdentifiedAssetsAcquiredAndLiabilitiesAssumedTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfRecognizedIdentifiedAssetsAcquiredAndLiabilitiesAssumedTableTextBlock" xlink:to="us-gaap_ScheduleOfRecognizedIdentifiedAssetsAcquiredAndLiabilitiesAssumedTableTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfRecognizedIdentifiedAssetsAcquiredAndLiabilitiesAssumedTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of Recognized Identified Assets Acquired and Liabilities Assumed [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_ScheduleOfRecognizedIdentifiedAssetsAcquiredAndLiabilitiesAssumedTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of fair values of the assets acquired and liabilities assumed in the acquisition</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfFiniteLivedIntangibleAssetsAcquiredAsPartOfBusinessCombinationTextBlock" xlink:label="us-gaap_ScheduleOfFiniteLivedIntangibleAssetsAcquiredAsPartOfBusinessCombinationTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfFiniteLivedIntangibleAssetsAcquiredAsPartOfBusinessCombinationTextBlock" xlink:to="us-gaap_ScheduleOfFiniteLivedIntangibleAssetsAcquiredAsPartOfBusinessCombinationTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfFiniteLivedIntangibleAssetsAcquiredAsPartOfBusinessCombinationTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Intangible Asset, Acquired, Finite-Lived [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_ScheduleOfFiniteLivedIntangibleAssetsAcquiredAsPartOfBusinessCombinationTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of preliminary fair values and estimated useful lives of the identifiable intangible assets acquired</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_OrganizationAndOperationsTable" xlink:label="cntm_OrganizationAndOperationsTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_OrganizationAndOperationsTable" xlink:to="cntm_OrganizationAndOperationsTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_OrganizationAndOperationsTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disclosure of information about organization and operations.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_OrganizationAndOperationsTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">ORGANIZATION AND OPERATIONS [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessAcquisitionAxis" xlink:label="us-gaap_BusinessAcquisitionAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessAcquisitionAxis" xlink:to="us-gaap_BusinessAcquisitionAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessAcquisitionAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Acquisition [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessAcquisitionAcquireeDomain" xlink:label="us-gaap_BusinessAcquisitionAcquireeDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessAcquisitionAcquireeDomain" xlink:to="us-gaap_BusinessAcquisitionAcquireeDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessAcquisitionAcquireeDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Acquisition, Acquiree [Domain]</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_HarryKahnAssociatesIncMember" xlink:label="cntm_HarryKahnAssociatesIncMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_HarryKahnAssociatesIncMember" xlink:to="cntm_HarryKahnAssociatesIncMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_HarryKahnAssociatesIncMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to Harry Kahn Associates, Inc.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_HarryKahnAssociatesIncMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Harry Kahn Associates, Inc [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_HarryKahnAssociatesIncMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Harry Kahn Associates, Inc</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementBusinessSegmentsAxis" xlink:label="us-gaap_StatementBusinessSegmentsAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StatementBusinessSegmentsAxis" xlink:to="us-gaap_StatementBusinessSegmentsAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StatementBusinessSegmentsAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Segments [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SegmentDomain" xlink:label="us-gaap_SegmentDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SegmentDomain" xlink:to="us-gaap_SegmentDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SegmentDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Segments [Domain]</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_KeenLabsSegmentMember" xlink:label="cntm_KeenLabsSegmentMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_KeenLabsSegmentMember" xlink:to="cntm_KeenLabsSegmentMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_KeenLabsSegmentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to Keen Labs' segment.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_KeenLabsSegmentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Keen Labs Segment [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_KeenLabsSegmentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Keen Labs Operations, Inc</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_KeenLabsSegmentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Keen Labs</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_StatementGeographicalAxis" xlink:label="srt_StatementGeographicalAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_StatementGeographicalAxis" xlink:to="srt_StatementGeographicalAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_StatementGeographicalAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Geographical [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_SegmentGeographicalDomain" xlink:label="srt_SegmentGeographicalDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_SegmentGeographicalDomain" xlink:to="srt_SegmentGeographicalDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_SegmentGeographicalDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Geographical [Domain]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/country/2026/country-2026.xsd#country_US" xlink:label="country_US" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="country_US" xlink:to="country_US_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="country_US_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">UNITED STATES</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="country_US_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">United States</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisposalGroupClassificationAxis" xlink:label="us-gaap_DisposalGroupClassificationAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DisposalGroupClassificationAxis" xlink:to="us-gaap_DisposalGroupClassificationAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DisposalGroupClassificationAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group Classification [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisposalGroupClassificationDomain" xlink:label="us-gaap_DisposalGroupClassificationDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DisposalGroupClassificationDomain" xlink:to="us-gaap_DisposalGroupClassificationDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DisposalGroupClassificationDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group Classification [Domain]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DiscontinuedOperationsDisposedOfByMeansOtherThanSaleExchangeMember" xlink:label="us-gaap_DiscontinuedOperationsDisposedOfByMeansOtherThanSaleExchangeMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DiscontinuedOperationsDisposedOfByMeansOtherThanSaleExchangeMember" xlink:to="us-gaap_DiscontinuedOperationsDisposedOfByMeansOtherThanSaleExchangeMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DiscontinuedOperationsDisposedOfByMeansOtherThanSaleExchangeMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Discontinued Operations, Disposed of by Means Other than Sale, Exchange [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DiscontinuedOperationsDisposedOfByMeansOtherThanSaleExchangeMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Discontinued operations</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_DiscontinuedOperationsDisposedOfByMeansOtherThanSaleExchangeMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Disposed of by Means Other than Sale, Not Discontinued Operations, Exchange</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_GlobalImpexIncMember" xlink:label="cntm_GlobalImpexIncMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_GlobalImpexIncMember" xlink:to="cntm_GlobalImpexIncMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_GlobalImpexIncMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to Global Impex Inc.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_GlobalImpexIncMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Global Impex Inc [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_GlobalImpexIncMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">GIX</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_GlobalImpexIncMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Global Impex Inc</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_OwnershipAxis" xlink:label="srt_OwnershipAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_OwnershipAxis" xlink:to="srt_OwnershipAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_OwnershipAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Ownership [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_OwnershipDomain" xlink:label="srt_OwnershipDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_OwnershipDomain" xlink:to="srt_OwnershipDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_OwnershipDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Ownership [Domain]</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_ConnectmTechnologySolutionsPrivateLimitedMember" xlink:label="cntm_ConnectmTechnologySolutionsPrivateLimitedMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConnectmTechnologySolutionsPrivateLimitedMember" xlink:to="cntm_ConnectmTechnologySolutionsPrivateLimitedMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConnectmTechnologySolutionsPrivateLimitedMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to ConnectM Technology Solutions Private Limited.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConnectmTechnologySolutionsPrivateLimitedMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">ConnectM Technology Solutions Private Limited [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConnectmTechnologySolutionsPrivateLimitedMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">ConnectM Technology Solutions Private Limited</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_OrganizationAndOperationsLineItems" xlink:label="cntm_OrganizationAndOperationsLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_OrganizationAndOperationsLineItems" xlink:to="cntm_OrganizationAndOperationsLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_OrganizationAndOperationsLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_OrganizationAndOperationsLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">ORGANIZATION AND OPERATIONS [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_OrganizationAndOperationsLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">ORGANIZATION AND OPERATIONS</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired" xlink:label="us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired" xlink:to="us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Acquisition, Percentage of Voting Interests Acquired</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of voting interest acquired</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of voting interest acquired</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MinorityInterestOwnershipPercentageByParent" xlink:label="us-gaap_MinorityInterestOwnershipPercentageByParent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_MinorityInterestOwnershipPercentageByParent" xlink:to="us-gaap_MinorityInterestOwnershipPercentageByParent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_MinorityInterestOwnershipPercentageByParent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Subsidiary, Ownership Percentage, Parent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_MinorityInterestOwnershipPercentageByParent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage owned</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_PercentageOfEquityInterestContributedFromOneSubsidiaryToAnotherSubsidiary" xlink:label="cntm_PercentageOfEquityInterestContributedFromOneSubsidiaryToAnotherSubsidiary" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_PercentageOfEquityInterestContributedFromOneSubsidiaryToAnotherSubsidiary" xlink:to="cntm_PercentageOfEquityInterestContributedFromOneSubsidiaryToAnotherSubsidiary_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_PercentageOfEquityInterestContributedFromOneSubsidiaryToAnotherSubsidiary_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of equity interest contributed from one subsidiary to another subsidiary.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_PercentageOfEquityInterestContributedFromOneSubsidiaryToAnotherSubsidiary_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of Equity Interest Contributed from one Subsidiary to Another Subsidiary</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_PercentageOfEquityInterestContributedFromOneSubsidiaryToAnotherSubsidiary_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of equity interest</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_PercentageOfEquityInterestDisposed" xlink:label="cntm_PercentageOfEquityInterestDisposed" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_PercentageOfEquityInterestDisposed" xlink:to="cntm_PercentageOfEquityInterestDisposed_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_PercentageOfEquityInterestDisposed_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of equity interest disposed.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_PercentageOfEquityInterestDisposed_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage Of Equity Interest Disposed</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_PercentageOfEquityInterestDisposed_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of interest disposed</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NumberOfOperatingSegments" xlink:label="us-gaap_NumberOfOperatingSegments" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NumberOfOperatingSegments" xlink:to="us-gaap_NumberOfOperatingSegments_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NumberOfOperatingSegments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of Operating Segments</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NumberOfOperatingSegments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of operating segments</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_SummaryOfSignificantAccountingPoliciesTable" xlink:label="cntm_SummaryOfSignificantAccountingPoliciesTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_SummaryOfSignificantAccountingPoliciesTable" xlink:to="cntm_SummaryOfSignificantAccountingPoliciesTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_SummaryOfSignificantAccountingPoliciesTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule reflecting a summary of significant accounting policies.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_SummaryOfSignificantAccountingPoliciesTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Summary of Significant Accounting Policies [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_RangeAxis" xlink:label="srt_RangeAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_RangeAxis" xlink:to="srt_RangeAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_RangeAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Statistical Measurement [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_RangeMember" xlink:label="srt_RangeMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_RangeMember" xlink:to="srt_RangeMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_RangeMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Statistical Measurement [Domain]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_MinimumMember" xlink:label="srt_MinimumMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_MinimumMember" xlink:to="srt_MinimumMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_MinimumMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Minimum [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_MinimumMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Minimum</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_MaximumMember" xlink:label="srt_MaximumMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_MaximumMember" xlink:to="srt_MaximumMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_MaximumMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Maximum [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_MaximumMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Maximum</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AllOtherSegmentsMember" xlink:label="us-gaap_AllOtherSegmentsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AllOtherSegmentsMember" xlink:to="us-gaap_AllOtherSegmentsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AllOtherSegmentsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other Operating Segment [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AllOtherSegmentsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Others</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_AllOtherSegmentsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Others</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_RestatementAxis" xlink:label="srt_RestatementAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_RestatementAxis" xlink:to="srt_RestatementAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_RestatementAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Revision of Prior Period [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_RestatementDomain" xlink:label="srt_RestatementDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_RestatementDomain" xlink:to="srt_RestatementDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_RestatementDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Revision of Prior Period [Domain]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ScenarioPreviouslyReportedMember" xlink:label="srt_ScenarioPreviouslyReportedMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_ScenarioPreviouslyReportedMember" xlink:to="srt_ScenarioPreviouslyReportedMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_ScenarioPreviouslyReportedMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Previously Reported [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_ScenarioPreviouslyReportedMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Previously reported</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_RestatementAdjustmentMember" xlink:label="srt_RestatementAdjustmentMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_RestatementAdjustmentMember" xlink:to="srt_RestatementAdjustmentMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_RestatementAdjustmentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Revision of Prior Period, Adjustment [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_RestatementAdjustmentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">revision adjustments</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_GlobalImpexLlcMember" xlink:label="cntm_GlobalImpexLlcMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_GlobalImpexLlcMember" xlink:to="cntm_GlobalImpexLlcMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_GlobalImpexLlcMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information pertaining to Global Impex LLC.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_GlobalImpexLlcMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Global Impex LLC [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_GlobalImpexLlcMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Global Impex LLC</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_GlobalImpexLlcMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Geo Impex</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_SummaryOfSignificantAccountingPoliciesLineItems" xlink:label="cntm_SummaryOfSignificantAccountingPoliciesLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_SummaryOfSignificantAccountingPoliciesLineItems" xlink:to="cntm_SummaryOfSignificantAccountingPoliciesLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_SummaryOfSignificantAccountingPoliciesLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_SummaryOfSignificantAccountingPoliciesLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Summary of Significant Accounting Policies [Line Items}</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_SummaryOfSignificantAccountingPoliciesLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">BASIS OF PRESENTATION AND SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_IncreaseInSellingGeneralAndAdministrativeExpenseDueToReversalOfCapitalizedCosts" xlink:label="cntm_IncreaseInSellingGeneralAndAdministrativeExpenseDueToReversalOfCapitalizedCosts" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_IncreaseInSellingGeneralAndAdministrativeExpenseDueToReversalOfCapitalizedCosts" xlink:to="cntm_IncreaseInSellingGeneralAndAdministrativeExpenseDueToReversalOfCapitalizedCosts_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_IncreaseInSellingGeneralAndAdministrativeExpenseDueToReversalOfCapitalizedCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of increase in selling, general and administrative expense due to reversal of previously capitalized costs.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_IncreaseInSellingGeneralAndAdministrativeExpenseDueToReversalOfCapitalizedCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Increase In Selling General And Administrative Expense Due To Reversal Of Capitalized Costs</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_IncreaseInSellingGeneralAndAdministrativeExpenseDueToReversalOfCapitalizedCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Increase in selling, general and administrative expense</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_Depreciations" xlink:label="cntm_Depreciations" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_Depreciations" xlink:to="cntm_Depreciations_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_Depreciations_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The amount of depreciation expense recognized in the current period.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_Depreciations_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Depreciations</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_Depreciations_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Depreciation</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_ExpenseReclassifiedFromSellingGeneralAndAdministrativeExpenseToCostOfRevenue" xlink:label="cntm_ExpenseReclassifiedFromSellingGeneralAndAdministrativeExpenseToCostOfRevenue" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ExpenseReclassifiedFromSellingGeneralAndAdministrativeExpenseToCostOfRevenue" xlink:to="cntm_ExpenseReclassifiedFromSellingGeneralAndAdministrativeExpenseToCostOfRevenue_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ExpenseReclassifiedFromSellingGeneralAndAdministrativeExpenseToCostOfRevenue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of expenses reclassified from selling, general and administrative expense to cost of revenue.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ExpenseReclassifiedFromSellingGeneralAndAdministrativeExpenseToCostOfRevenue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Expense Reclassified From Selling General And Administrative Expense To Cost Of Revenue</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ExpenseReclassifiedFromSellingGeneralAndAdministrativeExpenseToCostOfRevenue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cost of revenue</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_ChangeInFairValueOfDebtInstrumentsPriorToExtinguishment" xlink:label="cntm_ChangeInFairValueOfDebtInstrumentsPriorToExtinguishment" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ChangeInFairValueOfDebtInstrumentsPriorToExtinguishment" xlink:to="cntm_ChangeInFairValueOfDebtInstrumentsPriorToExtinguishment_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ChangeInFairValueOfDebtInstrumentsPriorToExtinguishment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of changes in fair value of debt instruments prior to extinguishment.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ChangeInFairValueOfDebtInstrumentsPriorToExtinguishment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Change In Fair Value Of Debt Instruments Prior To Extinguishment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ChangeInFairValueOfDebtInstrumentsPriorToExtinguishment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Changes in fair value</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_AdjustmentForPreviouslyUnrecordedAccruedExpenses" xlink:label="cntm_AdjustmentForPreviouslyUnrecordedAccruedExpenses" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_AdjustmentForPreviouslyUnrecordedAccruedExpenses" xlink:to="cntm_AdjustmentForPreviouslyUnrecordedAccruedExpenses_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_AdjustmentForPreviouslyUnrecordedAccruedExpenses_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of increase in expenses resulting from the recording of accrued expenses that were not recorded in the prior periods.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_AdjustmentForPreviouslyUnrecordedAccruedExpenses_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Adjustment For Previously Unrecorded Accrued Expenses</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_AdjustmentForPreviouslyUnrecordedAccruedExpenses_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Additional accrued expenses</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NumberOfReportableSegments" xlink:label="us-gaap_NumberOfReportableSegments" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NumberOfReportableSegments" xlink:to="us-gaap_NumberOfReportableSegments_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NumberOfReportableSegments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of Reportable Segments</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NumberOfReportableSegments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of reportable segments</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InventoryFinishedGoodsNetOfReserves" xlink:label="us-gaap_InventoryFinishedGoodsNetOfReserves" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InventoryFinishedGoodsNetOfReserves" xlink:to="us-gaap_InventoryFinishedGoodsNetOfReserves_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_InventoryFinishedGoodsNetOfReserves_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Inventory, Finished Goods, Net of Reserves</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_InventoryFinishedGoodsNetOfReserves_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finished Goods</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DisposalGroupIncludingDiscontinuedOperationEquitySharesReceivedOrReceivable" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationEquitySharesReceivedOrReceivable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DisposalGroupIncludingDiscontinuedOperationEquitySharesReceivedOrReceivable" xlink:to="cntm_DisposalGroupIncludingDiscontinuedOperationEquitySharesReceivedOrReceivable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationEquitySharesReceivedOrReceivable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of shares received or receivable upon exchange in a share swap transaction by the shareholders of the disposed entity.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationEquitySharesReceivedOrReceivable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Including Discontinued Operation, Equity Shares Received Or Receivable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationEquitySharesReceivedOrReceivable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of shares received upon exchange</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_EquitySecurityFvNiFairValuePerRestrictedShares" xlink:label="cntm_EquitySecurityFvNiFairValuePerRestrictedShares" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_EquitySecurityFvNiFairValuePerRestrictedShares" xlink:to="cntm_EquitySecurityFvNiFairValuePerRestrictedShares_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_EquitySecurityFvNiFairValuePerRestrictedShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The fair value per restricted share pursuant to investment in equity security measured at fair value with change in fair value recognized in net income (FV-NI).</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_EquitySecurityFvNiFairValuePerRestrictedShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity Security, FV-NI, Fair Value Per Restricted Shares</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_EquitySecurityFvNiFairValuePerRestrictedShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair value per restricted share</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquitySecurityFvNiContractualSaleRestrictionRemainingPeriod" xlink:label="us-gaap_EquitySecurityFvNiContractualSaleRestrictionRemainingPeriod" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EquitySecurityFvNiContractualSaleRestrictionRemainingPeriod" xlink:to="us-gaap_EquitySecurityFvNiContractualSaleRestrictionRemainingPeriod_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EquitySecurityFvNiContractualSaleRestrictionRemainingPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity Security, FV-NI, Contractual Sale Restriction, Remaining Period</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_EquitySecurityFvNiContractualSaleRestrictionRemainingPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity security remaining contractual restriction period</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_EquitySecurityFvNiNumberOfSharesSold" xlink:label="cntm_EquitySecurityFvNiNumberOfSharesSold" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_EquitySecurityFvNiNumberOfSharesSold" xlink:to="cntm_EquitySecurityFvNiNumberOfSharesSold_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_EquitySecurityFvNiNumberOfSharesSold_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of shares disposed pursuant to investment in equity security measured at fair value with change in fair value recognized in net income (FV-NI).</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_EquitySecurityFvNiNumberOfSharesSold_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity Security, FV-NI, Number Of Shares Sold</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_EquitySecurityFvNiNumberOfSharesSold_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of shares disposed</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GoodwillImpairmentLoss" xlink:label="us-gaap_GoodwillImpairmentLoss" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_GoodwillImpairmentLoss" xlink:to="us-gaap_GoodwillImpairmentLoss_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_GoodwillImpairmentLoss_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Goodwill, Impairment Loss</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_GoodwillImpairmentLoss_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Impairment of goodwill</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_UnrealizedGainLossOnFairValueMeasurementOfConvertibleDebt" xlink:label="cntm_UnrealizedGainLossOnFairValueMeasurementOfConvertibleDebt" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_UnrealizedGainLossOnFairValueMeasurementOfConvertibleDebt" xlink:to="cntm_UnrealizedGainLossOnFairValueMeasurementOfConvertibleDebt_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_UnrealizedGainLossOnFairValueMeasurementOfConvertibleDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of unrealized gain (loss) on change in fair value of convertible debt during the reporting period.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_UnrealizedGainLossOnFairValueMeasurementOfConvertibleDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Unrealized Gain (Loss) On Fair Value Measurement Of Convertible Debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_UnrealizedGainLossOnFairValueMeasurementOfConvertibleDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Change in fair value of convertible debt</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsTable" xlink:label="us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsTable" xlink:to="us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Groups, Including Discontinued Operations [Table]</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_GlobalImpxIncMember" xlink:label="cntm_GlobalImpxIncMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_GlobalImpxIncMember" xlink:to="cntm_GlobalImpxIncMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_GlobalImpxIncMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to Global Impex Inc.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_GlobalImpxIncMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Global Impx Inc [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_GlobalImpxIncMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">GIX</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_StatementScenarioAxis" xlink:label="srt_StatementScenarioAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_StatementScenarioAxis" xlink:to="srt_StatementScenarioAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_StatementScenarioAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Scenario [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ScenarioUnspecifiedDomain" xlink:label="srt_ScenarioUnspecifiedDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_ScenarioUnspecifiedDomain" xlink:to="srt_ScenarioUnspecifiedDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_ScenarioUnspecifiedDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Scenario [Domain]</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_RevisionOfPriorPeriodAdjustedBalanceMember" xlink:label="cntm_RevisionOfPriorPeriodAdjustedBalanceMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_RevisionOfPriorPeriodAdjustedBalanceMember" xlink:to="cntm_RevisionOfPriorPeriodAdjustedBalanceMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_RevisionOfPriorPeriodAdjustedBalanceMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to adjusted balance to previously issued financial statements. Includes, but is not limited to, adjustment for retrospective application of amendment to accounting standards, other change in accounting principle, correction of error, and other revision.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_RevisionOfPriorPeriodAdjustedBalanceMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Revision Of Prior Period, Adjusted Balance [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_RevisionOfPriorPeriodAdjustedBalanceMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Adjusted balances</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsLineItems" xlink:label="us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsLineItems" xlink:to="us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">DISPOSALS AND DISCONTINUED OPERATIONS</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_BusinessCombinationBargainPurchaseGainLossRecognizedAmount" xlink:label="cntm_BusinessCombinationBargainPurchaseGainLossRecognizedAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_BusinessCombinationBargainPurchaseGainLossRecognizedAmount" xlink:to="cntm_BusinessCombinationBargainPurchaseGainLossRecognizedAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_BusinessCombinationBargainPurchaseGainLossRecognizedAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The amount of gain (loss) recognized from bargain purchase under business combination.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_BusinessCombinationBargainPurchaseGainLossRecognizedAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Bargain Purchase, Gain (Loss) Recognized Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_BusinessCombinationBargainPurchaseGainLossRecognizedAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Bargain Purchase Gain</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisposalGroupNotDiscontinuedOperationIncomeStatementDisclosuresAbstract" xlink:label="us-gaap_DisposalGroupNotDiscontinuedOperationIncomeStatementDisclosuresAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DisposalGroupNotDiscontinuedOperationIncomeStatementDisclosuresAbstract" xlink:to="us-gaap_DisposalGroupNotDiscontinuedOperationIncomeStatementDisclosuresAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DisposalGroupNotDiscontinuedOperationIncomeStatementDisclosuresAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Including Discontinued Operation, Income Statement Disclosures [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DisposalGroupNotDiscontinuedOperationIncomeStatementDisclosuresAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Results of discontinued operations:</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisposalGroupIncludingDiscontinuedOperationRevenue" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationRevenue" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DisposalGroupIncludingDiscontinuedOperationRevenue" xlink:to="us-gaap_DisposalGroupIncludingDiscontinuedOperationRevenue_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationRevenue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Including Discontinued Operation, Revenue</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationRevenue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Revenues</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisposalGroupIncludingDiscontinuedOperationCostsOfGoodsSold" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationCostsOfGoodsSold" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DisposalGroupIncludingDiscontinuedOperationCostsOfGoodsSold" xlink:to="us-gaap_DisposalGroupIncludingDiscontinuedOperationCostsOfGoodsSold_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationCostsOfGoodsSold_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Including Discontinued Operation, Costs of Goods Sold</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationCostsOfGoodsSold_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cost of revenues</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisposalGroupIncludingDiscontinuedOperationGrossProfitLoss" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationGrossProfitLoss" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DisposalGroupIncludingDiscontinuedOperationGrossProfitLoss" xlink:to="us-gaap_DisposalGroupIncludingDiscontinuedOperationGrossProfitLoss_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationGrossProfitLoss_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Including Discontinued Operation, Gross Profit (Loss)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationGrossProfitLoss_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gross Profit</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DisposalGroupIncludingDiscontinuedOperationSellingGeneralAndAdministrativeExpense" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationSellingGeneralAndAdministrativeExpense" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DisposalGroupIncludingDiscontinuedOperationSellingGeneralAndAdministrativeExpense" xlink:to="cntm_DisposalGroupIncludingDiscontinuedOperationSellingGeneralAndAdministrativeExpense_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationSellingGeneralAndAdministrativeExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of selling, general and administrative expense attributable to disposal group, including, but not limited to, discontinued operation.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationSellingGeneralAndAdministrativeExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Including Discontinued Operation, Selling, General and Administrative Expense</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationSellingGeneralAndAdministrativeExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Selling, general and administrative expenses</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisposalGroupIncludingDiscontinuedOperationOperatingIncomeLoss" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationOperatingIncomeLoss" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DisposalGroupIncludingDiscontinuedOperationOperatingIncomeLoss" xlink:to="us-gaap_DisposalGroupIncludingDiscontinuedOperationOperatingIncomeLoss_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationOperatingIncomeLoss_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Including Discontinued Operation, Operating Income (Loss)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationOperatingIncomeLoss_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loss from operations</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DisposalGroupIncludingDiscontinuedOperationOtherIncomeExpenseAbstract" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationOtherIncomeExpenseAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DisposalGroupIncludingDiscontinuedOperationOtherIncomeExpenseAbstract" xlink:to="cntm_DisposalGroupIncludingDiscontinuedOperationOtherIncomeExpenseAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationOtherIncomeExpenseAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">n/a</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationOtherIncomeExpenseAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Including Discontinued Operation, Other Income (Expense) [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationOtherIncomeExpenseAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other income / (expense):</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisposalGroupIncludingDiscontinuedOperationInterestExpense" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationInterestExpense" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DisposalGroupIncludingDiscontinuedOperationInterestExpense" xlink:to="us-gaap_DisposalGroupIncludingDiscontinuedOperationInterestExpense_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationInterestExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Including Discontinued Operation, Interest Expense</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationInterestExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest expense</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationInterestExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest expense</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DisposalGroupIncludingDiscontinuedOperationBargainGain" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationBargainGain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DisposalGroupIncludingDiscontinuedOperationBargainGain" xlink:to="cntm_DisposalGroupIncludingDiscontinuedOperationBargainGain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationBargainGain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of bargain gain  attributable to disposal group, including, but not limited to, discontinued operation.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationBargainGain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Including Discontinued Operation, Bargain Gain</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationBargainGain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Bargain Purchase Gain</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationBargainGain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Bargain purchase gain</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DisposalGroupIncludingDiscontinuedOperationOtherIncomeExpenseNet" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationOtherIncomeExpenseNet" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DisposalGroupIncludingDiscontinuedOperationOtherIncomeExpenseNet" xlink:to="cntm_DisposalGroupIncludingDiscontinuedOperationOtherIncomeExpenseNet_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationOtherIncomeExpenseNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of other income (expense) attributable to disposal group, including, but not limited to, discontinued operation.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationOtherIncomeExpenseNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Including Discontinued Operation, Other Income (Expense), Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationOtherIncomeExpenseNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other income (expense), net</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DisposalGroupIncludingDiscontinuedOperationNonOperatingIncomeExpense" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationNonOperatingIncomeExpense" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DisposalGroupIncludingDiscontinuedOperationNonOperatingIncomeExpense" xlink:to="cntm_DisposalGroupIncludingDiscontinuedOperationNonOperatingIncomeExpense_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationNonOperatingIncomeExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The aggregate amount of income or expense from ancillary business-related activities (that is to say, excluding major activities considered part of the normal operations of the business) attributable to disposal group, including, but not limited to, discontinued operation.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationNonOperatingIncomeExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Including Discontinued Operation, Non-operating Income (Expense)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationNonOperatingIncomeExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total other income (expense), net</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis" xlink:to="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Antidilutive Securities [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AntidilutiveSecuritiesNameDomain" xlink:label="us-gaap_AntidilutiveSecuritiesNameDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AntidilutiveSecuritiesNameDomain" xlink:to="us-gaap_AntidilutiveSecuritiesNameDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AntidilutiveSecuritiesNameDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Antidilutive Securities, Name [Domain]</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_LegacyOptionsMember" xlink:label="cntm_LegacyOptionsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_LegacyOptionsMember" xlink:to="cntm_LegacyOptionsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_LegacyOptionsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to legacy options.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_LegacyOptionsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Legacy Options [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_LegacyOptionsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Options</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_LegacyWarrantsMember" xlink:label="cntm_LegacyWarrantsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_LegacyWarrantsMember" xlink:to="cntm_LegacyWarrantsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_LegacyWarrantsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to legacy warrants.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_LegacyWarrantsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Legacy Warrants [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_LegacyWarrantsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Warrants</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConvertibleDebtSecuritiesMember" xlink:label="us-gaap_ConvertibleDebtSecuritiesMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ConvertibleDebtSecuritiesMember" xlink:to="us-gaap_ConvertibleDebtSecuritiesMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ConvertibleDebtSecuritiesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Debt Securities [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ConvertibleDebtSecuritiesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible notes payable that convert into common stock</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount" xlink:to="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Antidilutive Securities Excluded from Computation of Earnings Per Share, Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Anti-dilutive effect</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfStockByClassTable" xlink:label="us-gaap_ScheduleOfStockByClassTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfStockByClassTable" xlink:to="us-gaap_ScheduleOfStockByClassTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfStockByClassTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock, Class of Stock [Table]</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_InstitutionalConvertibleDebtMember" xlink:label="cntm_InstitutionalConvertibleDebtMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_InstitutionalConvertibleDebtMember" xlink:to="cntm_InstitutionalConvertibleDebtMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_InstitutionalConvertibleDebtMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information pertaining to institutional convertible position.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_InstitutionalConvertibleDebtMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Institutional Convertible Debt [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_InstitutionalConvertibleDebtMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Institutional Convertible Debt</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_SeniorSecuredNotesMember" xlink:label="cntm_SeniorSecuredNotesMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_SeniorSecuredNotesMember" xlink:to="cntm_SeniorSecuredNotesMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_SeniorSecuredNotesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to senior secured notes.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_SeniorSecuredNotesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Senior Secured Notes [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_SeniorSecuredNotesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Senior secured notes</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_SeniorSecuredNote1Member" xlink:label="cntm_SeniorSecuredNote1Member" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_SeniorSecuredNote1Member" xlink:to="cntm_SeniorSecuredNote1Member_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_SeniorSecuredNote1Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to senior secured note 1.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_SeniorSecuredNote1Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Senior Secured Note 1 [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_SeniorSecuredNote1Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Notes 1</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_SeniorSecuredNote2Member" xlink:label="cntm_SeniorSecuredNote2Member" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_SeniorSecuredNote2Member" xlink:to="cntm_SeniorSecuredNote2Member_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_SeniorSecuredNote2Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to senior secured note 2.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_SeniorSecuredNote2Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Senior Secured Note 2 [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_SeniorSecuredNote2Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Notes 2</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsequentEventTypeAxis" xlink:label="us-gaap_SubsequentEventTypeAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SubsequentEventTypeAxis" xlink:to="us-gaap_SubsequentEventTypeAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SubsequentEventTypeAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Subsequent Event Type [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsequentEventTypeDomain" xlink:label="us-gaap_SubsequentEventTypeDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SubsequentEventTypeDomain" xlink:to="us-gaap_SubsequentEventTypeDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SubsequentEventTypeDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Subsequent Event Type [Domain]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsequentEventMember" xlink:label="us-gaap_SubsequentEventMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SubsequentEventMember" xlink:to="us-gaap_SubsequentEventMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SubsequentEventMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Subsequent Event [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SubsequentEventMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Subsequent events</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_PostExpirationOfShareLockInMember" xlink:label="cntm_PostExpirationOfShareLockInMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_PostExpirationOfShareLockInMember" xlink:to="cntm_PostExpirationOfShareLockInMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_PostExpirationOfShareLockInMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to scenario of post expiration of related share lock-in.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_PostExpirationOfShareLockInMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Post Expiration of Share Lock In [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_PostExpirationOfShareLockInMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Post expiration of related share lock-in</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ClassOfStockLineItems" xlink:label="us-gaap_ClassOfStockLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ClassOfStockLineItems" xlink:to="us-gaap_ClassOfStockLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ClassOfStockLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Class of Stock [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ClassOfStockLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Class of Stock</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Cash" xlink:label="us-gaap_Cash" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_Cash" xlink:to="us-gaap_Cash_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_Cash_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_Cash_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash and cash equivalents</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_WorkingCapitalDeficit" xlink:label="cntm_WorkingCapitalDeficit" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_WorkingCapitalDeficit" xlink:to="cntm_WorkingCapitalDeficit_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_WorkingCapitalDeficit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The amount of working capital where the current assets is less than the current liabilities.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_WorkingCapitalDeficit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Working Capital Deficit</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_WorkingCapitalDeficit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Working capital deficit</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_AmountRaisedThroughEquityAndDebtFinancings" xlink:label="cntm_AmountRaisedThroughEquityAndDebtFinancings" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_AmountRaisedThroughEquityAndDebtFinancings" xlink:to="cntm_AmountRaisedThroughEquityAndDebtFinancings_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_AmountRaisedThroughEquityAndDebtFinancings_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount raised through equity and debt financings.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_AmountRaisedThroughEquityAndDebtFinancings_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount Raised Through Equity and Debt Financings</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_AmountRaisedThroughEquityAndDebtFinancings_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount raised</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisposalGroupIncludingDiscontinuedOperationConsideration" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationConsideration" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DisposalGroupIncludingDiscontinuedOperationConsideration" xlink:to="us-gaap_DisposalGroupIncludingDiscontinuedOperationConsideration_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationConsideration_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Including Discontinued Operation, Consideration</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/positiveTerseLabel" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationConsideration_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Consideration</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationConsideration_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair value of consideration received - 160,000,000 Blue Cloud equity shares</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationConsideration_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total consideration</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConvertibleDebt" xlink:label="us-gaap_ConvertibleDebt" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ConvertibleDebt" xlink:to="us-gaap_ConvertibleDebt_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ConvertibleDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Debt...</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_ConvertibleDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible debt</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtConversionConvertedInstrumentAmount1" xlink:label="us-gaap_DebtConversionConvertedInstrumentAmount1" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtConversionConvertedInstrumentAmount1" xlink:to="us-gaap_DebtConversionConvertedInstrumentAmount1_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtConversionConvertedInstrumentAmount1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Conversion, Converted Instrument, Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DebtConversionConvertedInstrumentAmount1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Conversion of convertible debt to common stock</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_NumberOfSeniorSecuredNotes" xlink:label="cntm_NumberOfSeniorSecuredNotes" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_NumberOfSeniorSecuredNotes" xlink:to="cntm_NumberOfSeniorSecuredNotes_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_NumberOfSeniorSecuredNotes_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of senior secured notes under agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_NumberOfSeniorSecuredNotes_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of Senior Secured Notes</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_NumberOfSeniorSecuredNotes_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of notes</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentFaceAmount" xlink:label="us-gaap_DebtInstrumentFaceAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentFaceAmount" xlink:to="us-gaap_DebtInstrumentFaceAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentFaceAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Face Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DebtInstrumentFaceAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Principal amount</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_ProceedsFromIssuanceOfDebtUsedForRepaymentOfOtherDebts" xlink:label="cntm_ProceedsFromIssuanceOfDebtUsedForRepaymentOfOtherDebts" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ProceedsFromIssuanceOfDebtUsedForRepaymentOfOtherDebts" xlink:to="cntm_ProceedsFromIssuanceOfDebtUsedForRepaymentOfOtherDebts_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ProceedsFromIssuanceOfDebtUsedForRepaymentOfOtherDebts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The amount of proceeds from issuance of debt used for repayment of other debts.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ProceedsFromIssuanceOfDebtUsedForRepaymentOfOtherDebts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from Issuance of Debt used for Repayment of Other Debts</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ProceedsFromIssuanceOfDebtUsedForRepaymentOfOtherDebts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Repayment for debt</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentTerm" xlink:label="us-gaap_DebtInstrumentTerm" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentTerm" xlink:to="us-gaap_DebtInstrumentTerm_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentTerm_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Term</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DebtInstrumentTerm_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Term</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_DebtInstrumentTerm_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Maturity Date (from issuance date)</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_CommonStockCapitalValueReservedForFutureIssuance" xlink:label="cntm_CommonStockCapitalValueReservedForFutureIssuance" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_CommonStockCapitalValueReservedForFutureIssuance" xlink:to="cntm_CommonStockCapitalValueReservedForFutureIssuance_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_CommonStockCapitalValueReservedForFutureIssuance_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Value of common shares reserved for future issuance.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_CommonStockCapitalValueReservedForFutureIssuance_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common Stock, Capital Value Reserved for Future issuance</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_CommonStockCapitalValueReservedForFutureIssuance_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common shares reserved</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_ExpectedReductionInDiscretionarySpendings" xlink:label="cntm_ExpectedReductionInDiscretionarySpendings" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ExpectedReductionInDiscretionarySpendings" xlink:to="cntm_ExpectedReductionInDiscretionarySpendings_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ExpectedReductionInDiscretionarySpendings_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of expected reduction in discretionary spendings.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ExpectedReductionInDiscretionarySpendings_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Expected Reduction in Discretionary Spendings</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ExpectedReductionInDiscretionarySpendings_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Reduction in discretionary spendings</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_NumberOfMarketableSecurities" xlink:label="cntm_NumberOfMarketableSecurities" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_NumberOfMarketableSecurities" xlink:to="cntm_NumberOfMarketableSecurities_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_NumberOfMarketableSecurities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the number of marketable securities.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_NumberOfMarketableSecurities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of Marketable Securities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_NumberOfMarketableSecurities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of marketable securities</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_ExpectedProceedsFromCollateralizingMarketableSecurities" xlink:label="cntm_ExpectedProceedsFromCollateralizingMarketableSecurities" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ExpectedProceedsFromCollateralizingMarketableSecurities" xlink:to="cntm_ExpectedProceedsFromCollateralizingMarketableSecurities_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ExpectedProceedsFromCollateralizingMarketableSecurities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of expected proceeds from collateralizing marketable securities.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ExpectedProceedsFromCollateralizingMarketableSecurities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Expected Proceeds from Collateralizing Marketable Securities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ExpectedProceedsFromCollateralizingMarketableSecurities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Expected gross proceeds</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisposalGroupNotDiscontinuedOperationsMember" xlink:label="us-gaap_DisposalGroupNotDiscontinuedOperationsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DisposalGroupNotDiscontinuedOperationsMember" xlink:to="us-gaap_DisposalGroupNotDiscontinuedOperationsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DisposalGroupNotDiscontinuedOperationsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Not Discontinued Operations [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_DisposalGroupNotDiscontinuedOperationsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Continuing Operations</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis" xlink:label="us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis" xlink:to="us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finite-Lived Intangible Assets by Major Class [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:label="us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:to="us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finite-Lived Intangible Assets, Major Class Name [Domain]</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_NoncompeteAndNonSolicitAgreementsMember" xlink:label="cntm_NoncompeteAndNonSolicitAgreementsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_NoncompeteAndNonSolicitAgreementsMember" xlink:to="cntm_NoncompeteAndNonSolicitAgreementsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_NoncompeteAndNonSolicitAgreementsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Agreement in which one party agrees not to pursue a similar trade in competition with another party and non-solicit agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_NoncompeteAndNonSolicitAgreementsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Noncompete and Non-solicit Agreements [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_NoncompeteAndNonSolicitAgreementsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Non-compete and non-solicit</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DisposalGroupIncludingDiscontinuedOperationCashConsideration" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationCashConsideration" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DisposalGroupIncludingDiscontinuedOperationCashConsideration" xlink:to="cntm_DisposalGroupIncludingDiscontinuedOperationCashConsideration_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationCashConsideration_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of cash consideration received or receivable for the disposal of assets and liabilities, including discontinued operation.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationCashConsideration_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Including Discontinued Operation, Cash Consideration</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationCashConsideration_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash consideration</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationCashConsideration_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash paid</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DisposalGroupPercentageOfNonVotingNonDistributingEquityInterestRetained" xlink:label="cntm_DisposalGroupPercentageOfNonVotingNonDistributingEquityInterestRetained" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DisposalGroupPercentageOfNonVotingNonDistributingEquityInterestRetained" xlink:to="cntm_DisposalGroupPercentageOfNonVotingNonDistributingEquityInterestRetained_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DisposalGroupPercentageOfNonVotingNonDistributingEquityInterestRetained_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of non-voting, non-distributing equity interest retained by the company in a disposal group.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DisposalGroupPercentageOfNonVotingNonDistributingEquityInterestRetained_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Percentage Of Non-Voting, Non-Distributing Equity Interest Retained</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DisposalGroupPercentageOfNonVotingNonDistributingEquityInterestRetained_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of non-voting, non-distributing equity interest in ATS LLC</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DisposalGroupPercentageOfNetProceedsFromAssetsSold" xlink:label="cntm_DisposalGroupPercentageOfNetProceedsFromAssetsSold" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DisposalGroupPercentageOfNetProceedsFromAssetsSold" xlink:to="cntm_DisposalGroupPercentageOfNetProceedsFromAssetsSold_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DisposalGroupPercentageOfNetProceedsFromAssetsSold_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of net proceeds receivable by the company if the asset is sold by the disposal group within the given time frame.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DisposalGroupPercentageOfNetProceedsFromAssetsSold_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Percentage Of Net Proceeds From Assets Sold</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DisposalGroupPercentageOfNetProceedsFromAssetsSold_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of net proceeds receivable from ATS LLC</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DisposalGroupSaleOfTransferredAssetsPeriod" xlink:label="cntm_DisposalGroupSaleOfTransferredAssetsPeriod" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DisposalGroupSaleOfTransferredAssetsPeriod" xlink:to="cntm_DisposalGroupSaleOfTransferredAssetsPeriod_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DisposalGroupSaleOfTransferredAssetsPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Period during which the transferred asset is required to be sold by the disposal group, in PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DisposalGroupSaleOfTransferredAssetsPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Sale Of Transferred Assets, Period</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DisposalGroupSaleOfTransferredAssetsPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Period for selling assets</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DisposalGroupCovenantPeriod" xlink:label="cntm_DisposalGroupCovenantPeriod" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DisposalGroupCovenantPeriod" xlink:to="cntm_DisposalGroupCovenantPeriod_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DisposalGroupCovenantPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Period during which the company has agreed with disposal group, in PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DisposalGroupCovenantPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Covenant Period</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DisposalGroupCovenantPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Covenant period</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisposalGroupIncludingDiscontinuedOperationGoodwill1" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationGoodwill1" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DisposalGroupIncludingDiscontinuedOperationGoodwill1" xlink:to="us-gaap_DisposalGroupIncludingDiscontinuedOperationGoodwill1_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationGoodwill1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Including Discontinued Operation, Goodwill</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationGoodwill1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Carrying amount of goodwill</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationGoodwill1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Goodwill</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisposalGroupDisposedOfBySaleNotDiscontinuedOperationsMember" xlink:label="us-gaap_DisposalGroupDisposedOfBySaleNotDiscontinuedOperationsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DisposalGroupDisposedOfBySaleNotDiscontinuedOperationsMember" xlink:to="us-gaap_DisposalGroupDisposedOfBySaleNotDiscontinuedOperationsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DisposalGroupDisposedOfBySaleNotDiscontinuedOperationsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Disposed of by Sale, Not Discontinued Operations [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DisposalGroupDisposedOfBySaleNotDiscontinuedOperationsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposed by sale</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DisposalGroupIncludingDiscontinuedOperationCashConsiderationReceived" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationCashConsiderationReceived" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DisposalGroupIncludingDiscontinuedOperationCashConsiderationReceived" xlink:to="cntm_DisposalGroupIncludingDiscontinuedOperationCashConsiderationReceived_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationCashConsiderationReceived_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of cash consideration received or receivable for the disposal of assets and liabilities, including discontinued operation.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationCashConsiderationReceived_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Including Discontinued Operation, Cash Consideration Received</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationCashConsiderationReceived_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash consideration</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DisposalGroupIncludingDiscontinuedOperationHoldbackConsideration" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationHoldbackConsideration" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DisposalGroupIncludingDiscontinuedOperationHoldbackConsideration" xlink:to="cntm_DisposalGroupIncludingDiscontinuedOperationHoldbackConsideration_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationHoldbackConsideration_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of holdback consideration received or receivable for the disposal of assets and liabilities, including discontinued operation.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationHoldbackConsideration_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group Including Discontinued Operation, Holdback Consideration</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationHoldbackConsideration_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Consideration placed into holdback</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DisposalGroupIncludingDiscontinuedOperationHoldbackConsiderationReleasableUponCompletionOfDeliverySchedule" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationHoldbackConsiderationReleasableUponCompletionOfDeliverySchedule" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DisposalGroupIncludingDiscontinuedOperationHoldbackConsiderationReleasableUponCompletionOfDeliverySchedule" xlink:to="cntm_DisposalGroupIncludingDiscontinuedOperationHoldbackConsiderationReleasableUponCompletionOfDeliverySchedule_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationHoldbackConsiderationReleasableUponCompletionOfDeliverySchedule_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of disclosure holdback consideration releasable upon the Company's delivery of a completed disclosure schedule.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationHoldbackConsiderationReleasableUponCompletionOfDeliverySchedule_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group Including Discontinued Operation, Holdback Consideration Releasable upon Completion of Delivery Schedule</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationHoldbackConsiderationReleasableUponCompletionOfDeliverySchedule_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Holdback releasable upon delivery</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DisposalGroupIncludingDiscontinuedOperationHoldbackConsiderationReleasable90DaysAfterClosing" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationHoldbackConsiderationReleasable90DaysAfterClosing" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DisposalGroupIncludingDiscontinuedOperationHoldbackConsiderationReleasable90DaysAfterClosing" xlink:to="cntm_DisposalGroupIncludingDiscontinuedOperationHoldbackConsiderationReleasable90DaysAfterClosing_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationHoldbackConsiderationReleasable90DaysAfterClosing_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of general holdback consideration releasable 90 days after closing</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationHoldbackConsiderationReleasable90DaysAfterClosing_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group Including Discontinued Operation, Holdback Consideration Releasable 90 Days after Closing</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationHoldbackConsiderationReleasable90DaysAfterClosing_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Holdback releasable after 90 days</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DisposalGroupIncludingDiscontinuedOperationCashAndHoldbackConsideration" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationCashAndHoldbackConsideration" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DisposalGroupIncludingDiscontinuedOperationCashAndHoldbackConsideration" xlink:to="cntm_DisposalGroupIncludingDiscontinuedOperationCashAndHoldbackConsideration_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationCashAndHoldbackConsideration_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of cash and holdback consideration received or receivable for the disposal of assets and liabilities, including discontinued operation.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationCashAndHoldbackConsideration_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group Including Discontinued Operation, Cash and Holdback Consideration</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationCashAndHoldbackConsideration_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Full consideration at closing</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisposalGroupNotDiscontinuedOperationGainLossOnDisposalStatementOfIncomeExtensibleList" xlink:label="us-gaap_DisposalGroupNotDiscontinuedOperationGainLossOnDisposalStatementOfIncomeExtensibleList" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DisposalGroupNotDiscontinuedOperationGainLossOnDisposalStatementOfIncomeExtensibleList" xlink:to="us-gaap_DisposalGroupNotDiscontinuedOperationGainLossOnDisposalStatementOfIncomeExtensibleList_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DisposalGroupNotDiscontinuedOperationGainLossOnDisposalStatementOfIncomeExtensibleList_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Not Discontinued Operation, Gain (Loss) on Disposal, Statement of Income or Comprehensive Income [Extensible Enumeration]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DisposalGroupNotDiscontinuedOperationGainLossOnDisposalStatementOfIncomeExtensibleList_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Not Discontinued Operation, Gain (Loss) on Disposal, Statement of Income or Comprehensive Income [Extensible Enumeration]</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DisposalGroupIncludingDiscontinuedOperationNetIdentifiableAssets" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationNetIdentifiableAssets" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DisposalGroupIncludingDiscontinuedOperationNetIdentifiableAssets" xlink:to="cntm_DisposalGroupIncludingDiscontinuedOperationNetIdentifiableAssets_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationNetIdentifiableAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount classified as net identifiable assets attributable to disposal group held for sale or disposed of.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationNetIdentifiableAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Including Discontinued Operation, Net Identifiable Assets</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationNetIdentifiableAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net identifiable assets disposed</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DisposalGroupTransitionalAssistancePeriod" xlink:label="cntm_DisposalGroupTransitionalAssistancePeriod" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DisposalGroupTransitionalAssistancePeriod" xlink:to="cntm_DisposalGroupTransitionalAssistancePeriod_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DisposalGroupTransitionalAssistancePeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the period of transitional assistance with the disposal group.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DisposalGroupTransitionalAssistancePeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Transitional Assistance Period</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DisposalGroupTransitionalAssistancePeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Transitional assistance period</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DisposalGroupNonCompeteCovenantPeriod" xlink:label="cntm_DisposalGroupNonCompeteCovenantPeriod" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DisposalGroupNonCompeteCovenantPeriod" xlink:to="cntm_DisposalGroupNonCompeteCovenantPeriod_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DisposalGroupNonCompeteCovenantPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Period during which the company has agreed not to compete with disposal group, in PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DisposalGroupNonCompeteCovenantPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Non-Compete Covenant Period</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DisposalGroupNonCompeteCovenantPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Non-competed covenant period</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DisposalGroupIncludingDiscontinuedOperationConsiderationEquitySharesReceivedOrReceivable" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationConsiderationEquitySharesReceivedOrReceivable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DisposalGroupIncludingDiscontinuedOperationConsiderationEquitySharesReceivedOrReceivable" xlink:to="cntm_DisposalGroupIncludingDiscontinuedOperationConsiderationEquitySharesReceivedOrReceivable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationConsiderationEquitySharesReceivedOrReceivable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Aggregate number of shares received or receivable as consideration in connection with the disposal by means other than sale.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationConsiderationEquitySharesReceivedOrReceivable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Including Discontinued Operation, Consideration, Equity Shares Received Or Receivable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationConsiderationEquitySharesReceivedOrReceivable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity consideration</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_PostShareSwapTransactionEquityOwnershipPercentageHeldByEntity" xlink:label="cntm_PostShareSwapTransactionEquityOwnershipPercentageHeldByEntity" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_PostShareSwapTransactionEquityOwnershipPercentageHeldByEntity" xlink:to="cntm_PostShareSwapTransactionEquityOwnershipPercentageHeldByEntity_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_PostShareSwapTransactionEquityOwnershipPercentageHeldByEntity_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of equity ownership to be held by the entity post share swap transaction.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_PostShareSwapTransactionEquityOwnershipPercentageHeldByEntity_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Post Share Swap Transaction, Equity Ownership Percentage Held By Entity</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_PostShareSwapTransactionEquityOwnershipPercentageHeldByEntity_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of ownership held by entity post swap transaction</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SharePrice" xlink:label="us-gaap_SharePrice" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SharePrice" xlink:to="us-gaap_SharePrice_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SharePrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share Price</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SharePrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share price per unit</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_SharePrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Price per equity shares (in per share)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ForeignCurrencyExchangeRateTranslation1" xlink:label="us-gaap_ForeignCurrencyExchangeRateTranslation1" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ForeignCurrencyExchangeRateTranslation1" xlink:to="us-gaap_ForeignCurrencyExchangeRateTranslation1_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ForeignCurrencyExchangeRateTranslation1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Foreign Currency Exchange Rate, Translation</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ForeignCurrencyExchangeRateTranslation1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Exchange rate</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_ForeignCurrencyExchangeRateTranslation1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Spot exchange rate (Indian rupees per $)</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DisposalGroupIncludingDiscontinuedOperationConsiderationEquitySharePricePerShare" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationConsiderationEquitySharePricePerShare" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DisposalGroupIncludingDiscontinuedOperationConsiderationEquitySharePricePerShare" xlink:to="cntm_DisposalGroupIncludingDiscontinuedOperationConsiderationEquitySharePricePerShare_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationConsiderationEquitySharePricePerShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Per share price at which the equity shares are received or receivable as consideration in a share swap transaction upon disposal by means other than sale.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationConsiderationEquitySharePricePerShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Including Discontinued Operation, Consideration, Equity Share, Price Per Share</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationConsiderationEquitySharePricePerShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity consideration (in per share)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisposalGroupIncludingDiscontinuedOperationCashAndCashEquivalents" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationCashAndCashEquivalents" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DisposalGroupIncludingDiscontinuedOperationCashAndCashEquivalents" xlink:to="us-gaap_DisposalGroupIncludingDiscontinuedOperationCashAndCashEquivalents_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationCashAndCashEquivalents_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Including Discontinued Operation, Cash and Cash Equivalents</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationCashAndCashEquivalents_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash and cash equivalents</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_ComprehensiveIncomeLossFromDiscontinuedOperationsNetOfTaxIncludingPortionAttributableToNoncontrollingInterest" xlink:label="cntm_ComprehensiveIncomeLossFromDiscontinuedOperationsNetOfTaxIncludingPortionAttributableToNoncontrollingInterest" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ComprehensiveIncomeLossFromDiscontinuedOperationsNetOfTaxIncludingPortionAttributableToNoncontrollingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount after tax of comprehensive income (loss) from a discontinued operation including the portion attributable to the noncontrolling interest. Includes, but is not limited to, the income (loss) from operations during the phase-out period, gain (loss) on disposal, gain (loss) for reversal of write-down (write-down) to fair value, less cost to sell, and adjustments to a prior period gain (loss) on disposal.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ComprehensiveIncomeLossFromDiscontinuedOperationsNetOfTaxIncludingPortionAttributableToNoncontrollingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Comprehensive Income (Loss) from Discontinued Operations, Net of Tax, Including Portion Attributable to Noncontrolling Interest</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="cntm_ComprehensiveIncomeLossFromDiscontinuedOperationsNetOfTaxIncludingPortionAttributableToNoncontrollingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Comprehensive income from discontinued operations before noncontrolling interests</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_ComprehensiveIncomeLossFromDiscontinuedOperationsNetOfTaxAttributableToNoncontrollingInterest" xlink:label="cntm_ComprehensiveIncomeLossFromDiscontinuedOperationsNetOfTaxAttributableToNoncontrollingInterest" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ComprehensiveIncomeLossFromDiscontinuedOperationsNetOfTaxAttributableToNoncontrollingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount after tax of comprehensive income (loss) from a discontinued operation attributable to the noncontrolling interest. Includes, but is not limited to, the income (loss) from operations during the phase-out period, gain (loss) on disposal, gain (loss) for reversal of write-down (write-down) to fair value, less cost to sell, and adjustments to a prior period gain (loss) on disposal.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ComprehensiveIncomeLossFromDiscontinuedOperationsNetOfTaxAttributableToNoncontrollingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Comprehensive Income (Loss) from Discontinued Operations, Net of Tax, Attributable to Noncontrolling Interest</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ComprehensiveIncomeLossFromDiscontinuedOperationsNetOfTaxAttributableToNoncontrollingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Comprehensive income attributable to non-controlling interests</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_ComprehensiveIncomeLossFromDiscontinuedOperationsNetOfTaxAttributableToParent" xlink:label="cntm_ComprehensiveIncomeLossFromDiscontinuedOperationsNetOfTaxAttributableToParent" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ComprehensiveIncomeLossFromDiscontinuedOperationsNetOfTaxAttributableToParent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount after tax of comprehensive income (loss) from a discontinued operation attributable to the parent. Includes, but is not limited to, the income (loss) from operations during the phase-out period, gain (loss) on disposal, gain (loss) for reversal of write-down (write-down) to fair value, less cost to sell, and adjustments to a prior period gain (loss) on disposal.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ComprehensiveIncomeLossFromDiscontinuedOperationsNetOfTaxAttributableToParent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Comprehensive Income (Loss) from Discontinued Operations, Net of Tax, Attributable to Parent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="cntm_ComprehensiveIncomeLossFromDiscontinuedOperationsNetOfTaxAttributableToParent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Comprehensive Income from discontinued operations, net of tax</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DisposalGroupIncludingDiscontinuedOperationNoncontrollingInterestDerecognized" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationNoncontrollingInterestDerecognized" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DisposalGroupIncludingDiscontinuedOperationNoncontrollingInterestDerecognized" xlink:to="cntm_DisposalGroupIncludingDiscontinuedOperationNoncontrollingInterestDerecognized_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationNoncontrollingInterestDerecognized_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Carrying amount of noncontrolling interest in disposal group derecognized.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationNoncontrollingInterestDerecognized_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Including Discontinued Operation, Noncontrolling Interest Derecognized</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationNoncontrollingInterestDerecognized_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Carrying amount of noncontrolling interests derecognized</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DisposalGroupIncludingDiscontinuedOperationNetAssetsDerecognized" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationNetAssetsDerecognized" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationNetAssetsDerecognized_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Carrying amount of net assets of disposal group derecognized.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationNetAssetsDerecognized_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Including Discontinued Operation, Net Assets Derecognized</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationNetAssetsDerecognized_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Less: carrying amount of net assets of GIX derecognized (including amounts recognized in accumulated other comprehensive loss)</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_IncomeLossFromDiscontinuedOperationsNetOfTaxBeforeGainOnDisposalAttributableToNoncontrollingInterest" xlink:label="cntm_IncomeLossFromDiscontinuedOperationsNetOfTaxBeforeGainOnDisposalAttributableToNoncontrollingInterest" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_IncomeLossFromDiscontinuedOperationsNetOfTaxBeforeGainOnDisposalAttributableToNoncontrollingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount after tax of income (loss), before gain on disposal from a discontinued operation attributable to the noncontrolling interest. Includes, but is not limited to, the income (loss) from operations during the phase-out period, gain (loss) on disposal, gain (loss) for reversal of write-down (write-down) to fair value, less cost to sell, and adjustments to a prior period gain (loss) on disposal.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_IncomeLossFromDiscontinuedOperationsNetOfTaxBeforeGainOnDisposalAttributableToNoncontrollingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Income (Loss) from Discontinued Operations, Net of Tax, Before Gain On Disposal, Attributable to Noncontrolling Interest</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_IncomeLossFromDiscontinuedOperationsNetOfTaxBeforeGainOnDisposalAttributableToNoncontrollingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Comprehensive income (loss) from operations, before disposal gain (net of tax) - Noncontrolling interests</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_IncomeLossFromDiscontinuedOperationsNetOfTaxBeforeGainOnDisposalAttributableToParent" xlink:label="cntm_IncomeLossFromDiscontinuedOperationsNetOfTaxBeforeGainOnDisposalAttributableToParent" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_IncomeLossFromDiscontinuedOperationsNetOfTaxBeforeGainOnDisposalAttributableToParent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount after tax of income (loss), before gain on disposal from a discontinued operation attributable to the parent. Includes, but is not limited to, the income (loss) from operations during the phase-out period, gain (loss) on disposal, gain (loss) for reversal of write-down (write-down) to fair value, less cost to sell, and adjustments to a prior period gain (loss) on disposal.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_IncomeLossFromDiscontinuedOperationsNetOfTaxBeforeGainOnDisposalAttributableToParent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Income (Loss) from Discontinued Operations, Net of Tax, Before Gain On Disposal, Attributable to Parent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_IncomeLossFromDiscontinuedOperationsNetOfTaxBeforeGainOnDisposalAttributableToParent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Comprehensive income (loss) from operations, before disposal gain (net of tax) - ConnectM Technology Solutions, Inc</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DiscontinuedOperationGainLossOnDisposalOfDiscontinuedOperationNetOfTaxAttributableToParent" xlink:label="cntm_DiscontinuedOperationGainLossOnDisposalOfDiscontinuedOperationNetOfTaxAttributableToParent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DiscontinuedOperationGainLossOnDisposalOfDiscontinuedOperationNetOfTaxAttributableToParent" xlink:to="cntm_DiscontinuedOperationGainLossOnDisposalOfDiscontinuedOperationNetOfTaxAttributableToParent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DiscontinuedOperationGainLossOnDisposalOfDiscontinuedOperationNetOfTaxAttributableToParent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount after tax of gain (loss) not previously recognized resulting from the disposal of a discontinued operation, attributable to the parent.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DiscontinuedOperationGainLossOnDisposalOfDiscontinuedOperationNetOfTaxAttributableToParent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Discontinued Operation, Gain (Loss) on Disposal of Discontinued Operation, Net of Tax, Attributable to Parent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DiscontinuedOperationGainLossOnDisposalOfDiscontinuedOperationNetOfTaxAttributableToParent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gain on disposal - ConnectM Technology Solutions, Inc</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisposalGroupIncludingDiscontinuedOperationAccountsNotesAndLoansReceivableNet" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationAccountsNotesAndLoansReceivableNet" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DisposalGroupIncludingDiscontinuedOperationAccountsNotesAndLoansReceivableNet" xlink:to="us-gaap_DisposalGroupIncludingDiscontinuedOperationAccountsNotesAndLoansReceivableNet_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationAccountsNotesAndLoansReceivableNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Including Discontinued Operation, Accounts, Notes and Loans Receivable, Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationAccountsNotesAndLoansReceivableNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts receivable, net</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisposalGroupIncludingDiscontinuedOperationInventoryCurrent" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationInventoryCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DisposalGroupIncludingDiscontinuedOperationInventoryCurrent" xlink:to="us-gaap_DisposalGroupIncludingDiscontinuedOperationInventoryCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationInventoryCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Including Discontinued Operation, Inventory, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationInventoryCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Inventories, net</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DisposalGroupIncludingDiscontinuedOperationPrepaidExpensesCurrent" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationPrepaidExpensesCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DisposalGroupIncludingDiscontinuedOperationPrepaidExpensesCurrent" xlink:to="cntm_DisposalGroupIncludingDiscontinuedOperationPrepaidExpensesCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationPrepaidExpensesCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount classified as prepaid expenses attributable to disposal group held for sale or disposed of, expected to be disposed of within one year or the normal operating cycle, if longer.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationPrepaidExpensesCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Including Discontinued Operation, Prepaid Expenses, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationPrepaidExpensesCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Prepaid expenses</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DisposalGroupIncludingDiscontinuedOperationRightsOfUseAssetsOperatingLease" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationRightsOfUseAssetsOperatingLease" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DisposalGroupIncludingDiscontinuedOperationRightsOfUseAssetsOperatingLease" xlink:to="cntm_DisposalGroupIncludingDiscontinuedOperationRightsOfUseAssetsOperatingLease_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationRightsOfUseAssetsOperatingLease_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount classified as operating lease right-of-use assets attributable to disposal group held for sale or disposed of, expected to be disposed of within one year or the normal operating cycle, if longer.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationRightsOfUseAssetsOperatingLease_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Including Discontinued Operation, Rights Of Use Assets, Operating Lease</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationRightsOfUseAssetsOperatingLease_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Right-of-use asset - Operating Lease</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisposalGroupIncludingDiscontinuedOperationPropertyPlantAndEquipmentNoncurrent" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationPropertyPlantAndEquipmentNoncurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DisposalGroupIncludingDiscontinuedOperationPropertyPlantAndEquipmentNoncurrent" xlink:to="us-gaap_DisposalGroupIncludingDiscontinuedOperationPropertyPlantAndEquipmentNoncurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationPropertyPlantAndEquipmentNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Including Discontinued Operation, Property, Plant, and Equipment, Noncurrent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationPropertyPlantAndEquipmentNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Property and equipment, net</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisposalGroupIncludingDiscontinuedOperationIntangibleAssetsNoncurrent" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationIntangibleAssetsNoncurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DisposalGroupIncludingDiscontinuedOperationIntangibleAssetsNoncurrent" xlink:to="us-gaap_DisposalGroupIncludingDiscontinuedOperationIntangibleAssetsNoncurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationIntangibleAssetsNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Including Discontinued Operation, Intangible Assets, Noncurrent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationIntangibleAssetsNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Intangible assets, net</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperation" xlink:label="us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperation" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperation" xlink:to="us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperation_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Including Discontinued Operation, Assets</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total assets from discontinued operation</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisposalGroupIncludingDiscontinuedOperationAccountsPayableCurrent" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationAccountsPayableCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DisposalGroupIncludingDiscontinuedOperationAccountsPayableCurrent" xlink:to="us-gaap_DisposalGroupIncludingDiscontinuedOperationAccountsPayableCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationAccountsPayableCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Including Discontinued Operation, Accounts Payable, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationAccountsPayableCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts payable</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DisposalGroupIncludingDiscontinuedOperationAccruedExpensesAndOtherLiabilitiesCurrent" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationAccruedExpensesAndOtherLiabilitiesCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DisposalGroupIncludingDiscontinuedOperationAccruedExpensesAndOtherLiabilitiesCurrent" xlink:to="cntm_DisposalGroupIncludingDiscontinuedOperationAccruedExpensesAndOtherLiabilitiesCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationAccruedExpensesAndOtherLiabilitiesCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount classified as accrued expenses and other liabilities attributable to disposal group held for sale or disposed of, expected to be disposed of within one year or the normal operating cycle, if longer.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationAccruedExpensesAndOtherLiabilitiesCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Including Discontinued Operation, Accrued Expenses And Other Liabilities, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationAccruedExpensesAndOtherLiabilitiesCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accrued expenses and other current liabilities</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DisposalGroupIncludingDiscontinuedOperationDebtCurrentNetOfDebtDiscount" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationDebtCurrentNetOfDebtDiscount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DisposalGroupIncludingDiscontinuedOperationDebtCurrentNetOfDebtDiscount" xlink:to="cntm_DisposalGroupIncludingDiscontinuedOperationDebtCurrentNetOfDebtDiscount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationDebtCurrentNetOfDebtDiscount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount classified as debt, net of debt discount attributable to disposal group held for sale or disposed of, expected to be disposed of within one year or the normal operating cycle, if longer.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationDebtCurrentNetOfDebtDiscount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Including Discontinued Operation, Debt, Current, Net Of Debt Discount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationDebtCurrentNetOfDebtDiscount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt, net of debt discount</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DisposalGroupIncludingDiscontinuedOperationDeferredConsiderationCurrent" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationDeferredConsiderationCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DisposalGroupIncludingDiscontinuedOperationDeferredConsiderationCurrent" xlink:to="cntm_DisposalGroupIncludingDiscontinuedOperationDeferredConsiderationCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationDeferredConsiderationCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount classified as deferred consideration attributable to disposal group held for sale or disposed of, expected to be disposed of within one year or the normal operating cycle, if longer.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationDeferredConsiderationCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Including Discontinued Operation, Deferred Consideration, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationDeferredConsiderationCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Deferred Consideration</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DisposalGroupIncludingDiscontinuedOperationOperatingLeaseLiabilityCurrent" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationOperatingLeaseLiabilityCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DisposalGroupIncludingDiscontinuedOperationOperatingLeaseLiabilityCurrent" xlink:to="cntm_DisposalGroupIncludingDiscontinuedOperationOperatingLeaseLiabilityCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationOperatingLeaseLiabilityCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount classified as operating lease liabilities attributable to disposal group held for sale or disposed of, expected to be disposed of within one year or the normal operating cycle, if longer.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationOperatingLeaseLiabilityCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Including Discontinued Operation, Operating Lease Liability, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationOperatingLeaseLiabilityCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating lease liability</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisposalGroupIncludingDiscontinuedOperationDeferredRevenueCurrent" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationDeferredRevenueCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DisposalGroupIncludingDiscontinuedOperationDeferredRevenueCurrent" xlink:to="us-gaap_DisposalGroupIncludingDiscontinuedOperationDeferredRevenueCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationDeferredRevenueCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Including Discontinued Operation, Deferred Revenue, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationDeferredRevenueCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contract liabilities</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DisposalGroupIncludingDiscontinuedOperationDeferredTaxLiabilitiesCurrent" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationDeferredTaxLiabilitiesCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DisposalGroupIncludingDiscontinuedOperationDeferredTaxLiabilitiesCurrent" xlink:to="cntm_DisposalGroupIncludingDiscontinuedOperationDeferredTaxLiabilitiesCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationDeferredTaxLiabilitiesCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount classified as deferred tax liabilities attributable to disposal group held for sale or disposed of, expected to be disposed of within one year or the normal operating cycle, if longer.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationDeferredTaxLiabilitiesCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Including Discontinued Operation, Deferred Tax Liabilities, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationDeferredTaxLiabilitiesCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Deferred Tax Liabilities</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DisposalGroupIncludingDiscontinuedOperationDebtNoncurrent" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationDebtNoncurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DisposalGroupIncludingDiscontinuedOperationDebtNoncurrent" xlink:to="cntm_DisposalGroupIncludingDiscontinuedOperationDebtNoncurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationDebtNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount classified as debt, net of current portion attributable to disposal group held for sale or disposed of, expected to be disposed of beyond one year or the normal operating cycle, if longer.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationDebtNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Including Discontinued Operation, Debt, Noncurrent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationDebtNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt, net of current portion</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DisposalGroupIncludingDiscontinuedOperationOperatingLeaseLiabilityNoncurrent" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationOperatingLeaseLiabilityNoncurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DisposalGroupIncludingDiscontinuedOperationOperatingLeaseLiabilityNoncurrent" xlink:to="cntm_DisposalGroupIncludingDiscontinuedOperationOperatingLeaseLiabilityNoncurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationOperatingLeaseLiabilityNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount classified as operating lease liabilities, net of current portion attributable to disposal group held for sale or disposed of, expected to be disposed of beyond one year or the normal operating cycle, if longer.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationOperatingLeaseLiabilityNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Including Discontinued Operation, Operating Lease Liability, Noncurrent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationOperatingLeaseLiabilityNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating lease liabilities, net of current portion</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperation" xlink:label="us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperation" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperation" xlink:to="us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperation_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Including Discontinued Operation, Liabilities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total liabilities from discontinued operation</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DisposalGroupIncludingDiscontinuedOperationNoncontrollingInterests" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationNoncontrollingInterests" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DisposalGroupIncludingDiscontinuedOperationNoncontrollingInterests" xlink:to="cntm_DisposalGroupIncludingDiscontinuedOperationNoncontrollingInterests_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationNoncontrollingInterests_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of equity (deficit) attributable to noncontrolling interest in disposal group held for sale or disposed of, expected to be disposed of.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationNoncontrollingInterests_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Including Discontinued Operation, Noncontrolling Interests</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationNoncontrollingInterests_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Noncontrolling interest</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfEquityMethodInvestmentsTable" xlink:label="us-gaap_ScheduleOfEquityMethodInvestmentsTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfEquityMethodInvestmentsTable" xlink:to="us-gaap_ScheduleOfEquityMethodInvestmentsTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfEquityMethodInvestmentsTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity Method Investment [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis" xlink:label="srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis" xlink:to="srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Investment, Name [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_EquityMethodInvesteeNameDomain" xlink:label="srt_EquityMethodInvesteeNameDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_EquityMethodInvesteeNameDomain" xlink:to="srt_EquityMethodInvesteeNameDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_EquityMethodInvesteeNameDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Investment, Name [Domain]</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_SunSolarLlcMember" xlink:label="cntm_SunSolarLlcMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_SunSolarLlcMember" xlink:to="cntm_SunSolarLlcMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_SunSolarLlcMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to Sun Solar LLC.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_SunSolarLlcMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Sun Solar LLC [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_SunSolarLlcMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Sun Solar LLC</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_LegalEntityAxis" xlink:label="dei_LegalEntityAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_LegalEntityAxis" xlink:to="dei_LegalEntityAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_LegalEntityAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Legal Entity [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityDomain" xlink:label="dei_EntityDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityDomain" xlink:to="dei_EntityDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_EntityDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">All Entities [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="dei_EntityDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Entity [Domain]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CustomerRelationshipsMember" xlink:label="us-gaap_CustomerRelationshipsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CustomerRelationshipsMember" xlink:to="us-gaap_CustomerRelationshipsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CustomerRelationshipsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Customer Relationships [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CustomerRelationshipsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Customer relationships</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_CustomerRelationshipsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Customers relationship</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TradeNamesMember" xlink:label="us-gaap_TradeNamesMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_TradeNamesMember" xlink:to="us-gaap_TradeNamesMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_TradeNamesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Trade Names [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_TradeNamesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Trade name</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_TradeNamesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Trade Names</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_SellerMember" xlink:label="cntm_SellerMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_SellerMember" xlink:to="cntm_SellerMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_SellerMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents of sole member (the "Seller").</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_SellerMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Seller [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_SellerMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Seller</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfEquityMethodInvestmentsLineItems" xlink:label="us-gaap_ScheduleOfEquityMethodInvestmentsLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfEquityMethodInvestmentsLineItems" xlink:to="us-gaap_ScheduleOfEquityMethodInvestmentsLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfEquityMethodInvestmentsLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of Equity Method Investments [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ScheduleOfEquityMethodInvestmentsLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">RELATED PARTY TRANSACTIONS</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_ScheduleOfEquityMethodInvestmentsLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">EQUITY METHOD INVESTMENT</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_EquityMethodInvestmentNumberOfMembershipInterestsAcquired" xlink:label="cntm_EquityMethodInvestmentNumberOfMembershipInterestsAcquired" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_EquityMethodInvestmentNumberOfMembershipInterestsAcquired" xlink:to="cntm_EquityMethodInvestmentNumberOfMembershipInterestsAcquired_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_EquityMethodInvestmentNumberOfMembershipInterestsAcquired_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of membership interests acquired in investments accounted for under the equity method of accounting.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_EquityMethodInvestmentNumberOfMembershipInterestsAcquired_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity Method Investment, Number Of Membership Interests Acquired</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_EquityMethodInvestmentNumberOfMembershipInterestsAcquired_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of membership interest</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquityMethodInvestmentOwnershipPercentage" xlink:label="us-gaap_EquityMethodInvestmentOwnershipPercentage" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EquityMethodInvestmentOwnershipPercentage" xlink:to="us-gaap_EquityMethodInvestmentOwnershipPercentage_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EquityMethodInvestmentOwnershipPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity Method Investment, Ownership Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_EquityMethodInvestmentOwnershipPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Ownership Percentage</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LimitedPartnersCapitalAccountUnitsIssued" xlink:label="us-gaap_LimitedPartnersCapitalAccountUnitsIssued" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LimitedPartnersCapitalAccountUnitsIssued" xlink:to="us-gaap_LimitedPartnersCapitalAccountUnitsIssued_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LimitedPartnersCapitalAccountUnitsIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Limited Partners' Capital Account, Units Issued</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LimitedPartnersCapitalAccountUnitsIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Units issued</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_ProductSalesRevenue" xlink:label="cntm_ProductSalesRevenue" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ProductSalesRevenue" xlink:to="cntm_ProductSalesRevenue_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ProductSalesRevenue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The Amount of product sales revenue for the period.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ProductSalesRevenue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Product Sales Revenue</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ProductSalesRevenue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of product sales revenue</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LimitedPartnersCapitalAccountUnitsOutstanding" xlink:label="us-gaap_LimitedPartnersCapitalAccountUnitsOutstanding" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LimitedPartnersCapitalAccountUnitsOutstanding" xlink:to="us-gaap_LimitedPartnersCapitalAccountUnitsOutstanding_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LimitedPartnersCapitalAccountUnitsOutstanding_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Limited Partners' Capital Account, Units Outstanding</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LimitedPartnersCapitalAccountUnitsOutstanding_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Units outstanding</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LimitedLiabilityCompanyLLCOrLimitedPartnershipLPMembersOrLimitedPartnersOwnershipInterest" xlink:label="us-gaap_LimitedLiabilityCompanyLLCOrLimitedPartnershipLPMembersOrLimitedPartnersOwnershipInterest" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LimitedLiabilityCompanyLLCOrLimitedPartnershipLPMembersOrLimitedPartnersOwnershipInterest" xlink:to="us-gaap_LimitedLiabilityCompanyLLCOrLimitedPartnershipLPMembersOrLimitedPartnersOwnershipInterest_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LimitedLiabilityCompanyLLCOrLimitedPartnershipLPMembersOrLimitedPartnersOwnershipInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Limited Liability Company or Limited Partnership, Members or Limited Partners, Ownership Interest</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LimitedLiabilityCompanyLLCOrLimitedPartnershipLPMembersOrLimitedPartnersOwnershipInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Partners ownership percentage</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_IssuanceOfSharesForEquityMethodInvestment" xlink:label="cntm_IssuanceOfSharesForEquityMethodInvestment" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_IssuanceOfSharesForEquityMethodInvestment" xlink:to="cntm_IssuanceOfSharesForEquityMethodInvestment_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_IssuanceOfSharesForEquityMethodInvestment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The value of stock issued for equity method investment.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_IssuanceOfSharesForEquityMethodInvestment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance Of Shares For Equity Method Investment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_IssuanceOfSharesForEquityMethodInvestment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of shares for equity method investment</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_StockIssuedDuringPeriodSharesEquityMethodInvestment" xlink:label="cntm_StockIssuedDuringPeriodSharesEquityMethodInvestment" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_StockIssuedDuringPeriodSharesEquityMethodInvestment" xlink:to="cntm_StockIssuedDuringPeriodSharesEquityMethodInvestment_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_StockIssuedDuringPeriodSharesEquityMethodInvestment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of shares of stock issued during the period pursuant to an equity method investment.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_StockIssuedDuringPeriodSharesEquityMethodInvestment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period, Shares, Equity Method Investment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_StockIssuedDuringPeriodSharesEquityMethodInvestment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of shares of stock issued during the period</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_EquityMethodInvestmentInitialRecognitionCarryingAmount" xlink:label="cntm_EquityMethodInvestmentInitialRecognitionCarryingAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_EquityMethodInvestmentInitialRecognitionCarryingAmount" xlink:to="cntm_EquityMethodInvestmentInitialRecognitionCarryingAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_EquityMethodInvestmentInitialRecognitionCarryingAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Initial carrying amount of equity method investment recognized in the books.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_EquityMethodInvestmentInitialRecognitionCarryingAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity Method Investment, Initial Recognition, Carrying Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_EquityMethodInvestmentInitialRecognitionCarryingAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Initial carrying amount of the investment</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_EquityMethodInvestmentBasisDifferenceAmortization" xlink:label="cntm_EquityMethodInvestmentBasisDifferenceAmortization" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_EquityMethodInvestmentBasisDifferenceAmortization" xlink:to="cntm_EquityMethodInvestmentBasisDifferenceAmortization_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_EquityMethodInvestmentBasisDifferenceAmortization_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The amount of amortization expense related to the difference between the cost of an equity method investment and the underlying book value of the investee's net assets.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_EquityMethodInvestmentBasisDifferenceAmortization_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity Method Investment Basis Difference Amortization</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_EquityMethodInvestmentBasisDifferenceAmortization_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Basis difference amortization expense</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_EquityMethodInvestmentsPurchaseConsiderationAllocatedToIntangibleAssets" xlink:label="cntm_EquityMethodInvestmentsPurchaseConsiderationAllocatedToIntangibleAssets" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_EquityMethodInvestmentsPurchaseConsiderationAllocatedToIntangibleAssets" xlink:to="cntm_EquityMethodInvestmentsPurchaseConsiderationAllocatedToIntangibleAssets_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_EquityMethodInvestmentsPurchaseConsiderationAllocatedToIntangibleAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of purchase consideration from equity method investments allocated to individual intangible assets.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_EquityMethodInvestmentsPurchaseConsiderationAllocatedToIntangibleAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity Method Investments, Purchase Consideration Allocated To Intangible Assets</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_EquityMethodInvestmentsPurchaseConsiderationAllocatedToIntangibleAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of purchase consideration</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetUsefulLife" xlink:label="us-gaap_FiniteLivedIntangibleAssetUsefulLife" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FiniteLivedIntangibleAssetUsefulLife" xlink:to="us-gaap_FiniteLivedIntangibleAssetUsefulLife_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FiniteLivedIntangibleAssetUsefulLife_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finite-Lived Intangible Asset, Useful Life</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FiniteLivedIntangibleAssetUsefulLife_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Estimated useful life</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AmortizationOfIntangibleAssets" xlink:label="us-gaap_AmortizationOfIntangibleAssets" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AmortizationOfIntangibleAssets" xlink:to="us-gaap_AmortizationOfIntangibleAssets_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AmortizationOfIntangibleAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amortization of Intangible Assets</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AmortizationOfIntangibleAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amortization of intangible assets</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable" xlink:label="us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable" xlink:to="us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Intangible Asset, Finite-Lived [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NoncompeteAgreementsMember" xlink:label="us-gaap_NoncompeteAgreementsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NoncompeteAgreementsMember" xlink:to="us-gaap_NoncompeteAgreementsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NoncompeteAgreementsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Noncompete Agreements [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NoncompeteAgreementsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Noncompetition agreement</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IntellectualPropertyMember" xlink:label="us-gaap_IntellectualPropertyMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IntellectualPropertyMember" xlink:to="us-gaap_IntellectualPropertyMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IntellectualPropertyMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Intellectual Property [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IntellectualPropertyMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Intellectual property</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_ProprietaryTechnologyMember" xlink:label="cntm_ProprietaryTechnologyMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ProprietaryTechnologyMember" xlink:to="cntm_ProprietaryTechnologyMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ProprietaryTechnologyMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to proprietary technology.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ProprietaryTechnologyMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proprietary Technology [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ProprietaryTechnologyMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Intangible assets: Proprietary Technology</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_ProprietaryTechnologyMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proprietary Technology</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SoftwareDevelopmentMember" xlink:label="us-gaap_SoftwareDevelopmentMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SoftwareDevelopmentMember" xlink:to="us-gaap_SoftwareDevelopmentMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SoftwareDevelopmentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Software, Internally Developed [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SoftwareDevelopmentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Internally developed software</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PatentsMember" xlink:label="us-gaap_PatentsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PatentsMember" xlink:to="us-gaap_PatentsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PatentsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Patents [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PatentsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Intangible Assets: Patent</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TechnologyBasedIntangibleAssetsMember" xlink:label="us-gaap_TechnologyBasedIntangibleAssetsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_TechnologyBasedIntangibleAssetsMember" xlink:to="us-gaap_TechnologyBasedIntangibleAssetsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_TechnologyBasedIntangibleAssetsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Technology-Based Intangible Assets [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_TechnologyBasedIntangibleAssetsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Acquired technology</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_TechnologyBasedIntangibleAssetsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Technology</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DevelopedTechnologyRightsMember" xlink:label="us-gaap_DevelopedTechnologyRightsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DevelopedTechnologyRightsMember" xlink:to="us-gaap_DevelopedTechnologyRightsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DevelopedTechnologyRightsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Developed Technology Rights [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_DevelopedTechnologyRightsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Developed technology</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsLineItems" xlink:label="us-gaap_FiniteLivedIntangibleAssetsLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FiniteLivedIntangibleAssetsLineItems" xlink:to="us-gaap_FiniteLivedIntangibleAssetsLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FiniteLivedIntangibleAssetsLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finite-Lived Intangible Assets [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FiniteLivedIntangibleAssetsLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">INTANGIBLE ASSETS, NET</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsRemainingAmortizationPeriod1" xlink:label="us-gaap_FiniteLivedIntangibleAssetsRemainingAmortizationPeriod1" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FiniteLivedIntangibleAssetsRemainingAmortizationPeriod1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finite-Lived Intangible Assets, Remaining Amortization Period</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FiniteLivedIntangibleAssetsRemainingAmortizationPeriod1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Weighted Average Remaining Amortization Period (years)</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FiniteLivedIntangibleAssetsGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finite-Lived Intangible Assets, Gross</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FiniteLivedIntangibleAssetsGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gross Amount</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finite-Lived Intangible Assets, Accumulated Amortization</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accumulated Amortization</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsNet" xlink:label="us-gaap_FiniteLivedIntangibleAssetsNet" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FiniteLivedIntangibleAssetsNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finite-Lived Intangible Assets, Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FiniteLivedIntangibleAssetsNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net Amount</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ImpairmentOfIntangibleAssetsFinitelived" xlink:label="us-gaap_ImpairmentOfIntangibleAssetsFinitelived" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ImpairmentOfIntangibleAssetsFinitelived" xlink:to="us-gaap_ImpairmentOfIntangibleAssetsFinitelived_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ImpairmentOfIntangibleAssetsFinitelived_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Impairment of Intangible Assets, Finite-Lived</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_ImpairmentOfIntangibleAssetsFinitelived_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Impairment loss</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinitelivedIntangibleAssetsAcquired1" xlink:label="us-gaap_FinitelivedIntangibleAssetsAcquired1" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FinitelivedIntangibleAssetsAcquired1" xlink:to="us-gaap_FinitelivedIntangibleAssetsAcquired1_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FinitelivedIntangibleAssetsAcquired1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Intangible Asset, Finite-Lived, Acquired</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FinitelivedIntangibleAssetsAcquired1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Identifiable Intangible Assets Fair Value</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_FinitelivedIntangibleAssetsAcquired1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Identifiable Intangible assets fair value</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationRemainderOfFiscalYear" xlink:label="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationRemainderOfFiscalYear" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationRemainderOfFiscalYear" xlink:to="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationRemainderOfFiscalYear_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationRemainderOfFiscalYear_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of amortization for assets, excluding internally developed software, financial assets and goodwill, lacking physical substance with finite life expected to be recognized in remainder of current fiscal year.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationRemainderOfFiscalYear_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finite-Lived Intangible Asset Excluding Internally Developed Software, Expected Amortization, Remainder of Fiscal Year</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationRemainderOfFiscalYear_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2026 (six months)</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearOne" xlink:label="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearOne" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearOne" xlink:to="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearOne_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearOne_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of amortization for assets, excluding internally developed software, financial assets and goodwill, lacking physical substance with finite life expected to be recognized in next fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearOne_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finite-Lived Intangible Asset Excluding Internally Developed Software, Expected Amortization, Year One</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearOne_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2027</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearTwo" xlink:label="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearTwo" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearTwo" xlink:to="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearTwo_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearTwo_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of amortization for assets, excluding internally developed software, financial assets and goodwill, lacking physical substance with finite life expected to be recognized in second fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearTwo_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finite-Lived Intangible Asset Excluding Internally Developed Software, Expected Amortization, Year Two</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearTwo_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2028</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearThree" xlink:label="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearThree" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearThree" xlink:to="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearThree_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearThree_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of amortization for assets, excluding internally developed software, financial assets and goodwill, lacking physical substance with finite life expected to be recognized in third fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearThree_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finite-Lived Intangible Asset Excluding Internally Developed Software, Expected Amortization, Year Three</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearThree_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2029</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearFour" xlink:label="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearFour" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearFour" xlink:to="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearFour_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearFour_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of amortization for assets, excluding internally developed software, financial assets and goodwill, lacking physical substance with finite life expected to be recognized in fourth fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearFour_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finite-Lived Intangible Asset Excluding Internally Developed Software, Expected Amortization, Year Four</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearFour_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2030</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearFive" xlink:label="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearFive" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearFive_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of amortization for assets, excluding internally developed software, financial assets and goodwill, lacking physical substance with finite life expected to be recognized in fifth fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearFive_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finite-Lived Intangible Asset Excluding Internally Developed Software, Expected Amortization, Year Five</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearFive_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2031</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationAfterYearFive" xlink:label="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationAfterYearFive" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationAfterYearFive_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of amortization for assets, excluding internally developed software, financial assets and goodwill, lacking physical substance with finite life expected to be recognized in after fifth fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationAfterYearFive_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finite-Lived Intangible Asset Excluding Internally Developed Software, Expected Amortization, after Year Five</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationAfterYearFive_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Thereafter</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_ConvertibleNotes2025Member" xlink:label="cntm_ConvertibleNotes2025Member" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertibleNotes2025Member" xlink:to="cntm_ConvertibleNotes2025Member_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertibleNotes2025Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the member information pertaining to 2025 Convertible Notes.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertibleNotes2025Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Notes, 2025 [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertibleNotes2025Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2025 Convertible Notes</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_ConvertibleNotes2025Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2025 convertible notes</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_NineConvertibleNoteAgreementsMember" xlink:label="cntm_NineConvertibleNoteAgreementsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_NineConvertibleNoteAgreementsMember" xlink:to="cntm_NineConvertibleNoteAgreementsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_NineConvertibleNoteAgreementsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the member information pertaining to nine convertible note agreements.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_NineConvertibleNoteAgreementsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Nine Convertible Note Agreements [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_NineConvertibleNoteAgreementsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Nine Convertible Note Agreements</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_EighteenConvertibleNoteAgreementsMember" xlink:label="cntm_EighteenConvertibleNoteAgreementsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_EighteenConvertibleNoteAgreementsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the member information pertaining to eighteen convertible note agreements.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_EighteenConvertibleNoteAgreementsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Eighteen Convertible Note Agreements [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_EighteenConvertibleNoteAgreementsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Eighteen Convertible Note Agreements</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_StandbyEquityPurchaseAgreementMember" xlink:label="cntm_StandbyEquityPurchaseAgreementMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_StandbyEquityPurchaseAgreementMember" xlink:to="cntm_StandbyEquityPurchaseAgreementMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_StandbyEquityPurchaseAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to standby equity purchase agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_StandbyEquityPurchaseAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Standby Equity Purchase Agreement [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_StandbyEquityPurchaseAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Standby equity purchase agreement</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueByMeasurementBasisAxis" xlink:label="us-gaap_FairValueByMeasurementBasisAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueByMeasurementBasisAxis" xlink:to="us-gaap_FairValueByMeasurementBasisAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueByMeasurementBasisAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement Basis [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:label="us-gaap_PortionAtFairValueFairValueDisclosureMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:to="us-gaap_PortionAtFairValueFairValueDisclosureMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PortionAtFairValueFairValueDisclosureMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Portion at Fair Value Measurement [Member]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:label="us-gaap_CarryingReportedAmountFairValueDisclosureMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:to="us-gaap_CarryingReportedAmountFairValueDisclosureMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CarryingReportedAmountFairValueDisclosureMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Reported Value Measurement [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CarryingReportedAmountFairValueDisclosureMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Carrying Amount</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EstimateOfFairValueFairValueDisclosureMember" xlink:label="us-gaap_EstimateOfFairValueFairValueDisclosureMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EstimateOfFairValueFairValueDisclosureMember" xlink:to="us-gaap_EstimateOfFairValueFairValueDisclosureMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EstimateOfFairValueFairValueDisclosureMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Estimate of Fair Value Measurement [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_EstimateOfFairValueFairValueDisclosureMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Estimated Fair Value</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_CounterpartyNameAxis" xlink:label="srt_CounterpartyNameAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_CounterpartyNameAxis" xlink:to="srt_CounterpartyNameAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_CounterpartyNameAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Counterparty Name [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_RepurchaseAgreementCounterpartyNameDomain" xlink:label="srt_RepurchaseAgreementCounterpartyNameDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_RepurchaseAgreementCounterpartyNameDomain" xlink:to="srt_RepurchaseAgreementCounterpartyNameDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_RepurchaseAgreementCounterpartyNameDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Counterparty Name [Domain]</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_YaIiPnLimitedMember" xlink:label="cntm_YaIiPnLimitedMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_YaIiPnLimitedMember" xlink:to="cntm_YaIiPnLimitedMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_YaIiPnLimitedMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to YA II PN, Limited ("Yorkville").</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_YaIiPnLimitedMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">YA II PN, Limited [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_YaIiPnLimitedMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Yorkville</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_VanquishAndLabrysMember" xlink:label="cntm_VanquishAndLabrysMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_VanquishAndLabrysMember" xlink:to="cntm_VanquishAndLabrysMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_VanquishAndLabrysMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to Vanquish and Labrys.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_VanquishAndLabrysMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Vanquish and Labrys [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_VanquishAndLabrysMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Vanquish and Labrys</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_OtherPartiesMember" xlink:label="cntm_OtherPartiesMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_OtherPartiesMember" xlink:to="cntm_OtherPartiesMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_OtherPartiesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to other parties.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_OtherPartiesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other Parties [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_OtherPartiesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other parties</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DebtInstrumentConvertibleNumber" xlink:label="cntm_DebtInstrumentConvertibleNumber" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentConvertibleNumber" xlink:to="cntm_DebtInstrumentConvertibleNumber_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentConvertibleNumber_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The number of convertible debt notes issued by the entity during the reporting period.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentConvertibleNumber_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Convertible, Number</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentConvertibleNumber_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of individuals issued</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:label="us-gaap_DebtInstrumentInterestRateStatedPercentage" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:to="us-gaap_DebtInstrumentInterestRateStatedPercentage_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentInterestRateStatedPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Interest Rate, Stated Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DebtInstrumentInterestRateStatedPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest rate (in percentage)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_DebtInstrumentInterestRateStatedPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest rate (in percent)</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DebtInstrumentConvertibleOptionalConversionTerm" xlink:label="cntm_DebtInstrumentConvertibleOptionalConversionTerm" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentConvertibleOptionalConversionTerm" xlink:to="cntm_DebtInstrumentConvertibleOptionalConversionTerm_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentConvertibleOptionalConversionTerm_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the optional conversion period for notes payable.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentConvertibleOptionalConversionTerm_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Convertible, Optional Conversion Term</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentConvertibleOptionalConversionTerm_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Optional conversion period</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentConvertibleConversionPrice1" xlink:label="us-gaap_DebtInstrumentConvertibleConversionPrice1" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentConvertibleConversionPrice1" xlink:to="us-gaap_DebtInstrumentConvertibleConversionPrice1_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentConvertibleConversionPrice1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Convertible, Conversion Price</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DebtInstrumentConvertibleConversionPrice1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt instrument convertible conversion price</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_DebtInstrumentConvertibleConversionPrice1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Conversion Price (in dollars per share)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ExtinguishmentOfDebtAmount" xlink:label="us-gaap_ExtinguishmentOfDebtAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ExtinguishmentOfDebtAmount" xlink:to="us-gaap_ExtinguishmentOfDebtAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ExtinguishmentOfDebtAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Extinguishment of Debt, Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ExtinguishmentOfDebtAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Extinguishment of debt</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtConversionConvertedInstrumentSharesIssued1" xlink:label="us-gaap_DebtConversionConvertedInstrumentSharesIssued1" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtConversionConvertedInstrumentSharesIssued1" xlink:to="us-gaap_DebtConversionConvertedInstrumentSharesIssued1_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtConversionConvertedInstrumentSharesIssued1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Conversion, Converted Instrument, Shares Issued</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DebtConversionConvertedInstrumentSharesIssued1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Conversion of debt to shares</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConvertibleDebtFairValueDisclosures" xlink:label="us-gaap_ConvertibleDebtFairValueDisclosures" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ConvertibleDebtFairValueDisclosures" xlink:to="us-gaap_ConvertibleDebtFairValueDisclosures_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ConvertibleDebtFairValueDisclosures_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Debt, Fair Value Disclosures</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:label="us-gaap_ConvertibleDebtFairValueDisclosures_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total fair value of Pre-Paid Advance Obligation</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ConvertibleDebtFairValueDisclosures_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible debt</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConvertibleNotesPayable" xlink:label="us-gaap_ConvertibleNotesPayable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ConvertibleNotesPayable" xlink:to="us-gaap_ConvertibleNotesPayable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ConvertibleNotesPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Notes Payable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ConvertibleNotesPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible notes payable</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DebtInstrumentConvertibleSharesIssuable" xlink:label="cntm_DebtInstrumentConvertibleSharesIssuable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentConvertibleSharesIssuable" xlink:to="cntm_DebtInstrumentConvertibleSharesIssuable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentConvertibleSharesIssuable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of shares issuable to the holder of the debt instrument if the debt was converted into equity.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentConvertibleSharesIssuable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Convertible, Shares Issuable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentConvertibleSharesIssuable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common stock convertible notes</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromNotesPayable" xlink:label="us-gaap_ProceedsFromNotesPayable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ProceedsFromNotesPayable" xlink:to="us-gaap_ProceedsFromNotesPayable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ProceedsFromNotesPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from Notes Payable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_ProceedsFromNotesPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gross proceeds</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_ProceedsFromNotesPayableNet" xlink:label="cntm_ProceedsFromNotesPayableNet" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ProceedsFromNotesPayableNet" xlink:to="cntm_ProceedsFromNotesPayableNet_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ProceedsFromNotesPayableNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The net cash inflow after reduction of issuance and financing costs, from a borrowing supported by a written promise to pay an obligation.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ProceedsFromNotesPayableNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds From Notes Payable, Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ProceedsFromNotesPayableNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from notes payable net</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DebtInstrumentOriginalIssueDiscountPercentage" xlink:label="cntm_DebtInstrumentOriginalIssueDiscountPercentage" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentOriginalIssueDiscountPercentage" xlink:to="cntm_DebtInstrumentOriginalIssueDiscountPercentage_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentOriginalIssueDiscountPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The percentage rate of the original issue discount on the debt instrument.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentOriginalIssueDiscountPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Original Issue Discount, Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentOriginalIssueDiscountPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage rate of the original issue discount</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_RepaymentOfPrincipalAmountOfDebt" xlink:label="cntm_RepaymentOfPrincipalAmountOfDebt" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_RepaymentOfPrincipalAmountOfDebt" xlink:to="cntm_RepaymentOfPrincipalAmountOfDebt_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_RepaymentOfPrincipalAmountOfDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of cash outflow associated with repayment of principal amount of debt.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_RepaymentOfPrincipalAmountOfDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Repayment Of Principal Amount Of Debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_RepaymentOfPrincipalAmountOfDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Repayment of principal amount of debt</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_RepaymentsOfInterestPaidNet" xlink:label="cntm_RepaymentsOfInterestPaidNet" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_RepaymentsOfInterestPaidNet" xlink:to="cntm_RepaymentsOfInterestPaidNet_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_RepaymentsOfInterestPaidNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of cash paid for interest</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_RepaymentsOfInterestPaidNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Repayments Of Interest Paid Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_RepaymentsOfInterestPaidNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash paid for interest</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsOfDebtExtinguishmentCosts" xlink:label="us-gaap_PaymentsOfDebtExtinguishmentCosts" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PaymentsOfDebtExtinguishmentCosts" xlink:to="us-gaap_PaymentsOfDebtExtinguishmentCosts_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PaymentsOfDebtExtinguishmentCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payment for Debt Extinguishment or Debt Prepayment Cost</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PaymentsOfDebtExtinguishmentCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash payment</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DebtConversionOriginalDebtPrincipalAmount" xlink:label="cntm_DebtConversionOriginalDebtPrincipalAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtConversionOriginalDebtPrincipalAmount" xlink:to="cntm_DebtConversionOriginalDebtPrincipalAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtConversionOriginalDebtPrincipalAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Principal amount of original debt converted during the period.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtConversionOriginalDebtPrincipalAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Conversion, Original Debt, Principal, Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtConversionOriginalDebtPrincipalAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Original debt, principal</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DebtConversionOriginalDebtAccruedInterestAmount" xlink:label="cntm_DebtConversionOriginalDebtAccruedInterestAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtConversionOriginalDebtAccruedInterestAmount" xlink:to="cntm_DebtConversionOriginalDebtAccruedInterestAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtConversionOriginalDebtAccruedInterestAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accrued interest amount of original debt converted during the period.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtConversionOriginalDebtAccruedInterestAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Conversion, Original Debt, Accrued Interest, Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtConversionOriginalDebtAccruedInterestAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Original debt, accrued interest</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentConvertibleStockPriceTrigger" xlink:label="us-gaap_DebtInstrumentConvertibleStockPriceTrigger" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentConvertibleStockPriceTrigger" xlink:to="us-gaap_DebtInstrumentConvertibleStockPriceTrigger_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentConvertibleStockPriceTrigger_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Convertible, Stock Price Trigger</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DebtInstrumentConvertibleStockPriceTrigger_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">SEPA Convertible Note, variable price (in $ per share)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NotesPayable" xlink:label="us-gaap_NotesPayable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NotesPayable" xlink:to="us-gaap_NotesPayable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NotesPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Notes Payable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NotesPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_NotesPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Carrying value</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_ConvertibleNotes2026IssuanceOneMember" xlink:label="cntm_ConvertibleNotes2026IssuanceOneMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertibleNotes2026IssuanceOneMember" xlink:to="cntm_ConvertibleNotes2026IssuanceOneMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertibleNotes2026IssuanceOneMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to first issuance of convertible notes 2026.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertibleNotes2026IssuanceOneMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Notes 2026, Issuance One [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertibleNotes2026IssuanceOneMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">1/1/2026</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_ConvertibleNotes2026IssuanceTwoMember" xlink:label="cntm_ConvertibleNotes2026IssuanceTwoMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertibleNotes2026IssuanceTwoMember" xlink:to="cntm_ConvertibleNotes2026IssuanceTwoMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertibleNotes2026IssuanceTwoMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to second issuance of convertible notes 2026.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertibleNotes2026IssuanceTwoMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Notes 2026, Issuance Two [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertibleNotes2026IssuanceTwoMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">1/7/2026</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_ConvertibleNotes2026IssuanceThreeMember" xlink:label="cntm_ConvertibleNotes2026IssuanceThreeMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertibleNotes2026IssuanceThreeMember" xlink:to="cntm_ConvertibleNotes2026IssuanceThreeMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertibleNotes2026IssuanceThreeMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to third issuance of convertible notes 2026.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertibleNotes2026IssuanceThreeMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Notes 2026, Issuance Three [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertibleNotes2026IssuanceThreeMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">1/13/2026</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_ConvertibleNotes2026IssuanceFourMember" xlink:label="cntm_ConvertibleNotes2026IssuanceFourMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertibleNotes2026IssuanceFourMember" xlink:to="cntm_ConvertibleNotes2026IssuanceFourMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertibleNotes2026IssuanceFourMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to fourth issuance of convertible notes 2026.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertibleNotes2026IssuanceFourMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Notes 2026, Issuance Four [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertibleNotes2026IssuanceFourMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">1/14/2026</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_ConvertibleNotes2026IssuanceFiveMember" xlink:label="cntm_ConvertibleNotes2026IssuanceFiveMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertibleNotes2026IssuanceFiveMember" xlink:to="cntm_ConvertibleNotes2026IssuanceFiveMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertibleNotes2026IssuanceFiveMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to fifth issuance of convertible notes 2026.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertibleNotes2026IssuanceFiveMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Notes 2026, Issuance Five [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertibleNotes2026IssuanceFiveMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">1/20/2026</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_ConvertibleNotes2026IssuanceSixMember" xlink:label="cntm_ConvertibleNotes2026IssuanceSixMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertibleNotes2026IssuanceSixMember" xlink:to="cntm_ConvertibleNotes2026IssuanceSixMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertibleNotes2026IssuanceSixMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to sixth issuance of convertible notes 2026.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertibleNotes2026IssuanceSixMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Notes 2026, Issuance Six [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertibleNotes2026IssuanceSixMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">1/22/2026</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_ConvertibleNotes2026IssuanceSevenMember" xlink:label="cntm_ConvertibleNotes2026IssuanceSevenMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertibleNotes2026IssuanceSevenMember" xlink:to="cntm_ConvertibleNotes2026IssuanceSevenMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertibleNotes2026IssuanceSevenMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to seventh issuance of convertible notes 2026.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertibleNotes2026IssuanceSevenMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Notes 2026, Issuance Seven [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertibleNotes2026IssuanceSevenMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">1/27/2026</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_ConvertibleNotes2026IssuanceEightMember" xlink:label="cntm_ConvertibleNotes2026IssuanceEightMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertibleNotes2026IssuanceEightMember" xlink:to="cntm_ConvertibleNotes2026IssuanceEightMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertibleNotes2026IssuanceEightMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to eighth issuance of convertible notes 2026.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertibleNotes2026IssuanceEightMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Notes 2026, Issuance Eight [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertibleNotes2026IssuanceEightMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2/12/2026</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_ConvertibleNotes2026IssuanceNineMember" xlink:label="cntm_ConvertibleNotes2026IssuanceNineMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertibleNotes2026IssuanceNineMember" xlink:to="cntm_ConvertibleNotes2026IssuanceNineMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertibleNotes2026IssuanceNineMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to nineth issuance of convertible notes 2026.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertibleNotes2026IssuanceNineMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Notes 2026, Issuance Nine [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertibleNotes2026IssuanceNineMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">3/30/2026</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_ConvertibleNotes2026IssuanceTenMember" xlink:label="cntm_ConvertibleNotes2026IssuanceTenMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertibleNotes2026IssuanceTenMember" xlink:to="cntm_ConvertibleNotes2026IssuanceTenMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertibleNotes2026IssuanceTenMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to tenth issuance of convertible notes 2026.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertibleNotes2026IssuanceTenMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Notes 2026, Issuance Ten [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertibleNotes2026IssuanceTenMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">4/2/2026</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_ConvertibleNotes2026IssuanceElevenMember" xlink:label="cntm_ConvertibleNotes2026IssuanceElevenMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertibleNotes2026IssuanceElevenMember" xlink:to="cntm_ConvertibleNotes2026IssuanceElevenMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertibleNotes2026IssuanceElevenMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to eleventh issuance of convertible notes 2026.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertibleNotes2026IssuanceElevenMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Notes 2026, Issuance Eleven [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertibleNotes2026IssuanceElevenMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">4/2/2026</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_ConvertibleNotes2026IssuanceTwelveMember" xlink:label="cntm_ConvertibleNotes2026IssuanceTwelveMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertibleNotes2026IssuanceTwelveMember" xlink:to="cntm_ConvertibleNotes2026IssuanceTwelveMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertibleNotes2026IssuanceTwelveMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to twelfth issuance of convertible notes 2026.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertibleNotes2026IssuanceTwelveMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Notes 2026, Issuance Twelve [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertibleNotes2026IssuanceTwelveMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">4/2/2026</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_ConvertibleNotes2026IssuanceThirteenMember" xlink:label="cntm_ConvertibleNotes2026IssuanceThirteenMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertibleNotes2026IssuanceThirteenMember" xlink:to="cntm_ConvertibleNotes2026IssuanceThirteenMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertibleNotes2026IssuanceThirteenMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to thirteenth issuance of convertible notes 2026.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertibleNotes2026IssuanceThirteenMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Notes 2026, Issuance Thirteen [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertibleNotes2026IssuanceThirteenMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">4/8/2026</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_ConvertibleNotes2026IssuanceFourteenMember" xlink:label="cntm_ConvertibleNotes2026IssuanceFourteenMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertibleNotes2026IssuanceFourteenMember" xlink:to="cntm_ConvertibleNotes2026IssuanceFourteenMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertibleNotes2026IssuanceFourteenMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to fourteenth issuance of convertible notes 2026.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertibleNotes2026IssuanceFourteenMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Notes 2026, Issuance Fourteen [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertibleNotes2026IssuanceFourteenMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">4/20/2026</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_ConvertibleNotes2026IssuanceFifteenMember" xlink:label="cntm_ConvertibleNotes2026IssuanceFifteenMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertibleNotes2026IssuanceFifteenMember" xlink:to="cntm_ConvertibleNotes2026IssuanceFifteenMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertibleNotes2026IssuanceFifteenMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to fifteenth issuance of convertible notes 2026.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertibleNotes2026IssuanceFifteenMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Notes 2026, Issuance Fifteen [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertibleNotes2026IssuanceFifteenMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">4/27/2026</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_ConvertibleNotes2026IssuanceSixteenMember" xlink:label="cntm_ConvertibleNotes2026IssuanceSixteenMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertibleNotes2026IssuanceSixteenMember" xlink:to="cntm_ConvertibleNotes2026IssuanceSixteenMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertibleNotes2026IssuanceSixteenMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to sixteenth issuance of convertible notes 2026.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertibleNotes2026IssuanceSixteenMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Notes 2026, Issuance Sixteen [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertibleNotes2026IssuanceSixteenMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">6/1/2026</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_ConvertibleNotes2026IssuanceSeventeenMember" xlink:label="cntm_ConvertibleNotes2026IssuanceSeventeenMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertibleNotes2026IssuanceSeventeenMember" xlink:to="cntm_ConvertibleNotes2026IssuanceSeventeenMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertibleNotes2026IssuanceSeventeenMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to seventeenth issuance of convertible notes 2026.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertibleNotes2026IssuanceSeventeenMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Notes 2026, Issuance Seventeen [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertibleNotes2026IssuanceSeventeenMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">6/9/2026</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_ConvertibleNotes2026IssuanceEighteenMember" xlink:label="cntm_ConvertibleNotes2026IssuanceEighteenMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertibleNotes2026IssuanceEighteenMember" xlink:to="cntm_ConvertibleNotes2026IssuanceEighteenMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertibleNotes2026IssuanceEighteenMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to eighteenth issuance of convertible notes 2026.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertibleNotes2026IssuanceEighteenMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Notes 2026, Issuance Eighteen [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertibleNotes2026IssuanceEighteenMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">6/10/2026</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DebtInstrumentConvertibleTermFromIssuance" xlink:label="cntm_DebtInstrumentConvertibleTermFromIssuance" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentConvertibleTermFromIssuance" xlink:to="cntm_DebtInstrumentConvertibleTermFromIssuance_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentConvertibleTermFromIssuance_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the term for conversion of debt instrument.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentConvertibleTermFromIssuance_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Convertible, Term from Issuance</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_DebtInstrumentConvertibleTermFromIssuance_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Conversion Option Period of Exercisability (from issuance date)</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_ConvertibleNoteConversionNumberOfTradingDays" xlink:label="cntm_ConvertibleNoteConversionNumberOfTradingDays" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertibleNoteConversionNumberOfTradingDays" xlink:to="cntm_ConvertibleNoteConversionNumberOfTradingDays_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertibleNoteConversionNumberOfTradingDays_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of trading days preceding which conversion of convertible note into common shares is calculated at volume weighted average price.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertibleNoteConversionNumberOfTradingDays_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Note, Conversion, Number of Trading Days</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertibleNoteConversionNumberOfTradingDays_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of trading days</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_SecuredPromissoryNoteMember" xlink:label="cntm_SecuredPromissoryNoteMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_SecuredPromissoryNoteMember" xlink:to="cntm_SecuredPromissoryNoteMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_SecuredPromissoryNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to secured promissory notes.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_SecuredPromissoryNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Secured Promissory Note [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_SecuredPromissoryNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Secured Promissory Notes</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_SmalBusinessAdministrationLoansMember" xlink:label="cntm_SmalBusinessAdministrationLoansMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_SmalBusinessAdministrationLoansMember" xlink:to="cntm_SmalBusinessAdministrationLoansMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_SmalBusinessAdministrationLoansMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to small business administration loans.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_SmalBusinessAdministrationLoansMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Smal Business Administration Loans [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_SmalBusinessAdministrationLoansMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Small Business Administration Loans</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NotesPayableOtherPayablesMember" xlink:label="us-gaap_NotesPayableOtherPayablesMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NotesPayableOtherPayablesMember" xlink:to="us-gaap_NotesPayableOtherPayablesMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NotesPayableOtherPayablesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Notes Payable, Other Payables [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NotesPayableOtherPayablesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Promissory Note</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_VehicleNotesMember" xlink:label="cntm_VehicleNotesMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_VehicleNotesMember" xlink:to="cntm_VehicleNotesMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_VehicleNotesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to vehicle notes.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_VehicleNotesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Vehicle Notes [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_VehicleNotesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Vehicle Notes</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_SellerNotesMember" xlink:label="cntm_SellerNotesMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_SellerNotesMember" xlink:to="cntm_SellerNotesMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_SellerNotesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information relating to seller notes.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_SellerNotesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Seller Notes [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_SellerNotesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Seller Notes</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_RealEstatePromissoryNoteMember" xlink:label="cntm_RealEstatePromissoryNoteMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_RealEstatePromissoryNoteMember" xlink:to="cntm_RealEstatePromissoryNoteMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_RealEstatePromissoryNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to real estate promissory note.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_RealEstatePromissoryNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Real Estate Promissory Note [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_RealEstatePromissoryNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Real Estate Promissory Note</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_BusinessLoanAndSecurityAgreementMember" xlink:label="cntm_BusinessLoanAndSecurityAgreementMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_BusinessLoanAndSecurityAgreementMember" xlink:to="cntm_BusinessLoanAndSecurityAgreementMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_BusinessLoanAndSecurityAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to business loan and security agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_BusinessLoanAndSecurityAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Loan And Security Agreement [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_BusinessLoanAndSecurityAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Loan and Security Agreement</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_SaleOfFutureReceiptsMember" xlink:label="cntm_SaleOfFutureReceiptsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_SaleOfFutureReceiptsMember" xlink:to="cntm_SaleOfFutureReceiptsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_SaleOfFutureReceiptsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information relating to the sale of future receipts.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_SaleOfFutureReceiptsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Sale Of Future Receipts [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_SaleOfFutureReceiptsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Sale of Future Receipts</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_PurchaseOrderFinancingMember" xlink:label="cntm_PurchaseOrderFinancingMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_PurchaseOrderFinancingMember" xlink:to="cntm_PurchaseOrderFinancingMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_PurchaseOrderFinancingMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to purchase order financing.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_PurchaseOrderFinancingMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Purchase Order Financing [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_PurchaseOrderFinancingMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Purchase Order Financing</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_SaleOfFutureReceiptsLibertasMember" xlink:label="cntm_SaleOfFutureReceiptsLibertasMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_SaleOfFutureReceiptsLibertasMember" xlink:to="cntm_SaleOfFutureReceiptsLibertasMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_SaleOfFutureReceiptsLibertasMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to sale of future receipts - Libertas.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_SaleOfFutureReceiptsLibertasMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Sale of Future Receipts - Libertas [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_SaleOfFutureReceiptsLibertasMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Notes Payable</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentUnamortizedDiscountPremiumAndDebtIssuanceCostsNet" xlink:label="us-gaap_DebtInstrumentUnamortizedDiscountPremiumAndDebtIssuanceCostsNet" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentUnamortizedDiscountPremiumAndDebtIssuanceCostsNet" xlink:to="us-gaap_DebtInstrumentUnamortizedDiscountPremiumAndDebtIssuanceCostsNet_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentUnamortizedDiscountPremiumAndDebtIssuanceCostsNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Unamortized Discount (Premium) and Debt Issuance Costs, Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_DebtInstrumentUnamortizedDiscountPremiumAndDebtIssuanceCostsNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Less: debt discount and issuance costs</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_NotesPayablesCurrent" xlink:label="cntm_NotesPayablesCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_NotesPayablesCurrent" xlink:to="cntm_NotesPayablesCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_NotesPayablesCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Sum of the carrying values as of the balance sheet date of the portions of long-term notes payable due within one year or the operating cycle if longer.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_NotesPayablesCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Notes Payables, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_NotesPayablesCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Less: notes payable, current portion</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_NotesPayablesNoncurrent" xlink:label="cntm_NotesPayablesNoncurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_NotesPayablesNoncurrent" xlink:to="cntm_NotesPayablesNoncurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_NotesPayablesNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Carrying value as of the balance sheet date of notes payable (with maturities initially due after one year or beyond the operating cycle if longer), excluding current portion.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_NotesPayablesNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Notes Payables, Noncurrent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="cntm_NotesPayablesNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Notes payable, net of debt issuance costs and current portion</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestExpenseDebt" xlink:label="us-gaap_InterestExpenseDebt" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InterestExpenseDebt" xlink:to="us-gaap_InterestExpenseDebt_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_InterestExpenseDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest Expense, Debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_InterestExpenseDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest expense</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_AccruedInterestOnDebt" xlink:label="cntm_AccruedInterestOnDebt" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_AccruedInterestOnDebt" xlink:to="cntm_AccruedInterestOnDebt_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_AccruedInterestOnDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of accrued interest on debt instrument.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_AccruedInterestOnDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accrued Interest On Debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_AccruedInterestOnDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of accrued interest on debt instrument</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_AstrabridgeIncMember" xlink:label="cntm_AstrabridgeIncMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_AstrabridgeIncMember" xlink:to="cntm_AstrabridgeIncMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_AstrabridgeIncMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to AstraBridge Inc.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_AstrabridgeIncMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">AstraBridge Inc [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_AstrabridgeIncMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">AstraBridge Inc.</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ConsolidatedEntitiesAxis" xlink:label="srt_ConsolidatedEntitiesAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_ConsolidatedEntitiesAxis" xlink:to="srt_ConsolidatedEntitiesAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_ConsolidatedEntitiesAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Consolidated Entities [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ConsolidatedEntitiesDomain" xlink:label="srt_ConsolidatedEntitiesDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_ConsolidatedEntitiesDomain" xlink:to="srt_ConsolidatedEntitiesDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_ConsolidatedEntitiesDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Consolidated Entities [Domain]</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DebtInstrumentRedemptionPremiumPercentageOfOriginalPrincipalAmount" xlink:label="cntm_DebtInstrumentRedemptionPremiumPercentageOfOriginalPrincipalAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentRedemptionPremiumPercentageOfOriginalPrincipalAmount" xlink:to="cntm_DebtInstrumentRedemptionPremiumPercentageOfOriginalPrincipalAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentRedemptionPremiumPercentageOfOriginalPrincipalAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Redemption premium as a percentage of original principal amount.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentRedemptionPremiumPercentageOfOriginalPrincipalAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Redemption Premium, Percentage of Original Principal Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentRedemptionPremiumPercentageOfOriginalPrincipalAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Redemption premium as a percentage</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_ExtinguishmentOfDebtSharesIssued" xlink:label="cntm_ExtinguishmentOfDebtSharesIssued" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ExtinguishmentOfDebtSharesIssued" xlink:to="cntm_ExtinguishmentOfDebtSharesIssued_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ExtinguishmentOfDebtSharesIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of shares issued upon extinguishment of debt.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ExtinguishmentOfDebtSharesIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Extinguishment Of Debt, Shares Issued</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ExtinguishmentOfDebtSharesIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of shares issued on debt</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_PercentageOfEquityInterestAcquired" xlink:label="cntm_PercentageOfEquityInterestAcquired" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_PercentageOfEquityInterestAcquired" xlink:to="cntm_PercentageOfEquityInterestAcquired_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_PercentageOfEquityInterestAcquired_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The percentage of equity interest acquired during the period.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_PercentageOfEquityInterestAcquired_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage Of Equity Interest Acquired</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_PercentageOfEquityInterestAcquired_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of equity interest acquired</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentFairValue" xlink:label="us-gaap_DebtInstrumentFairValue" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentFairValue" xlink:to="us-gaap_DebtInstrumentFairValue_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentFairValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Fair Value Disclosure</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DebtInstrumentFairValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt instrument fair value</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_BusinessLoanAndSecurityAgreementJanuary2026Member" xlink:label="cntm_BusinessLoanAndSecurityAgreementJanuary2026Member" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_BusinessLoanAndSecurityAgreementJanuary2026Member" xlink:to="cntm_BusinessLoanAndSecurityAgreementJanuary2026Member_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_BusinessLoanAndSecurityAgreementJanuary2026Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to the January 2026 business loan and security agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_BusinessLoanAndSecurityAgreementJanuary2026Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Loan And Security Agreement, January 2026 [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_BusinessLoanAndSecurityAgreementJanuary2026Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">January 2026 Term Loan</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_BusinessLoanAndSecurityAgreementMarch2026Member" xlink:label="cntm_BusinessLoanAndSecurityAgreementMarch2026Member" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_BusinessLoanAndSecurityAgreementMarch2026Member" xlink:to="cntm_BusinessLoanAndSecurityAgreementMarch2026Member_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_BusinessLoanAndSecurityAgreementMarch2026Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to the March 2026 business loan and security agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_BusinessLoanAndSecurityAgreementMarch2026Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Loan And Security Agreement, March 2026 [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_BusinessLoanAndSecurityAgreementMarch2026Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">March 2026 Term Loan</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DebtInstrumentNumberOfPeriodicPayment" xlink:label="cntm_DebtInstrumentNumberOfPeriodicPayment" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentNumberOfPeriodicPayment" xlink:to="cntm_DebtInstrumentNumberOfPeriodicPayment_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentNumberOfPeriodicPayment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of periodic payment for a debt instrument.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentNumberOfPeriodicPayment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Number of Periodic Payment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentNumberOfPeriodicPayment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of periodic payment</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentPeriodicPayment" xlink:label="us-gaap_DebtInstrumentPeriodicPayment" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentPeriodicPayment" xlink:to="us-gaap_DebtInstrumentPeriodicPayment_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentPeriodicPayment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Periodic Payment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DebtInstrumentPeriodicPayment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Periodic payments</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_DebtInstrumentPeriodicPayment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Bi-weekly payment amount</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DebtInstrumentAggregateOfPrincipalAndInterest" xlink:label="cntm_DebtInstrumentAggregateOfPrincipalAndInterest" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentAggregateOfPrincipalAndInterest" xlink:to="cntm_DebtInstrumentAggregateOfPrincipalAndInterest_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentAggregateOfPrincipalAndInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Aggregate amount of principal and interest of a debt instrument.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentAggregateOfPrincipalAndInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Aggregate Of Principal And Interest</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentAggregateOfPrincipalAndInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Aggregate amount of principal and interest</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LineOfCreditMember" xlink:label="us-gaap_LineOfCreditMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LineOfCreditMember" xlink:to="us-gaap_LineOfCreditMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LineOfCreditMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Line of Credit [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_LineOfCreditMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Line of Credit</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_NumberOfLineOfCredit" xlink:label="cntm_NumberOfLineOfCredit" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_NumberOfLineOfCredit" xlink:to="cntm_NumberOfLineOfCredit_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_NumberOfLineOfCredit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of line of credit facility entered by the entity.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_NumberOfLineOfCredit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number Of Line Of Credit</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_NumberOfLineOfCredit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of line of credit facility entered</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LineOfCredit" xlink:label="us-gaap_LineOfCredit" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LineOfCredit" xlink:to="us-gaap_LineOfCredit_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LineOfCredit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Long-Term Line of Credit</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_LineOfCredit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Outstanding balance</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_FutureReceiptsSoldAndAssignedValue" xlink:label="cntm_FutureReceiptsSoldAndAssignedValue" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FutureReceiptsSoldAndAssignedValue" xlink:to="cntm_FutureReceiptsSoldAndAssignedValue_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FutureReceiptsSoldAndAssignedValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Value of Future Receipts sold and assigned by the company.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FutureReceiptsSoldAndAssignedValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Future Receipts Sold And Assigned Value</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FutureReceiptsSoldAndAssignedValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Company sold and assigned</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_FeeReceivedForFutureReceiptsSoldAndAssigned" xlink:label="cntm_FeeReceivedForFutureReceiptsSoldAndAssigned" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FeeReceivedForFutureReceiptsSoldAndAssigned" xlink:to="cntm_FeeReceivedForFutureReceiptsSoldAndAssigned_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FeeReceivedForFutureReceiptsSoldAndAssigned_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The amount of fees received from Future Receipts sold and assigned, pursuant to an agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FeeReceivedForFutureReceiptsSoldAndAssigned_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fee Received For Future Receipts Sold And Assigned</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FeeReceivedForFutureReceiptsSoldAndAssigned_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fee of future receipts</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_FactoringArrangementPurchaseOrderAndAccountsReceivableFinancingMember" xlink:label="cntm_FactoringArrangementPurchaseOrderAndAccountsReceivableFinancingMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FactoringArrangementPurchaseOrderAndAccountsReceivableFinancingMember" xlink:to="cntm_FactoringArrangementPurchaseOrderAndAccountsReceivableFinancingMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FactoringArrangementPurchaseOrderAndAccountsReceivableFinancingMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining purchase order and accounts receivable financing under factoring and security agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FactoringArrangementPurchaseOrderAndAccountsReceivableFinancingMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Factoring Arrangement, Purchase Order And Accounts Receivable Financing [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FactoringArrangementPurchaseOrderAndAccountsReceivableFinancingMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">PO and AR financing</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_FactoringArrangementPurchaseOrderFinancingMember" xlink:label="cntm_FactoringArrangementPurchaseOrderFinancingMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FactoringArrangementPurchaseOrderFinancingMember" xlink:to="cntm_FactoringArrangementPurchaseOrderFinancingMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FactoringArrangementPurchaseOrderFinancingMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining purchase order financing under factoring and security agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FactoringArrangementPurchaseOrderFinancingMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Factoring Arrangement, Purchase Order Financing [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FactoringArrangementPurchaseOrderFinancingMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">PO financing</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_FactoringArrangementAccountsReceivableFinancingMember" xlink:label="cntm_FactoringArrangementAccountsReceivableFinancingMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FactoringArrangementAccountsReceivableFinancingMember" xlink:to="cntm_FactoringArrangementAccountsReceivableFinancingMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FactoringArrangementAccountsReceivableFinancingMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining accounts receivable financing under factoring and security agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FactoringArrangementAccountsReceivableFinancingMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Factoring Arrangement, Accounts Receivable Financing [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FactoringArrangementAccountsReceivableFinancingMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">AR financing</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_CountyComfortServicesLlcMember" xlink:label="cntm_CountyComfortServicesLlcMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_CountyComfortServicesLlcMember" xlink:to="cntm_CountyComfortServicesLlcMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_CountyComfortServicesLlcMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to County Comfort Services, LLC.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_CountyComfortServicesLlcMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">County Comfort Services, LLC [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_CountyComfortServicesLlcMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">CCS</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_KeenLabsOperationsIncMember" xlink:label="cntm_KeenLabsOperationsIncMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_KeenLabsOperationsIncMember" xlink:to="cntm_KeenLabsOperationsIncMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_KeenLabsOperationsIncMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to Keen Labs Operations Inc.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_KeenLabsOperationsIncMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Keen Labs Operations Inc [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_KeenLabsOperationsIncMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Keen Labs Operations, Inc</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_ChargeAfter30DaysMember" xlink:label="cntm_ChargeAfter30DaysMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ChargeAfter30DaysMember" xlink:to="cntm_ChargeAfter30DaysMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ChargeAfter30DaysMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to a scenario specifying the charge rate for each additional 10 day period after 30 days.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ChargeAfter30DaysMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Charge, After 30 Days [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ChargeAfter30DaysMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">After 30 days</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_ChargeInvoicesOutstandingForMoreThan60DaysMember" xlink:label="cntm_ChargeInvoicesOutstandingForMoreThan60DaysMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ChargeInvoicesOutstandingForMoreThan60DaysMember" xlink:to="cntm_ChargeInvoicesOutstandingForMoreThan60DaysMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ChargeInvoicesOutstandingForMoreThan60DaysMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to a scenario specifying invoices outstanding for more than 60 days.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ChargeInvoicesOutstandingForMoreThan60DaysMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Charge, Invoices Outstanding For More Than 60 Days [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ChargeInvoicesOutstandingForMoreThan60DaysMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Invoice outstanding for more than 60 days</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_FinancingFacilityMaximumBorrowingCapacity" xlink:label="cntm_FinancingFacilityMaximumBorrowingCapacity" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FinancingFacilityMaximumBorrowingCapacity" xlink:to="cntm_FinancingFacilityMaximumBorrowingCapacity_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FinancingFacilityMaximumBorrowingCapacity_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Maximum borrowing capacity under receivable financing facility that could be borrowed by the entity.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FinancingFacilityMaximumBorrowingCapacity_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Financing Facility, Maximum Borrowing Capacity</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FinancingFacilityMaximumBorrowingCapacity_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Maximum borrowing capacity</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_FinancingFacilityMaximumAdvanceAsPercentageOfEligibleReceivables" xlink:label="cntm_FinancingFacilityMaximumAdvanceAsPercentageOfEligibleReceivables" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FinancingFacilityMaximumAdvanceAsPercentageOfEligibleReceivables" xlink:to="cntm_FinancingFacilityMaximumAdvanceAsPercentageOfEligibleReceivables_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FinancingFacilityMaximumAdvanceAsPercentageOfEligibleReceivables_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Maximum percentage of receivables that could be borrowed under the financing facility by the entity.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FinancingFacilityMaximumAdvanceAsPercentageOfEligibleReceivables_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Financing Facility, Maximum Advance As Percentage Of Eligible Receivables</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FinancingFacilityMaximumAdvanceAsPercentageOfEligibleReceivables_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Maximum advance on eligible receivables, percentage</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_FinancingFacilityThresholdPeriodPostInvoiceDateConsideredForEligibleReceivables" xlink:label="cntm_FinancingFacilityThresholdPeriodPostInvoiceDateConsideredForEligibleReceivables" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FinancingFacilityThresholdPeriodPostInvoiceDateConsideredForEligibleReceivables" xlink:to="cntm_FinancingFacilityThresholdPeriodPostInvoiceDateConsideredForEligibleReceivables_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FinancingFacilityThresholdPeriodPostInvoiceDateConsideredForEligibleReceivables_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Threshold period post invoice date is considered for determination of eligible receivables for advance under financing facility expressed in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FinancingFacilityThresholdPeriodPostInvoiceDateConsideredForEligibleReceivables_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Financing Facility, Threshold Period Post Invoice Date Considered For Eligible Receivables</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FinancingFacilityThresholdPeriodPostInvoiceDateConsideredForEligibleReceivables_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Eligible receivables, threshold number of days post invoice</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_FinancingFacilityBaseChargeRatePercentage" xlink:label="cntm_FinancingFacilityBaseChargeRatePercentage" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FinancingFacilityBaseChargeRatePercentage" xlink:to="cntm_FinancingFacilityBaseChargeRatePercentage_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FinancingFacilityBaseChargeRatePercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Base charge rate for funds borrowed under financing facility.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FinancingFacilityBaseChargeRatePercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Financing Facility, Base Charge Rate, Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FinancingFacilityBaseChargeRatePercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Base charge rate</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_FinancingFacilityBaseChargeRateInitialTerm" xlink:label="cntm_FinancingFacilityBaseChargeRateInitialTerm" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FinancingFacilityBaseChargeRateInitialTerm" xlink:to="cntm_FinancingFacilityBaseChargeRateInitialTerm_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FinancingFacilityBaseChargeRateInitialTerm_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Period considered for base charge rate under the financing facility expressed in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FinancingFacilityBaseChargeRateInitialTerm_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Financing Facility, Base Charge Rate, Initial Term</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FinancingFacilityBaseChargeRateInitialTerm_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Base charge rate, initial term</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_FinancingFacilityAdditionalChargeRatePercentage" xlink:label="cntm_FinancingFacilityAdditionalChargeRatePercentage" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FinancingFacilityAdditionalChargeRatePercentage" xlink:to="cntm_FinancingFacilityAdditionalChargeRatePercentage_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FinancingFacilityAdditionalChargeRatePercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Additional charge rate over the base rate for funds borrowed and outstanding after initial term under the financing facility.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FinancingFacilityAdditionalChargeRatePercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Financing Facility, Additional Charge Rate, Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FinancingFacilityAdditionalChargeRatePercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Additional charge rate</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_FinancingFacilityAdditionalChargeRateThresholdAdditionalPeriod" xlink:label="cntm_FinancingFacilityAdditionalChargeRateThresholdAdditionalPeriod" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FinancingFacilityAdditionalChargeRateThresholdAdditionalPeriod" xlink:to="cntm_FinancingFacilityAdditionalChargeRateThresholdAdditionalPeriod_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FinancingFacilityAdditionalChargeRateThresholdAdditionalPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Threshold each additional period considered in the determination of additional charge rate under the financing facility expressed in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FinancingFacilityAdditionalChargeRateThresholdAdditionalPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Financing Facility, Additional Charge Rate, Threshold Additional Period</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FinancingFacilityAdditionalChargeRateThresholdAdditionalPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Additional charge rate, each additional period</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_FinancingFacilityOutstandingMinimumPastDuePeriod" xlink:label="cntm_FinancingFacilityOutstandingMinimumPastDuePeriod" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FinancingFacilityOutstandingMinimumPastDuePeriod" xlink:to="cntm_FinancingFacilityOutstandingMinimumPastDuePeriod_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FinancingFacilityOutstandingMinimumPastDuePeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Aged invoices minimum past due period taken for determination of additional charge under financing facility, expressed in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FinancingFacilityOutstandingMinimumPastDuePeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Financing Facility, Outstanding, Minimum Past Due Period</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FinancingFacilityOutstandingMinimumPastDuePeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Minimum past due period</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_FinancingFacilityMinimumAdditionalFeesPerInvoice" xlink:label="cntm_FinancingFacilityMinimumAdditionalFeesPerInvoice" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FinancingFacilityMinimumAdditionalFeesPerInvoice" xlink:to="cntm_FinancingFacilityMinimumAdditionalFeesPerInvoice_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FinancingFacilityMinimumAdditionalFeesPerInvoice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Minimum additional fee charged per invoice for aged receivables under the financing facility.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FinancingFacilityMinimumAdditionalFeesPerInvoice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Financing Facility, Minimum Additional Fees Per Invoice</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FinancingFacilityMinimumAdditionalFeesPerInvoice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Minimum additional fee per invoice</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_FinancingFacilityBaseChargeRateThresholdEachPeriodPostDisbursementTillVerification" xlink:label="cntm_FinancingFacilityBaseChargeRateThresholdEachPeriodPostDisbursementTillVerification" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FinancingFacilityBaseChargeRateThresholdEachPeriodPostDisbursementTillVerification" xlink:to="cntm_FinancingFacilityBaseChargeRateThresholdEachPeriodPostDisbursementTillVerification_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FinancingFacilityBaseChargeRateThresholdEachPeriodPostDisbursementTillVerification_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Threshold each period considered in the determination of base charge rate under the financing facility expressed in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FinancingFacilityBaseChargeRateThresholdEachPeriodPostDisbursementTillVerification_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Financing Facility, Base Charge Rate, Threshold Each Period Post Disbursement Till Verification</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FinancingFacilityBaseChargeRateThresholdEachPeriodPostDisbursementTillVerification_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Base charge rate, threshold period post invoice</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_FinancingFacilityTerm" xlink:label="cntm_FinancingFacilityTerm" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FinancingFacilityTerm" xlink:to="cntm_FinancingFacilityTerm_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FinancingFacilityTerm_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Term for which the financing facility agreement been entered expressed in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FinancingFacilityTerm_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Financing Facility, Term</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FinancingFacilityTerm_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Term</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_FinancingFacilityMinimumAnnualVolumeRequirementAsPercentageOfFacility" xlink:label="cntm_FinancingFacilityMinimumAnnualVolumeRequirementAsPercentageOfFacility" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FinancingFacilityMinimumAnnualVolumeRequirementAsPercentageOfFacility" xlink:to="cntm_FinancingFacilityMinimumAnnualVolumeRequirementAsPercentageOfFacility_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FinancingFacilityMinimumAnnualVolumeRequirementAsPercentageOfFacility_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Minimum annual volume requirement expressed as percentage of facility.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FinancingFacilityMinimumAnnualVolumeRequirementAsPercentageOfFacility_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Financing Facility, Minimum Annual Volume Requirement As Percentage Of Facility</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FinancingFacilityMinimumAnnualVolumeRequirementAsPercentageOfFacility_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Minimum annual volume requirement, percentage</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_ProceedsFromFinancingFacility" xlink:label="cntm_ProceedsFromFinancingFacility" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ProceedsFromFinancingFacility" xlink:to="cntm_ProceedsFromFinancingFacility_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ProceedsFromFinancingFacility_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of cash inflow from the financing facility.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ProceedsFromFinancingFacility_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds From Financing Facility</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ProceedsFromFinancingFacility_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Advance received</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_NumberOfPurchaseOrdersFinanced" xlink:label="cntm_NumberOfPurchaseOrdersFinanced" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_NumberOfPurchaseOrdersFinanced" xlink:to="cntm_NumberOfPurchaseOrdersFinanced_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_NumberOfPurchaseOrdersFinanced_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of purchase orders financed.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_NumberOfPurchaseOrdersFinanced_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number Of Purchase Orders Financed</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_NumberOfPurchaseOrdersFinanced_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of purchase orders financed</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:to="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Recurring and Nonrecurring [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueByMeasurementFrequencyAxis" xlink:label="us-gaap_FairValueByMeasurementFrequencyAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueByMeasurementFrequencyAxis" xlink:to="us-gaap_FairValueByMeasurementFrequencyAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueByMeasurementFrequencyAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement Frequency [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueMeasurementFrequencyDomain" xlink:label="us-gaap_FairValueMeasurementFrequencyDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueMeasurementFrequencyDomain" xlink:to="us-gaap_FairValueMeasurementFrequencyDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueMeasurementFrequencyDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement Frequency [Domain]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueMeasurementsRecurringMember" xlink:label="us-gaap_FairValueMeasurementsRecurringMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueMeasurementsRecurringMember" xlink:to="us-gaap_FairValueMeasurementsRecurringMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueMeasurementsRecurringMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Recurring [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FairValueMeasurementsRecurringMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Recurring</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:label="us-gaap_FairValueByFairValueHierarchyLevelAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:to="us-gaap_FairValueByFairValueHierarchyLevelAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueByFairValueHierarchyLevelAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value Hierarchy and NAV [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:label="us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:to="us-gaap_FairValueMeasurementsFairValueHierarchyDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueMeasurementsFairValueHierarchyDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value Hierarchy and NAV [Domain]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueInputsLevel1Member" xlink:label="us-gaap_FairValueInputsLevel1Member" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueInputsLevel1Member" xlink:to="us-gaap_FairValueInputsLevel1Member_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueInputsLevel1Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Inputs, Level 1 [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FairValueInputsLevel1Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Level 1</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueInputsLevel3Member" xlink:label="us-gaap_FairValueInputsLevel3Member" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueInputsLevel3Member" xlink:to="us-gaap_FairValueInputsLevel3Member_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueInputsLevel3Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Inputs, Level 3 [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FairValueInputsLevel3Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Level 3</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:to="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">FAIR VALUE MEASUREMENTS</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetsFairValueDisclosureAbstract" xlink:label="us-gaap_AssetsFairValueDisclosureAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetsFairValueDisclosureAbstract" xlink:to="us-gaap_AssetsFairValueDisclosureAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AssetsFairValueDisclosureAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Assets</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetsFairValueDisclosure" xlink:label="us-gaap_AssetsFairValueDisclosure" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetsFairValueDisclosure" xlink:to="us-gaap_AssetsFairValueDisclosure_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AssetsFairValueDisclosure_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Assets, Fair Value Disclosure</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_AssetsFairValueDisclosure_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total assets</label>
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    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LiabilitiesFairValueDisclosureAbstract" xlink:to="us-gaap_LiabilitiesFairValueDisclosureAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LiabilitiesFairValueDisclosureAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Liabilities, Fair Value Disclosure [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LiabilitiesFairValueDisclosureAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Liabilities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeLiabilities" xlink:label="us-gaap_DerivativeLiabilities" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DerivativeLiabilities" xlink:to="us-gaap_DerivativeLiabilities_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DerivativeLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative Liability</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DerivativeLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative liabilities</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_BusinessCombinationContingentConsiderationLiabilityFairValueDisclosure" xlink:label="cntm_BusinessCombinationContingentConsiderationLiabilityFairValueDisclosure" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_BusinessCombinationContingentConsiderationLiabilityFairValueDisclosure" xlink:to="cntm_BusinessCombinationContingentConsiderationLiabilityFairValueDisclosure_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_BusinessCombinationContingentConsiderationLiabilityFairValueDisclosure_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Contingent Consideration, Liability, Fair Value Disclosure</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_BusinessCombinationContingentConsiderationLiabilityFairValueDisclosure_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contingent consideration</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesFairValueDisclosure" xlink:label="us-gaap_LiabilitiesFairValueDisclosure" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LiabilitiesFairValueDisclosure" xlink:to="us-gaap_LiabilitiesFairValueDisclosure_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LiabilitiesFairValueDisclosure_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Liabilities, Fair Value Disclosure</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_LiabilitiesFairValueDisclosure_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total liabilities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeFinancialInstrumentsLiabilitiesMember" xlink:label="us-gaap_DerivativeFinancialInstrumentsLiabilitiesMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DerivativeFinancialInstrumentsLiabilitiesMember" xlink:to="us-gaap_DerivativeFinancialInstrumentsLiabilitiesMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DerivativeFinancialInstrumentsLiabilitiesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative Financial Instruments, Liabilities [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DerivativeFinancialInstrumentsLiabilitiesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative liabilities</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_BusinessCombinationContingentConsiderationLiabilityMember" xlink:label="cntm_BusinessCombinationContingentConsiderationLiabilityMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_BusinessCombinationContingentConsiderationLiabilityMember" xlink:to="cntm_BusinessCombinationContingentConsiderationLiabilityMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_BusinessCombinationContingentConsiderationLiabilityMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to business combination contingent consideration liability.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_BusinessCombinationContingentConsiderationLiabilityMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Contingent Consideration, Liability [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_BusinessCombinationContingentConsiderationLiabilityMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contingent consideration</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConvertibleDebtMember" xlink:label="us-gaap_ConvertibleDebtMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ConvertibleDebtMember" xlink:to="us-gaap_ConvertibleDebtMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ConvertibleDebtMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Debt [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ConvertibleDebtMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible debt</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementOfIncomeLocationBalanceAxis" xlink:label="us-gaap_StatementOfIncomeLocationBalanceAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StatementOfIncomeLocationBalanceAxis" xlink:to="us-gaap_StatementOfIncomeLocationBalanceAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StatementOfIncomeLocationBalanceAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Location, Statement of Income, Balance [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:label="us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:to="us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Liabilities Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair value, liabilities measured on recurring basis</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue" xlink:label="us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue" xlink:to="us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Liability Value</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedPeriodEndLabel" xlink:label="us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Ending balance</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedPeriodStartLabel" xlink:label="us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Beginning balance</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySettlementsCashPaid" xlink:label="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySettlementsCashPaid" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySettlementsCashPaid" xlink:to="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySettlementsCashPaid_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySettlementsCashPaid_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of settlement by cash of financial instrument classified as a liability measured using unobservable inputs that reflect the entity's own assumption about the assumptions market participants would use in pricing.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySettlementsCashPaid_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Liability, Settlements, Cash Paid</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySettlementsCashPaid_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash payment/(receipt)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityIssues" xlink:label="us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityIssues" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityIssues" xlink:to="us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityIssues_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityIssues_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Liability, Issuances</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityIssues_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuances</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityCommitmentSharesIssued" xlink:label="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityCommitmentSharesIssued" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityCommitmentSharesIssued" xlink:to="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityCommitmentSharesIssued_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityCommitmentSharesIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of issuances of financial instrument classified as a liability measured using Commitment shares issued about the assumptions market participants would use in pricing</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityCommitmentSharesIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value Measurement With Unobservable Inputs Reconciliation Recurring Basis Liability Commitment shares issued</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityCommitmentSharesIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Commitment shares issued</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySettlementsStockIssued" xlink:label="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySettlementsStockIssued" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySettlementsStockIssued" xlink:to="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySettlementsStockIssued_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySettlementsStockIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of settlement by issuance of stock of financial instrument classified as a liability measured using unobservable inputs that reflect the entity's own assumption about the assumptions market participants would use in pricing.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySettlementsStockIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Liability, Settlements, Stock Issued</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySettlementsStockIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Settlement through issuance of Company's common stock</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossOnIssuanceOfFinancialInstruments" xlink:label="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossOnIssuanceOfFinancialInstruments" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossOnIssuanceOfFinancialInstruments" xlink:to="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossOnIssuanceOfFinancialInstruments_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossOnIssuanceOfFinancialInstruments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of gain (loss) on issuance of financial instrument classified as a liability measured using unobservable inputs that reflect the entity's own assumption about the assumptions market participants would use in pricing.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossOnIssuanceOfFinancialInstruments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Liability, Gain (Loss) On Issuance of Financial Instruments</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossOnIssuanceOfFinancialInstruments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loss on issuance of financial instruments</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityAdditionalSettlementObligation" xlink:label="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityAdditionalSettlementObligation" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">FAIR VALUE MEASUREMENTS</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FinancialInstrumentAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Financial Instrument [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain" xlink:label="us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTable" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTable" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MeasurementInputTypeAxis" xlink:label="us-gaap_MeasurementInputTypeAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MeasurementInputTypeDomain" xlink:label="us-gaap_MeasurementInputTypeDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_MeasurementInputTypeDomain" xlink:to="us-gaap_MeasurementInputTypeDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_MeasurementInputTypeDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement Input Type [Domain]</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_MeasurementInputDiscountRateMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement Input, Discount Rate [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_MeasurementInputDiscountRateMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Discount rate</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_MeasurementInputProbabilityOfRedemptionAtMaturityScenarioMember" xlink:label="cntm_MeasurementInputProbabilityOfRedemptionAtMaturityScenarioMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_MeasurementInputProbabilityOfRedemptionAtMaturityScenarioMember" xlink:to="cntm_MeasurementInputProbabilityOfRedemptionAtMaturityScenarioMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_MeasurementInputProbabilityOfRedemptionAtMaturityScenarioMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement input using probability of redemption at maturity scenario.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_MeasurementInputProbabilityOfRedemptionAtMaturityScenarioMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement Input, Probability Of Redemption At Maturity Scenario [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_MeasurementInputProbabilityOfRedemptionAtMaturityScenarioMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Probability of redemption at maturity Scenario</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_MeasurementInputProbabilityOfVoluntaryConversionScenarioMember" xlink:label="cntm_MeasurementInputProbabilityOfVoluntaryConversionScenarioMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_MeasurementInputProbabilityOfVoluntaryConversionScenarioMember" xlink:to="cntm_MeasurementInputProbabilityOfVoluntaryConversionScenarioMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_MeasurementInputProbabilityOfVoluntaryConversionScenarioMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement input using probability of voluntary conversion scenario.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_MeasurementInputProbabilityOfVoluntaryConversionScenarioMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement Input, Probability Of Voluntary Conversion Scenario [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_MeasurementInputProbabilityOfVoluntaryConversionScenarioMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Probability of voluntary conversion scenario/event of default scenarios</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_MeasurementInputRemainingTermForConversionAtMaturityScenarioMember" xlink:label="cntm_MeasurementInputRemainingTermForConversionAtMaturityScenarioMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_MeasurementInputRemainingTermForConversionAtMaturityScenarioMember" xlink:to="cntm_MeasurementInputRemainingTermForConversionAtMaturityScenarioMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_MeasurementInputRemainingTermForConversionAtMaturityScenarioMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement input using remaining term for conversion at maturity scenario.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_MeasurementInputRemainingTermForConversionAtMaturityScenarioMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement Input, Remaining Term For Conversion At Maturity Scenario [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_MeasurementInputRemainingTermForConversionAtMaturityScenarioMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Remaining term for conversion at maturity scenario/event of default scenarios</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_MeasurementInputRemainingTermForVoluntaryConversionScenarioMember" xlink:label="cntm_MeasurementInputRemainingTermForVoluntaryConversionScenarioMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_MeasurementInputRemainingTermForVoluntaryConversionScenarioMember" xlink:to="cntm_MeasurementInputRemainingTermForVoluntaryConversionScenarioMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_MeasurementInputRemainingTermForVoluntaryConversionScenarioMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement input using remaining term for voluntary conversion scenario.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_MeasurementInputRemainingTermForVoluntaryConversionScenarioMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement Input, Remaining Term For Voluntary Conversion Scenario [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_MeasurementInputRemainingTermForVoluntaryConversionScenarioMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Remaining term for voluntary conversion scenario</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value Measurement Inputs and Valuation Techniques [Line Items]</label>
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentMeasurementInput" xlink:label="us-gaap_DebtInstrumentMeasurementInput" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DebtInstrumentMeasurementInput_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair value measurement input</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_MeasurementInputDiscountRateIceBofaCccAndLowerUsHighYieldIndexMember" xlink:label="cntm_MeasurementInputDiscountRateIceBofaCccAndLowerUsHighYieldIndexMember" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_MeasurementInputDiscountRateIceBofaCccAndLowerUsHighYieldIndexMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement Input, Discount Rate, Ice Bofa Ccc And Lower Us High Yield Index [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_MeasurementInputDiscountRateIceBofaCccAndLowerUsHighYieldIndexMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">ICE BofA CCC &amp; Lower US High Yield Index</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_MeasurementInputDiscountRateSAndPUsHighYieldCorporateBondCccIndexMember" xlink:label="cntm_MeasurementInputDiscountRateSAndPUsHighYieldCorporateBondCccIndexMember" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_MeasurementInputDiscountRateSAndPUsHighYieldCorporateBondCccIndexMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement input using interest rate relating to the S&amp;P U.S. High Yield Corporate Bond CCC index  to determine present value of future cash flows.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_MeasurementInputDiscountRateSAndPUsHighYieldCorporateBondCccIndexMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement Input, Discount Rate, S And P Us High Yield Corporate Bond Ccc Index [Member</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_MeasurementInputDiscountRateSAndPUsHighYieldCorporateBondCccIndexMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">S&amp;P U.S. High Yield Corporate Bond CCC index</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_MeasurementInputDiscountRatePepperdinePrivateCapitalMarketsMezzanineRateOfReturnMember" xlink:label="cntm_MeasurementInputDiscountRatePepperdinePrivateCapitalMarketsMezzanineRateOfReturnMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_MeasurementInputDiscountRatePepperdinePrivateCapitalMarketsMezzanineRateOfReturnMember" xlink:to="cntm_MeasurementInputDiscountRatePepperdinePrivateCapitalMarketsMezzanineRateOfReturnMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_MeasurementInputDiscountRatePepperdinePrivateCapitalMarketsMezzanineRateOfReturnMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement input using interest rate relating to the Pepperdine Private Capital Markets mezzanine required rate of return to determine present value of future cash flows.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_MeasurementInputDiscountRatePepperdinePrivateCapitalMarketsMezzanineRateOfReturnMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement Input, Discount Rate, Pepperdine Private Capital Markets Mezzanine Rate Of Return [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_MeasurementInputDiscountRatePepperdinePrivateCapitalMarketsMezzanineRateOfReturnMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Pepperdine Private Capital Markets mezzanine required rate of return</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_SettlementAndTerminationAgreementMember" xlink:label="cntm_SettlementAndTerminationAgreementMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_SettlementAndTerminationAgreementMember" xlink:to="cntm_SettlementAndTerminationAgreementMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_SettlementAndTerminationAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to settlement and termination agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_SettlementAndTerminationAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Settlement And Termination Agreement [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_SettlementAndTerminationAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Settlement and Termination Agreement</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_SettlementAndTerminationAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Yorkville Agreement</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentCarryingAmount" xlink:label="us-gaap_DebtInstrumentCarryingAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentCarryingAmount" xlink:to="us-gaap_DebtInstrumentCarryingAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentCarryingAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Long-Term Debt, Gross</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_DebtInstrumentCarryingAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Outstanding balance</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_ConvertibleDebtFairValueBeforeTermination" xlink:label="cntm_ConvertibleDebtFairValueBeforeTermination" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertibleDebtFairValueBeforeTermination" xlink:to="cntm_ConvertibleDebtFairValueBeforeTermination_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertibleDebtFairValueBeforeTermination_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair value portion of convertible debt before settlement and termination agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertibleDebtFairValueBeforeTermination_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Debt, Fair Value Before Termination</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertibleDebtFairValueBeforeTermination_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair value of outstanding balance</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DebtInstrumentTerminationFeePayable" xlink:label="cntm_DebtInstrumentTerminationFeePayable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentTerminationFeePayable" xlink:to="cntm_DebtInstrumentTerminationFeePayable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentTerminationFeePayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of termination fee payable in common stock for settlement of debt.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentTerminationFeePayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Termination Fee Payable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentTerminationFeePayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Termination fee (payable in Common Stock at IPO price)</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_FairValueOfTerminatedAgreement" xlink:label="cntm_FairValueOfTerminatedAgreement" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FairValueOfTerminatedAgreement" xlink:to="cntm_FairValueOfTerminatedAgreement_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FairValueOfTerminatedAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The fair value amount of the terminated agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FairValueOfTerminatedAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value Of Terminated Agreement</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FairValueOfTerminatedAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair value Of terminated agreement</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_BaseCaseScenarioMember" xlink:label="cntm_BaseCaseScenarioMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_BaseCaseScenarioMember" xlink:to="cntm_BaseCaseScenarioMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_BaseCaseScenarioMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to base case scenario.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_BaseCaseScenarioMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Base Case Scenario [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_BaseCaseScenarioMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Base case scenario</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DefaultScenarioMember" xlink:label="cntm_DefaultScenarioMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DefaultScenarioMember" xlink:to="cntm_DefaultScenarioMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DefaultScenarioMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to default scenario.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DefaultScenarioMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Default Scenario [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DefaultScenarioMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Default scenario</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MeasurementInputSharePriceMember" xlink:label="us-gaap_MeasurementInputSharePriceMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_MeasurementInputSharePriceMember" xlink:to="us-gaap_MeasurementInputSharePriceMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_MeasurementInputSharePriceMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement Input, Share Price [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_MeasurementInputSharePriceMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock price as of valuation date</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_MeasurementInputEquityVolatilityMember" xlink:label="cntm_MeasurementInputEquityVolatilityMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_MeasurementInputEquityVolatilityMember" xlink:to="cntm_MeasurementInputEquityVolatilityMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_MeasurementInputEquityVolatilityMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement input using equity volatility.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_MeasurementInputEquityVolatilityMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement Input, Equity Volatility [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_MeasurementInputEquityVolatilityMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity volatility</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MeasurementInputRiskFreeInterestRateMember" xlink:label="us-gaap_MeasurementInputRiskFreeInterestRateMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_MeasurementInputRiskFreeInterestRateMember" xlink:to="us-gaap_MeasurementInputRiskFreeInterestRateMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_MeasurementInputRiskFreeInterestRateMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement Input, Risk Free Interest Rate [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_MeasurementInputRiskFreeInterestRateMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Risk-free rate</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MeasurementInputExpectedTermMember" xlink:label="us-gaap_MeasurementInputExpectedTermMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_MeasurementInputExpectedTermMember" xlink:to="us-gaap_MeasurementInputExpectedTermMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_MeasurementInputExpectedTermMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement Input, Expected Term [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_MeasurementInputExpectedTermMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Expected term</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_MeasurementInputDriftTermMember" xlink:label="cntm_MeasurementInputDriftTermMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_MeasurementInputDriftTermMember" xlink:to="cntm_MeasurementInputDriftTermMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_MeasurementInputDriftTermMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement input using drift term.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_MeasurementInputDriftTermMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement Input, Drift Term [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_MeasurementInputDriftTermMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Drift term</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_OtherLiabilitiesAgreedToBeSettledInShares" xlink:label="cntm_OtherLiabilitiesAgreedToBeSettledInShares" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_OtherLiabilitiesAgreedToBeSettledInShares" xlink:to="cntm_OtherLiabilitiesAgreedToBeSettledInShares_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_OtherLiabilitiesAgreedToBeSettledInShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of other liabilities settled through shares in non-cash transactions.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_OtherLiabilitiesAgreedToBeSettledInShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other Liabilities Agreed To Be Settled In Shares</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_OtherLiabilitiesAgreedToBeSettledInShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Overdue liabilities agreed to be settled in shares</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_SettlementAgreementFairValueAdjustment" xlink:label="cntm_SettlementAgreementFairValueAdjustment" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_SettlementAgreementFairValueAdjustment" xlink:to="cntm_SettlementAgreementFairValueAdjustment_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_SettlementAgreementFairValueAdjustment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of expense (income) related to adjustment to fair value of settlement agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_SettlementAgreementFairValueAdjustment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Settlement Agreement, Fair Value Adjustment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_SettlementAgreementFairValueAdjustment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Change in fair value</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_NumberOfTrials" xlink:label="cntm_NumberOfTrials" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_NumberOfTrials" xlink:to="cntm_NumberOfTrials_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_NumberOfTrials_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the number of trials under a scenario-based framework.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_NumberOfTrials_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number Of Trials</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_NumberOfTrials_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of trials</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_BaseCaseScenarioProbabilityPercentage" xlink:label="cntm_BaseCaseScenarioProbabilityPercentage" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_BaseCaseScenarioProbabilityPercentage" xlink:to="cntm_BaseCaseScenarioProbabilityPercentage_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_BaseCaseScenarioProbabilityPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The percentage of base case scenario probability.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_BaseCaseScenarioProbabilityPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Base Case Scenario Probability, Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_BaseCaseScenarioProbabilityPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Base case scenario probability (in percent)</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_PercentageOfMarketPriceUsedToDetermineConversionPrice" xlink:label="cntm_PercentageOfMarketPriceUsedToDetermineConversionPrice" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_PercentageOfMarketPriceUsedToDetermineConversionPrice" xlink:to="cntm_PercentageOfMarketPriceUsedToDetermineConversionPrice_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_PercentageOfMarketPriceUsedToDetermineConversionPrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of market price used to determine conversion price.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_PercentageOfMarketPriceUsedToDetermineConversionPrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage Of Market Price Used To Determine Conversion Price</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_PercentageOfMarketPriceUsedToDetermineConversionPrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of market price used to determine conversion price</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DefaultScenarioProbabilityPercentage" xlink:label="cntm_DefaultScenarioProbabilityPercentage" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DefaultScenarioProbabilityPercentage" xlink:to="cntm_DefaultScenarioProbabilityPercentage_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DefaultScenarioProbabilityPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The percentage of base case scenario probability.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DefaultScenarioProbabilityPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Default Scenario Probability, Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DefaultScenarioProbabilityPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Default scenario probability (in percent)</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_SettlementAgreementMeasurementInput" xlink:label="cntm_SettlementAgreementMeasurementInput" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_SettlementAgreementMeasurementInput" xlink:to="cntm_SettlementAgreementMeasurementInput_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_SettlementAgreementMeasurementInput_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Value of input used to measure settlement agreement for shares issued under Section 3(a)(10) of the Securities Act.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_SettlementAgreementMeasurementInput_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Settlement Agreement, Measurement Input</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_SettlementAgreementMeasurementInput_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement input</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:label="us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:to="us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Related Party Transaction [Table]</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_MontereyCapitalAcquisitionCorporationMember" xlink:label="cntm_MontereyCapitalAcquisitionCorporationMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_MontereyCapitalAcquisitionCorporationMember" xlink:to="cntm_MontereyCapitalAcquisitionCorporationMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_MontereyCapitalAcquisitionCorporationMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information pertaining to Monterey Capital Acquisition Corporation.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_MontereyCapitalAcquisitionCorporationMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Monterey Capital Acquisition Corporation [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_MontereyCapitalAcquisitionCorporationMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Monterey Capital Acquisition Corporation</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_MontereyCapitalAcquisitionCorporationMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">MCAC</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyMember" xlink:label="us-gaap_RelatedPartyMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RelatedPartyMember" xlink:to="us-gaap_RelatedPartyMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RelatedPartyMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Related Party [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RelatedPartyMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Related party</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_SponsorMember" xlink:label="cntm_SponsorMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_SponsorMember" xlink:to="cntm_SponsorMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_SponsorMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">This member stands for sponsor.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_SponsorMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Sponsor [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_SponsorMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Sponsor</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_UnsecuredPromissoryNoteMember" xlink:label="cntm_UnsecuredPromissoryNoteMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_UnsecuredPromissoryNoteMember" xlink:to="cntm_UnsecuredPromissoryNoteMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_UnsecuredPromissoryNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to unsecured promissory note.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_UnsecuredPromissoryNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Unsecured Promissory Note [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_UnsecuredPromissoryNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Unsecured promissory note</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyTransactionLineItems" xlink:label="us-gaap_RelatedPartyTransactionLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RelatedPartyTransactionLineItems" xlink:to="us-gaap_RelatedPartyTransactionLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RelatedPartyTransactionLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Related Party Transaction [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RelatedPartyTransactionLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">RELATED PARTY TRANSACTIONS</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesLongTermDebt" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesLongTermDebt" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesLongTermDebt" xlink:to="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesLongTermDebt_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesLongTermDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Current Liabilities, Long-Term Debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesLongTermDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Unsecured promissory notes</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesLongTermDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Line of credit</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsReceivables" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsReceivables" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsReceivables" xlink:to="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsReceivables_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsReceivables_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Current Assets, Receivables</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsReceivables_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts receivable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsReceivables_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts receivables, net</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_AggregateOwnershipPercentageOfIndividualLenderMaximum" xlink:label="cntm_AggregateOwnershipPercentageOfIndividualLenderMaximum" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_AggregateOwnershipPercentageOfIndividualLenderMaximum" xlink:to="cntm_AggregateOwnershipPercentageOfIndividualLenderMaximum_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_AggregateOwnershipPercentageOfIndividualLenderMaximum_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The maximum percentage of ownership by an individual lender as per the terms of debt conversion.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_AggregateOwnershipPercentageOfIndividualLenderMaximum_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Aggregate Ownership Percentage Of Individual Lender, Maximum</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_AggregateOwnershipPercentageOfIndividualLenderMaximum_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Maximum percentage of ownership by an individual lender</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_ExtinguishmentOfAccountsPayableAndAccruedExpensesAmount" xlink:label="cntm_ExtinguishmentOfAccountsPayableAndAccruedExpensesAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ExtinguishmentOfAccountsPayableAndAccruedExpensesAmount" xlink:to="cntm_ExtinguishmentOfAccountsPayableAndAccruedExpensesAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ExtinguishmentOfAccountsPayableAndAccruedExpensesAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The total amount of accounts payable and accrued expenses extinguished by the entity during the reporting period.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ExtinguishmentOfAccountsPayableAndAccruedExpensesAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Extinguishment Of Accounts Payable And Accrued Expenses, Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ExtinguishmentOfAccountsPayableAndAccruedExpensesAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Extinguishment of accounts payable and accrued expenses</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_PromissoryNote2024Member" xlink:label="cntm_PromissoryNote2024Member" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_PromissoryNote2024Member" xlink:to="cntm_PromissoryNote2024Member_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_PromissoryNote2024Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information relating to the 2024 promissory note.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_PromissoryNote2024Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Promissory Note 2024 [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_PromissoryNote2024Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2024 Promissory Note</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ChiefExecutiveOfficerMember" xlink:label="srt_ChiefExecutiveOfficerMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_ChiefExecutiveOfficerMember" xlink:to="srt_ChiefExecutiveOfficerMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_ChiefExecutiveOfficerMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Chief Executive Officer [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_ChiefExecutiveOfficerMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Chief executive officer</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DistributedEnergyAndRenewablesMember" xlink:label="cntm_DistributedEnergyAndRenewablesMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DistributedEnergyAndRenewablesMember" xlink:to="cntm_DistributedEnergyAndRenewablesMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DistributedEnergyAndRenewablesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information pertaining to distributed energy and renewables segment.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DistributedEnergyAndRenewablesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Distributed Energy and Renewables [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DistributedEnergyAndRenewablesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Distributed Energy &amp; Renewables</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_NonEmployeeDirectorMember" xlink:label="cntm_NonEmployeeDirectorMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_NonEmployeeDirectorMember" xlink:to="cntm_NonEmployeeDirectorMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_NonEmployeeDirectorMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information pertaining to non-employee director.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_NonEmployeeDirectorMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Non Employee Director [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_NonEmployeeDirectorMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Non-employee directors</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AwardDateAxis" xlink:label="us-gaap_AwardDateAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AwardDateAxis" xlink:to="us-gaap_AwardDateAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AwardDateAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Award Date [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AwardDateDomain" xlink:label="us-gaap_AwardDateDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AwardDateDomain" xlink:to="us-gaap_AwardDateDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AwardDateDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Award Date [Domain]</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_May272025Member" xlink:label="cntm_May272025Member" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_May272025Member" xlink:to="cntm_May272025Member_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_May272025Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">This member stands for grant date May 27, 2025.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_May272025Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">May 27, 2025 [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_May272025Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">May 27, 2025</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_June182025Member" xlink:label="cntm_June182025Member" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_June182025Member" xlink:to="cntm_June182025Member_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_June182025Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">This member stands for the grant date June 18, 2025.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_June182025Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">June 18, 2025 [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_June182025Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">June 18, 2025</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_June232025Member" xlink:label="cntm_June232025Member" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_June232025Member" xlink:to="cntm_June232025Member_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_June232025Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">This member stands for the grant date June 23, 2025.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_June232025Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">June 23, 2025 [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_June232025Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">June 23, 2025</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RestrictedStockMember" xlink:label="us-gaap_RestrictedStockMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RestrictedStockMember" xlink:to="us-gaap_RestrictedStockMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RestrictedStockMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Restricted Stock [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RestrictedStockMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Restricted common stock</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_PeriodOfNoticeForTermination" xlink:label="cntm_PeriodOfNoticeForTermination" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_PeriodOfNoticeForTermination" xlink:to="cntm_PeriodOfNoticeForTermination_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_PeriodOfNoticeForTermination_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Period of notice for termination by either parties.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_PeriodOfNoticeForTermination_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Period Of Notice For Termination</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_MarkupOnTotalCostPercentage" xlink:label="cntm_MarkupOnTotalCostPercentage" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_MarkupOnTotalCostPercentage" xlink:to="cntm_MarkupOnTotalCostPercentage_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_MarkupOnTotalCostPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of mark up applied to total cost, including product cost, procurement and logistics fees, and marketing and other professional service costs.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_MarkupOnTotalCostPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Markup On Total Cost, Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_MarkupOnTotalCostPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Mark-up percentage</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_IntraEntityGrossProfitInInventory" xlink:label="cntm_IntraEntityGrossProfitInInventory" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_IntraEntityGrossProfitInInventory" xlink:to="cntm_IntraEntityGrossProfitInInventory_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_IntraEntityGrossProfitInInventory_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of intra-entity gross profit remaining in inventory.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_IntraEntityGrossProfitInInventory_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Intra-Entity Gross Profit In Inventory</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssuedDuringPeriodSharesRestrictedStockAwardGross" xlink:label="us-gaap_StockIssuedDuringPeriodSharesRestrictedStockAwardGross" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockIssuedDuringPeriodSharesRestrictedStockAwardGross" xlink:to="us-gaap_StockIssuedDuringPeriodSharesRestrictedStockAwardGross_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockIssuedDuringPeriodSharesRestrictedStockAwardGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period, Shares, Restricted Stock Award, Gross</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_StockIssuedDuringPeriodSharesRestrictedStockAwardGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Company issued restricted common stock</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AllocatedShareBasedCompensationExpense" xlink:label="us-gaap_AllocatedShareBasedCompensationExpense" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AllocatedShareBasedCompensationExpense" xlink:to="us-gaap_AllocatedShareBasedCompensationExpense_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AllocatedShareBasedCompensationExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Payment Arrangement, Expense</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_AllocatedShareBasedCompensationExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock-based compensation expense</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:to="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Grants in Period, Weighted Average Grant Date Fair Value</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Grant date fair value</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_CommitmentsAndContingenciesTable" xlink:label="cntm_CommitmentsAndContingenciesTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_CommitmentsAndContingenciesTable" xlink:to="cntm_CommitmentsAndContingenciesTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_CommitmentsAndContingenciesTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule reflecting a Commitments and Contingencies.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_CommitmentsAndContingenciesTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">COMMITMENTS AND CONTINGENCIES [Table]</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_CommitmentsAndContingenciesLineItems" xlink:label="cntm_CommitmentsAndContingenciesLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_CommitmentsAndContingenciesLineItems" xlink:to="cntm_CommitmentsAndContingenciesLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_CommitmentsAndContingenciesLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_CommitmentsAndContingenciesLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Commitments and Contingencies [Line items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_CommitmentsAndContingenciesLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">COMMITMENTS AND CONTINGENCIES</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LossContingencyDamagesSoughtValue" xlink:label="us-gaap_LossContingencyDamagesSoughtValue" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LossContingencyDamagesSoughtValue" xlink:to="us-gaap_LossContingencyDamagesSoughtValue_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LossContingencyDamagesSoughtValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loss Contingency, Damages Sought, Value</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LossContingencyDamagesSoughtValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Obligation payments</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_LossContingencyAmountOfferedInSettlement" xlink:label="cntm_LossContingencyAmountOfferedInSettlement" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_LossContingencyAmountOfferedInSettlement" xlink:to="cntm_LossContingencyAmountOfferedInSettlement_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_LossContingencyAmountOfferedInSettlement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The monetary value offered in connection with the settlement of the legal matter.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_LossContingencyAmountOfferedInSettlement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loss Contingency, Amount Offered In Settlement</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_LossContingencyAmountOfferedInSettlement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount in settlement</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LossContingencyAccrualAtCarryingValue" xlink:label="us-gaap_LossContingencyAccrualAtCarryingValue" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LossContingencyAccrualAtCarryingValue" xlink:to="us-gaap_LossContingencyAccrualAtCarryingValue_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LossContingencyAccrualAtCarryingValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loss Contingency Accrual</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LossContingencyAccrualAtCarryingValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loss contingency accrual</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_GainLossOnExtinguishmentOfContingentConsiderationLiability" xlink:label="cntm_GainLossOnExtinguishmentOfContingentConsiderationLiability" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_GainLossOnExtinguishmentOfContingentConsiderationLiability" xlink:to="cntm_GainLossOnExtinguishmentOfContingentConsiderationLiability_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_GainLossOnExtinguishmentOfContingentConsiderationLiability_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of gain or loss recognized during the period resulting from the extinguishment, settlement, termination, or cancellation of earnout obligations under a contingent earnout arrangement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_GainLossOnExtinguishmentOfContingentConsiderationLiability_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gain (Loss) on Extinguishment of Contingent Consideration Liability</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_GainLossOnExtinguishmentOfContingentConsiderationLiability_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gain on extinguishment</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessCombinationContingentConsiderationLiabilityCurrent" xlink:label="us-gaap_BusinessCombinationContingentConsiderationLiabilityCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessCombinationContingentConsiderationLiabilityCurrent" xlink:to="us-gaap_BusinessCombinationContingentConsiderationLiabilityCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessCombinationContingentConsiderationLiabilityCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Contingent Consideration, Liability, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_BusinessCombinationContingentConsiderationLiabilityCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Current portion of contingent consideration</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_LossContingencyMortgageAndPromissoryNote" xlink:label="cntm_LossContingencyMortgageAndPromissoryNote" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_LossContingencyMortgageAndPromissoryNote" xlink:to="cntm_LossContingencyMortgageAndPromissoryNote_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_LossContingencyMortgageAndPromissoryNote_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Estimated liability for a loss contingency arising from claims related to a mortgage and promissory note.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_LossContingencyMortgageAndPromissoryNote_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loss Contingency, Mortgage And Promissory Note</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_LossContingencyMortgageAndPromissoryNote_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Mortgage and promissory note payable</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_LossContingencyStockPurchaseAgreement" xlink:label="cntm_LossContingencyStockPurchaseAgreement" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_LossContingencyStockPurchaseAgreement" xlink:to="cntm_LossContingencyStockPurchaseAgreement_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_LossContingencyStockPurchaseAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Estimated liability for a loss contingency arising from claims related to stock purchase agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_LossContingencyStockPurchaseAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loss Contingency, Stock Purchase Agreement</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_LossContingencyStockPurchaseAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Damages relating to additional claims</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_AttorneysFeesAndCosts" xlink:label="cntm_AttorneysFeesAndCosts" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_AttorneysFeesAndCosts" xlink:to="cntm_AttorneysFeesAndCosts_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_AttorneysFeesAndCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of attorney's fees and costs incurred.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_AttorneysFeesAndCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Attorneys Fees And Costs</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_AttorneysFeesAndCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Attorneys' fees and costs</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_ArbitratorsFeesAndCosts" xlink:label="cntm_ArbitratorsFeesAndCosts" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ArbitratorsFeesAndCosts" xlink:to="cntm_ArbitratorsFeesAndCosts_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ArbitratorsFeesAndCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of arbitrator's fees and costs incurred.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ArbitratorsFeesAndCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Arbitrators Fees And Costs</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ArbitratorsFeesAndCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Arbitrators' fees and costs</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LitigationReserveNoncurrent" xlink:label="us-gaap_LitigationReserveNoncurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LitigationReserveNoncurrent" xlink:to="us-gaap_LitigationReserveNoncurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LitigationReserveNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Estimated Litigation Liability, Noncurrent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LitigationReserveNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Litigation reserve</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LitigationReserveCurrent" xlink:label="us-gaap_LitigationReserveCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LitigationReserveCurrent" xlink:to="us-gaap_LitigationReserveCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LitigationReserveCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Estimated Litigation Liability, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LitigationReserveCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Litigation reserve within debt and accrued expenses and other current liabilities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DefinedContributionPlanMaximumAnnualContributionsPerEmployeePercent" xlink:label="us-gaap_DefinedContributionPlanMaximumAnnualContributionsPerEmployeePercent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DefinedContributionPlanMaximumAnnualContributionsPerEmployeePercent" xlink:to="us-gaap_DefinedContributionPlanMaximumAnnualContributionsPerEmployeePercent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DefinedContributionPlanMaximumAnnualContributionsPerEmployeePercent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Defined Contribution Plan, Maximum Annual Contributions Per Employee, Percent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DefinedContributionPlanMaximumAnnualContributionsPerEmployeePercent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of employee contribution</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DefinedContributionPlanCostRecognized" xlink:label="us-gaap_DefinedContributionPlanCostRecognized" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DefinedContributionPlanCostRecognized" xlink:to="us-gaap_DefinedContributionPlanCostRecognized_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DefinedContributionPlanCostRecognized_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Defined Contribution Plan, Cost</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DefinedContributionPlanCostRecognized_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contribution cost</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisaggregationOfRevenueTable" xlink:label="us-gaap_DisaggregationOfRevenueTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DisaggregationOfRevenueTable" xlink:to="us-gaap_DisaggregationOfRevenueTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DisaggregationOfRevenueTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disaggregation of Revenue [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisaggregationOfRevenueLineItems" xlink:label="us-gaap_DisaggregationOfRevenueLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DisaggregationOfRevenueLineItems" xlink:to="us-gaap_DisaggregationOfRevenueLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DisaggregationOfRevenueLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disaggregation of Revenue [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DisaggregationOfRevenueLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">REVENUES</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ContractWithCustomerAssetNet" xlink:label="us-gaap_ContractWithCustomerAssetNet" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ContractWithCustomerAssetNet" xlink:to="us-gaap_ContractWithCustomerAssetNet_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ContractWithCustomerAssetNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contract with Customer, Asset, after Allowance for Credit Loss</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:label="us-gaap_ContractWithCustomerAssetNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Ending balance</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:label="us-gaap_ContractWithCustomerAssetNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Beginning balance</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_ContractWithCustomerAssetCostsRecognized" xlink:label="cntm_ContractWithCustomerAssetCostsRecognized" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ContractWithCustomerAssetCostsRecognized" xlink:to="cntm_ContractWithCustomerAssetCostsRecognized_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ContractWithCustomerAssetCostsRecognized_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of costs recognized on contracts where performance obligations are completed during the period.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ContractWithCustomerAssetCostsRecognized_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contract with Customer, Asset, Costs Recognized</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ContractWithCustomerAssetCostsRecognized_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Recognition of costs on contracts where performance obligations completed during the period</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_ContractWithCustomerAssetDeferralOfCosts" xlink:label="cntm_ContractWithCustomerAssetDeferralOfCosts" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ContractWithCustomerAssetDeferralOfCosts" xlink:to="cntm_ContractWithCustomerAssetDeferralOfCosts_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ContractWithCustomerAssetDeferralOfCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of deferral of costs on contracts where performance obligations were not completed during the period.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ContractWithCustomerAssetDeferralOfCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contract with Customer, Asset, Deferral Of Costs</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ContractWithCustomerAssetDeferralOfCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Deferral of costs on contracts where performance obligations were not complete</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ContractWithCustomerLiabilityRevenueRecognized" xlink:label="us-gaap_ContractWithCustomerLiabilityRevenueRecognized" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ContractWithCustomerLiabilityRevenueRecognized" xlink:to="us-gaap_ContractWithCustomerLiabilityRevenueRecognized_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ContractWithCustomerLiabilityRevenueRecognized_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contract with Customer, Liability, Revenue Recognized</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_ContractWithCustomerLiabilityRevenueRecognized_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Recognition of revenue recorded as a contract liability</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_ContractWithCustomerLiabilitiesRevenueRecognizedIncludingCurrentPeriod" xlink:label="cntm_ContractWithCustomerLiabilitiesRevenueRecognizedIncludingCurrentPeriod" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ContractWithCustomerLiabilitiesRevenueRecognizedIncludingCurrentPeriod" xlink:to="cntm_ContractWithCustomerLiabilitiesRevenueRecognizedIncludingCurrentPeriod_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ContractWithCustomerLiabilitiesRevenueRecognizedIncludingCurrentPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of revenue recognized including current period balance that was previously included in balance of obligation to transfer good or service to customer for which consideration from customer has been received or is due.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ContractWithCustomerLiabilitiesRevenueRecognizedIncludingCurrentPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contract With Customer Liabilities Revenue Recognized Including Current Period</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="cntm_ContractWithCustomerLiabilitiesRevenueRecognizedIncludingCurrentPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Recognition of revenue recorded as a contract liability</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_ContractWithCustomerLiabilityAdvancePayments" xlink:label="cntm_ContractWithCustomerLiabilityAdvancePayments" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ContractWithCustomerLiabilityAdvancePayments" xlink:to="cntm_ContractWithCustomerLiabilityAdvancePayments_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ContractWithCustomerLiabilityAdvancePayments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of advance payments received from customers for goods or services not yet delivered.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ContractWithCustomerLiabilityAdvancePayments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contract with Customer, Liability, Advance Payments</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ContractWithCustomerLiabilityAdvancePayments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Customer advance payments</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxContingencyTable" xlink:label="us-gaap_IncomeTaxContingencyTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncomeTaxContingencyTable" xlink:to="us-gaap_IncomeTaxContingencyTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncomeTaxContingencyTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Income Tax Contingency [Table]</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_BlueCloudSoftechSolutionsLimitedMember" xlink:label="cntm_BlueCloudSoftechSolutionsLimitedMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_BlueCloudSoftechSolutionsLimitedMember" xlink:to="cntm_BlueCloudSoftechSolutionsLimitedMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_BlueCloudSoftechSolutionsLimitedMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to Blue Cloud Softech Solutions Limited.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_BlueCloudSoftechSolutionsLimitedMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Blue Cloud Softech Solutions Limited [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_BlueCloudSoftechSolutionsLimitedMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Blue Cloud</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxContingencyLineItems" xlink:label="us-gaap_IncomeTaxContingencyLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncomeTaxContingencyLineItems" xlink:to="us-gaap_IncomeTaxContingencyLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncomeTaxContingencyLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Income Tax Contingency [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IncomeTaxContingencyLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">INCOME TAXES</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DisposalGroupIncludingDiscontinuedOperationNumberOfSharesExchanged" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationNumberOfSharesExchanged" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DisposalGroupIncludingDiscontinuedOperationNumberOfSharesExchanged" xlink:to="cntm_DisposalGroupIncludingDiscontinuedOperationNumberOfSharesExchanged_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationNumberOfSharesExchanged_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of shares exchanged in share swap as part of disposal by means other than sale.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationNumberOfSharesExchanged_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Including Discontinued Operation, Number Of Shares Exchanged</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationNumberOfSharesExchanged_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of shares exchanged</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_PaymentsProceedsFromDivestitureOfBusinessByParties" xlink:label="cntm_PaymentsProceedsFromDivestitureOfBusinessByParties" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_PaymentsProceedsFromDivestitureOfBusinessByParties" xlink:to="cntm_PaymentsProceedsFromDivestitureOfBusinessByParties_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_PaymentsProceedsFromDivestitureOfBusinessByParties_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of cash outflow (inflow) from divestiture of business by parties to the agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_PaymentsProceedsFromDivestitureOfBusinessByParties_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments (Proceeds) From Divestiture Of Business By Parties</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_PaymentsProceedsFromDivestitureOfBusinessByParties_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash paid or received</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_TaxableGainLossOnDisposalOfDiscontinuedOperations" xlink:label="cntm_TaxableGainLossOnDisposalOfDiscontinuedOperations" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_TaxableGainLossOnDisposalOfDiscontinuedOperations" xlink:to="cntm_TaxableGainLossOnDisposalOfDiscontinuedOperations_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_TaxableGainLossOnDisposalOfDiscontinuedOperations_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of gain (loss) recognized for U.S. federal income tax purposes in connection with the disposal of a discontinued operation.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_TaxableGainLossOnDisposalOfDiscontinuedOperations_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Taxable Gain (Loss) On Disposal Of Discontinued Operations</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_TaxableGainLossOnDisposalOfDiscontinuedOperations_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Taxable gain (loss)</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_EstimatedAdjustedTaxBasisInShares" xlink:label="cntm_EstimatedAdjustedTaxBasisInShares" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_EstimatedAdjustedTaxBasisInShares" xlink:to="cntm_EstimatedAdjustedTaxBasisInShares_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_EstimatedAdjustedTaxBasisInShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The estimated adjusted tax basis, for U.S. federal income tax purposes, of shares held by the entity immediately prior to their disposition or exchange.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_EstimatedAdjustedTaxBasisInShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Estimated Adjusted Tax Basis In Shares</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_EstimatedAdjustedTaxBasisInShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of adjusted tax basis</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_FederalOperatingLossCarryforwardsUtilized" xlink:label="cntm_FederalOperatingLossCarryforwardsUtilized" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FederalOperatingLossCarryforwardsUtilized" xlink:to="cntm_FederalOperatingLossCarryforwardsUtilized_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FederalOperatingLossCarryforwardsUtilized_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of federal operating loss carryforwards utilized from taxable gain upon disposal of discontinued operations.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FederalOperatingLossCarryforwardsUtilized_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Federal Operating Loss Carryforwards Utilized</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FederalOperatingLossCarryforwardsUtilized_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Carryforwards of federal operating loss</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_RemainingTaxableGainLossOnDisposalOfDiscontinuedOperations" xlink:label="cntm_RemainingTaxableGainLossOnDisposalOfDiscontinuedOperations" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_RemainingTaxableGainLossOnDisposalOfDiscontinuedOperations" xlink:to="cntm_RemainingTaxableGainLossOnDisposalOfDiscontinuedOperations_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_RemainingTaxableGainLossOnDisposalOfDiscontinuedOperations_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of remaining gain (loss) recognized for U.S. federal income tax purposes in connection with the disposal of a discontinued operation.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_RemainingTaxableGainLossOnDisposalOfDiscontinuedOperations_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Remaining Taxable Gain (Loss) On Disposal Of Discontinued Operations</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_RemainingTaxableGainLossOnDisposalOfDiscontinuedOperations_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Residual tax gains</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DiscontinuedOperationTaxEffectOfIncomeLossFromDisposalOfDiscontinuedOperation" xlink:label="us-gaap_DiscontinuedOperationTaxEffectOfIncomeLossFromDisposalOfDiscontinuedOperation" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DiscontinuedOperationTaxEffectOfIncomeLossFromDisposalOfDiscontinuedOperation" xlink:to="us-gaap_DiscontinuedOperationTaxEffectOfIncomeLossFromDisposalOfDiscontinuedOperation_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DiscontinuedOperationTaxEffectOfIncomeLossFromDisposalOfDiscontinuedOperation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Discontinued Operation, Tax Effect of Gain (Loss) from Disposal of Discontinued Operation</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DiscontinuedOperationTaxEffectOfIncomeLossFromDisposalOfDiscontinuedOperation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Tax expense</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_FederalAndStateIncomeTaxRatePercent" xlink:label="cntm_FederalAndStateIncomeTaxRatePercent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FederalAndStateIncomeTaxRatePercent" xlink:to="cntm_FederalAndStateIncomeTaxRatePercent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FederalAndStateIncomeTaxRatePercent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of blended federal and state income rate used in the computation of tax expense (benefit) on gain (loss) of disposal group including discontinued operations.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FederalAndStateIncomeTaxRatePercent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Federal And State Income Tax Rate, percent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FederalAndStateIncomeTaxRatePercent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Federal and State income tax rate</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_IncomeTaxPayableOnAssumedLongTermCapitalGain" xlink:label="cntm_IncomeTaxPayableOnAssumedLongTermCapitalGain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_IncomeTaxPayableOnAssumedLongTermCapitalGain" xlink:to="cntm_IncomeTaxPayableOnAssumedLongTermCapitalGain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_IncomeTaxPayableOnAssumedLongTermCapitalGain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of income tax exposure arising from the assumed long-term capital gain under the applicable Indian income-tax rules.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_IncomeTaxPayableOnAssumedLongTermCapitalGain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Income Tax Payable On Assumed Long Term Capital Gain</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_IncomeTaxPayableOnAssumedLongTermCapitalGain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Income tax exposure arising from assumed long-term capital gain</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_EffectiveTaxRateOnLongTermCapitalGainsPercent" xlink:label="cntm_EffectiveTaxRateOnLongTermCapitalGainsPercent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_EffectiveTaxRateOnLongTermCapitalGainsPercent" xlink:to="cntm_EffectiveTaxRateOnLongTermCapitalGainsPercent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_EffectiveTaxRateOnLongTermCapitalGainsPercent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of effective tax rate on long-term capital gains under Indian income-tax rules.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_EffectiveTaxRateOnLongTermCapitalGainsPercent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Effective Tax Rate On Long Term Capital Gains, Percent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_EffectiveTaxRateOnLongTermCapitalGainsPercent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Effective tax rate on long-term capital gains</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_MaximumIncomeTaxExposureOnAssumedCapitalGainInAdverseScenario" xlink:label="cntm_MaximumIncomeTaxExposureOnAssumedCapitalGainInAdverseScenario" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_MaximumIncomeTaxExposureOnAssumedCapitalGainInAdverseScenario" xlink:to="cntm_MaximumIncomeTaxExposureOnAssumedCapitalGainInAdverseScenario_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_MaximumIncomeTaxExposureOnAssumedCapitalGainInAdverseScenario_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Maximum Indian income tax exposure on the assumed capital gain under the adverse scenario, based on short-term capital-gains treatment and application of GAAR.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_MaximumIncomeTaxExposureOnAssumedCapitalGainInAdverseScenario_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Maximum Income Tax Exposure On Assumed Capital Gain In Adverse Scenario</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_MaximumIncomeTaxExposureOnAssumedCapitalGainInAdverseScenario_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Maximum income tax exposure on assumed capital gain under adverse scenario</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_EffectiveTaxRateOnCapitalGainsInAdverseScenarioPercent" xlink:label="cntm_EffectiveTaxRateOnCapitalGainsInAdverseScenarioPercent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_EffectiveTaxRateOnCapitalGainsInAdverseScenarioPercent" xlink:to="cntm_EffectiveTaxRateOnCapitalGainsInAdverseScenarioPercent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_EffectiveTaxRateOnCapitalGainsInAdverseScenarioPercent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of effective tax rate used in the computation of income tax exposure on assumed capital gains under the adverse scenario, based on short-term capital-gains treatment and application of GAAR.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_EffectiveTaxRateOnCapitalGainsInAdverseScenarioPercent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Effective Tax Rate On Capital Gains In Adverse Scenario, Percent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_EffectiveTaxRateOnCapitalGainsInAdverseScenarioPercent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Effective tax rate exposure on assumed capital gains under adverse scenario</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_NoncashChargeRecognizedAsDiscreteTaxReserve" xlink:label="cntm_NoncashChargeRecognizedAsDiscreteTaxReserve" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_NoncashChargeRecognizedAsDiscreteTaxReserve" xlink:to="cntm_NoncashChargeRecognizedAsDiscreteTaxReserve_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_NoncashChargeRecognizedAsDiscreteTaxReserve_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Non-cash charge recognized as an aggregate discrete tax reserve within income tax expense.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_NoncashChargeRecognizedAsDiscreteTaxReserve_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Noncash Charge Recognized As Discrete Tax Reserve</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_NoncashChargeRecognizedAsDiscreteTaxReserve_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Aggregate discrete tax reserve</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:label="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:to="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of Segment Reporting Information, by Segment [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NonUsMember" xlink:label="us-gaap_NonUsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NonUsMember" xlink:to="us-gaap_NonUsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NonUsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Non-US [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NonUsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_NonUsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Non-US</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SegmentReportingInformationLineItems" xlink:label="us-gaap_SegmentReportingInformationLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SegmentReportingInformationLineItems" xlink:to="us-gaap_SegmentReportingInformationLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SegmentReportingInformationLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Segment Reporting Information [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SegmentReportingInformationLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">REPORTABLE SEGMENTS</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_NumberOfCustomers" xlink:label="cntm_NumberOfCustomers" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_NumberOfCustomers" xlink:to="cntm_NumberOfCustomers_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_NumberOfCustomers_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the number of customers.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_NumberOfCustomers_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of Customers</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_NumberOfCustomers_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of customers</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_OwnedServiceNetworkSegmentMember" xlink:label="cntm_OwnedServiceNetworkSegmentMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_OwnedServiceNetworkSegmentMember" xlink:to="cntm_OwnedServiceNetworkSegmentMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_OwnedServiceNetworkSegmentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information relating to the entity's Owned Service Network segment.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_OwnedServiceNetworkSegmentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Owned Service Network Segment [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_OwnedServiceNetworkSegmentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Owned Service Network</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_ManagedSolutionsSegmentMember" xlink:label="cntm_ManagedSolutionsSegmentMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ManagedSolutionsSegmentMember" xlink:to="cntm_ManagedSolutionsSegmentMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ManagedSolutionsSegmentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information relating to the entity's managed solutions segment.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ManagedSolutionsSegmentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Managed Solutions Segment [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ManagedSolutionsSegmentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Managed Solutions</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_LogisticsSegmentMember" xlink:label="cntm_LogisticsSegmentMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_LogisticsSegmentMember" xlink:to="cntm_LogisticsSegmentMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_LogisticsSegmentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information relating to the entity's logistics segment.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_LogisticsSegmentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Logistics Segment [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_LogisticsSegmentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Logistics</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SellingGeneralAndAdministrativeExpenseAbstract" xlink:label="us-gaap_SellingGeneralAndAdministrativeExpenseAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SellingGeneralAndAdministrativeExpenseAbstract" xlink:to="us-gaap_SellingGeneralAndAdministrativeExpenseAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SellingGeneralAndAdministrativeExpenseAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Selling, General and Administrative Expense [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SellingGeneralAndAdministrativeExpenseAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Selling, general and administrative expenses</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_FacilityCost" xlink:label="cntm_FacilityCost" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FacilityCost" xlink:to="cntm_FacilityCost_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FacilityCost_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of facility expenses.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FacilityCost_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Facility Cost</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FacilityCost_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Facility costs</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GeneralInsuranceExpense" xlink:label="us-gaap_GeneralInsuranceExpense" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_GeneralInsuranceExpense" xlink:to="us-gaap_GeneralInsuranceExpense_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_GeneralInsuranceExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">General Insurance Expense</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_GeneralInsuranceExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Insurance expenses</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MarketingExpense" xlink:label="us-gaap_MarketingExpense" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_MarketingExpense" xlink:to="us-gaap_MarketingExpense_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_MarketingExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Marketing Expense</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_MarketingExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Marketing expenses</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_OperationalExpenses" xlink:label="cntm_OperationalExpenses" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_OperationalExpenses" xlink:to="cntm_OperationalExpenses_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_OperationalExpenses_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of operational expenses.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_OperationalExpenses_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operational Expenses</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_OperationalExpenses_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operational expenses</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LaborAndRelatedExpense" xlink:label="us-gaap_LaborAndRelatedExpense" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LaborAndRelatedExpense" xlink:to="us-gaap_LaborAndRelatedExpense_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LaborAndRelatedExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Labor and Related Expense</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LaborAndRelatedExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Compensation and related benefits</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TravelAndEntertainmentExpense" xlink:label="us-gaap_TravelAndEntertainmentExpense" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_TravelAndEntertainmentExpense" xlink:to="us-gaap_TravelAndEntertainmentExpense_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_TravelAndEntertainmentExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Travel and Entertainment Expense</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_TravelAndEntertainmentExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Travel &amp; entertainment</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_VehicleExpenses" xlink:label="cntm_VehicleExpenses" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_VehicleExpenses" xlink:to="cntm_VehicleExpenses_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_VehicleExpenses_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of expenses for vehicle.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_VehicleExpenses_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Vehicle Expenses</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_VehicleExpenses_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Vehicle expenses</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AdjustmentForAmortization" xlink:label="us-gaap_AdjustmentForAmortization" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AdjustmentForAmortization" xlink:to="us-gaap_AdjustmentForAmortization_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AdjustmentForAmortization_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amortization</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AdjustmentForAmortization_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amortization</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GoodwillAndIntangibleAssetImpairment" xlink:label="us-gaap_GoodwillAndIntangibleAssetImpairment" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_GoodwillAndIntangibleAssetImpairment" xlink:to="us-gaap_GoodwillAndIntangibleAssetImpairment_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_GoodwillAndIntangibleAssetImpairment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Goodwill and Intangible Asset Impairment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_GoodwillAndIntangibleAssetImpairment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loss on impairment</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SegmentExpenditureAdditionToLongLivedAssets" xlink:label="us-gaap_SegmentExpenditureAdditionToLongLivedAssets" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SegmentExpenditureAdditionToLongLivedAssets" xlink:to="us-gaap_SegmentExpenditureAdditionToLongLivedAssets_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SegmentExpenditureAdditionToLongLivedAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Segment, Expenditure, Addition to Long-Lived Assets</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SegmentExpenditureAdditionToLongLivedAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Capital expenditures</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ReportableSegmentAggregationBeforeOtherOperatingSegmentMember" xlink:label="us-gaap_ReportableSegmentAggregationBeforeOtherOperatingSegmentMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ReportableSegmentAggregationBeforeOtherOperatingSegmentMember" xlink:to="us-gaap_ReportableSegmentAggregationBeforeOtherOperatingSegmentMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ReportableSegmentAggregationBeforeOtherOperatingSegmentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Reportable Segment, Aggregation before Other Operating Segment [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ReportableSegmentAggregationBeforeOtherOperatingSegmentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Reportable Segment, Aggregation before Other Operating Segment</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xlink:label="us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xlink:to="us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of Business Acquisitions, by Acquisition [Table]</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_HarryKahnAssociatesInc.Member" xlink:label="cntm_HarryKahnAssociatesInc.Member" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_HarryKahnAssociatesInc.Member" xlink:to="cntm_HarryKahnAssociatesInc.Member_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_HarryKahnAssociatesInc.Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to Harry Kahn Associates, Inc.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_HarryKahnAssociatesInc.Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Harry Kahn Associates, Inc. [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_HarryKahnAssociatesInc.Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Harry Kahn Associates, Inc.</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessAcquisitionLineItems" xlink:label="us-gaap_BusinessAcquisitionLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessAcquisitionLineItems" xlink:to="us-gaap_BusinessAcquisitionLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessAcquisitionLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Acquisition [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_BusinessAcquisitionLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">ACQUISITIONS</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessCombinationConsiderationTransferred1" xlink:label="us-gaap_BusinessCombinationConsiderationTransferred1" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessCombinationConsiderationTransferred1" xlink:to="us-gaap_BusinessCombinationConsiderationTransferred1_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessCombinationConsiderationTransferred1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Consideration Transferred</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_BusinessCombinationConsiderationTransferred1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Purchase consideration</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued" xlink:label="us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued" xlink:to="us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Acquisition, Equity Interest Issued or Issuable, Number of Shares</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business combination, number of shares issued</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total number of shares issued</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessAcquisitionEquityInterestIssuedOrIssuableValueAssigned" xlink:label="us-gaap_BusinessAcquisitionEquityInterestIssuedOrIssuableValueAssigned" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessAcquisitionEquityInterestIssuedOrIssuableValueAssigned" xlink:to="us-gaap_BusinessAcquisitionEquityInterestIssuedOrIssuableValueAssigned_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessAcquisitionEquityInterestIssuedOrIssuableValueAssigned_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Acquisition, Equity Interest Issued or Issuable, Value Assigned</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_BusinessAcquisitionEquityInterestIssuedOrIssuableValueAssigned_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Acquisition-date fair value of equity interest</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessAcquisitionSharePrice" xlink:label="us-gaap_BusinessAcquisitionSharePrice" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessAcquisitionSharePrice" xlink:to="us-gaap_BusinessAcquisitionSharePrice_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessAcquisitionSharePrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Acquisition, Share Price</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_BusinessAcquisitionSharePrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share price of acquisition (in dollars per share)</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_BusinessCombinationConsiderationTransferredLiabilitiesIncurredUndiscountedAmount" xlink:label="cntm_BusinessCombinationConsiderationTransferredLiabilitiesIncurredUndiscountedAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_BusinessCombinationConsiderationTransferredLiabilitiesIncurredUndiscountedAmount" xlink:to="cntm_BusinessCombinationConsiderationTransferredLiabilitiesIncurredUndiscountedAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_BusinessCombinationConsiderationTransferredLiabilitiesIncurredUndiscountedAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of undiscounted value of liabilities incurred by the acquirer as part of consideration transferred in a business combination.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_BusinessCombinationConsiderationTransferredLiabilitiesIncurredUndiscountedAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Consideration Transferred, Liabilities Incurred, Undiscounted Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_BusinessCombinationConsiderationTransferredLiabilitiesIncurredUndiscountedAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Undiscounted value of future consideration payable</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessCombinationConsiderationTransferredLiabilitiesIncurred" xlink:label="us-gaap_BusinessCombinationConsiderationTransferredLiabilitiesIncurred" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessCombinationConsiderationTransferredLiabilitiesIncurred" xlink:to="us-gaap_BusinessCombinationConsiderationTransferredLiabilitiesIncurred_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessCombinationConsiderationTransferredLiabilitiesIncurred_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Consideration Transferred, Liabilities Incurred</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_BusinessCombinationConsiderationTransferredLiabilitiesIncurred_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Settlement of liabilities with NCLT plan</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_BusinessCombinationConsiderationTransferredLiabilitiesIncurredDiscountRate" xlink:label="cntm_BusinessCombinationConsiderationTransferredLiabilitiesIncurredDiscountRate" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedContractAsset_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contract assets</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedPropertyPlantAndEquipment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Property and equipment</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedRightOfUseAsset" xlink:label="cntm_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedRightOfUseAsset" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedRightOfUseAsset_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Right Of Use Asset</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedRightOfUseAsset_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">ROU assets</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibles_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Intangible Assets</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_BusinessCombinationRecognizedAssetAcquiredAndGoodwill_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Recognized Asset Acquired And Goodwill</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCapitalLeaseObligation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating lease liabilities</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNoncurrentLiabilitiesLongTermDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Note payable</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilities" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilities" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Liabilities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total liabilities assumed</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredGoodwillAndLiabilitiesAssumedNet" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredGoodwillAndLiabilitiesAssumedNet" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredGoodwillAndLiabilitiesAssumedNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Recognized Identifiable Assets Acquired, Goodwill, and Liabilities Assumed, Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredGoodwillAndLiabilitiesAssumedNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net assets acquired</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsAcquiredAsPartOfBusinessCombinationTable" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAcquiredAsPartOfBusinessCombinationTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FiniteLivedIntangibleAssetsAcquiredAsPartOfBusinessCombinationTable" xlink:to="us-gaap_FiniteLivedIntangibleAssetsAcquiredAsPartOfBusinessCombinationTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAcquiredAsPartOfBusinessCombinationTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Intangible Asset, Acquired, Finite-Lived [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AcquiredFiniteLivedIntangibleAssetsLineItems" xlink:label="us-gaap_AcquiredFiniteLivedIntangibleAssetsLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AcquiredFiniteLivedIntangibleAssetsLineItems" xlink:to="us-gaap_AcquiredFiniteLivedIntangibleAssetsLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AcquiredFiniteLivedIntangibleAssetsLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Intangible Asset, Finite-Lived, Acquired [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AcquiredFiniteLivedIntangibleAssetsLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">ACQUISITION</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife" xlink:label="us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife" xlink:to="us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Acquired Finite-Lived Intangible Assets, Weighted Average Useful Life</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Remaining Useful Life</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsequentEventTable" xlink:label="us-gaap_SubsequentEventTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SubsequentEventTable" xlink:to="us-gaap_SubsequentEventTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SubsequentEventTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Subsequent Event [Table]</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_BlueRibbonIceIncMember" xlink:label="cntm_BlueRibbonIceIncMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_BlueRibbonIceIncMember" xlink:to="cntm_BlueRibbonIceIncMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_BlueRibbonIceIncMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to Blue Ribbon ice Inc.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_BlueRibbonIceIncMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Blue Ribbon Ice Inc [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_BlueRibbonIceIncMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Blue Ribbon Ice Inc</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsequentEventLineItems" xlink:label="us-gaap_SubsequentEventLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SubsequentEventLineItems" xlink:to="us-gaap_SubsequentEventLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SubsequentEventLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Subsequent Event [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SubsequentEventLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">SUBSEQUENT EVENTS</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners" xlink:label="us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners" xlink:to="us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Subsidiary, Ownership Percentage, Noncontrolling Owner</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of voting interest held by NCI</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_NumberOfAdvancesReceived" xlink:label="cntm_NumberOfAdvancesReceived" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_NumberOfAdvancesReceived" xlink:to="cntm_NumberOfAdvancesReceived_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_NumberOfAdvancesReceived_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of advances received under purchase order financing arrangement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_NumberOfAdvancesReceived_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number Of Advances Received</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_NumberOfAdvancesReceived_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number Of advances received</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_FinancingAdvanceInvoicedAmount" xlink:label="cntm_FinancingAdvanceInvoicedAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FinancingAdvanceInvoicedAmount" xlink:to="cntm_FinancingAdvanceInvoicedAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FinancingAdvanceInvoicedAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the invoiced amount pertaining to financing advance.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FinancingAdvanceInvoicedAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Financing Advance, Invoiced Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FinancingAdvanceInvoicedAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Invoiced amount</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_FinancingFacilityLenderAdvancedAmount" xlink:label="cntm_FinancingFacilityLenderAdvancedAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FinancingFacilityLenderAdvancedAmount" xlink:to="cntm_FinancingFacilityLenderAdvancedAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FinancingFacilityLenderAdvancedAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the lender advanced amount under financing facility.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FinancingFacilityLenderAdvancedAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Financing Facility, Lender Advanced Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FinancingFacilityLenderAdvancedAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Lender advanced amount</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_FinancingAdvanceRetainedAsHoldBack" xlink:label="cntm_FinancingAdvanceRetainedAsHoldBack" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FinancingAdvanceRetainedAsHoldBack" xlink:to="cntm_FinancingAdvanceRetainedAsHoldBack_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FinancingAdvanceRetainedAsHoldBack_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of financing advance retained as hold back.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FinancingAdvanceRetainedAsHoldBack_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Financing Advance, Retained as Hold Back</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FinancingAdvanceRetainedAsHoldBack_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Retained as hold back amount</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_FinancingFacilityAdvancesReleasedFromEscrow" xlink:label="cntm_FinancingFacilityAdvancesReleasedFromEscrow" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FinancingFacilityAdvancesReleasedFromEscrow" xlink:to="cntm_FinancingFacilityAdvancesReleasedFromEscrow_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FinancingFacilityAdvancesReleasedFromEscrow_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of advances released from escrow under the financing facility.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FinancingFacilityAdvancesReleasedFromEscrow_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Financing Facility, Advances Released from Escrow</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FinancingFacilityAdvancesReleasedFromEscrow_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Advances released from escrow</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_FinancingFacilityAdvancesRemittedToVendor" xlink:label="cntm_FinancingFacilityAdvancesRemittedToVendor" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FinancingFacilityAdvancesRemittedToVendor" xlink:to="cntm_FinancingFacilityAdvancesRemittedToVendor_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FinancingFacilityAdvancesRemittedToVendor_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of advances remitted to vendor from the proceeds released from escrow under financing facility.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FinancingFacilityAdvancesRemittedToVendor_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Financing Facility, Advances Remitted to Vendor</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FinancingFacilityAdvancesRemittedToVendor_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Advances remitted to vendor</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_InstitutionalConvertibleNotesMember" xlink:label="cntm_InstitutionalConvertibleNotesMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_InstitutionalConvertibleNotesMember" xlink:to="cntm_InstitutionalConvertibleNotesMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_InstitutionalConvertibleNotesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to institutional convertible notes.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_InstitutionalConvertibleNotesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Institutional Convertible Notes [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_InstitutionalConvertibleNotesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Institutional convertible notes</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_ShareholderLoansMember" xlink:label="cntm_ShareholderLoansMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ShareholderLoansMember" xlink:to="cntm_ShareholderLoansMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ShareholderLoansMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to shareholder loans.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ShareholderLoansMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Shareholder Loans [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ShareholderLoansMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Shareholder loans</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_MerchantCashAdvancesMember" xlink:label="cntm_MerchantCashAdvancesMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_MerchantCashAdvancesMember" xlink:to="cntm_MerchantCashAdvancesMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_MerchantCashAdvancesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information pertaining to merchant cash advances.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_MerchantCashAdvancesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Merchant Cash Advances [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_MerchantCashAdvancesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Merchant cash advances</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DebtInstrumentCollateralNumberOfShares" xlink:label="cntm_DebtInstrumentCollateralNumberOfShares" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentCollateralNumberOfShares" xlink:to="cntm_DebtInstrumentCollateralNumberOfShares_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentCollateralNumberOfShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of shares pledged to secure a debt instrument.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentCollateralNumberOfShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Collateral, Number of Shares</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentCollateralNumberOfShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of collateral shares</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PreferredStockDividendRatePercentage" xlink:label="us-gaap_PreferredStockDividendRatePercentage" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PreferredStockDividendRatePercentage" xlink:to="us-gaap_PreferredStockDividendRatePercentage_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PreferredStockDividendRatePercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Preferred Stock, Dividend Rate, Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_PreferredStockDividendRatePercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Dividend rate</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_WarrantsAndRightsOutstandingTerm" xlink:label="us-gaap_WarrantsAndRightsOutstandingTerm" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_WarrantsAndRightsOutstandingTerm" xlink:to="us-gaap_WarrantsAndRightsOutstandingTerm_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_WarrantsAndRightsOutstandingTerm_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Warrants and Rights Outstanding, Term</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_WarrantsAndRightsOutstandingTerm_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Public Warrants expiration term</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_WarrantsAndRightsOutstandingDebtPrincipalOutstandingPercentage" xlink:label="cntm_WarrantsAndRightsOutstandingDebtPrincipalOutstandingPercentage" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_WarrantsAndRightsOutstandingDebtPrincipalOutstandingPercentage" xlink:to="cntm_WarrantsAndRightsOutstandingDebtPrincipalOutstandingPercentage_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_WarrantsAndRightsOutstandingDebtPrincipalOutstandingPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of warrants and rights outstanding to the debt principal amount.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_WarrantsAndRightsOutstandingDebtPrincipalOutstandingPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Warrants And Rights Outstanding, Debt Principal, Outstanding Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_WarrantsAndRightsOutstandingDebtPrincipalOutstandingPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of warrants to combined principal</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DebtInstrumentExpectedRepaymentAmount" xlink:label="cntm_DebtInstrumentExpectedRepaymentAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentExpectedRepaymentAmount" xlink:to="cntm_DebtInstrumentExpectedRepaymentAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentExpectedRepaymentAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of debt instrument expected to be repaid.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentExpectedRepaymentAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Expected Repayment Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentExpectedRepaymentAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt expected prepayment</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_BridgeNoteMember" xlink:label="cntm_BridgeNoteMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_BridgeNoteMember" xlink:to="cntm_BridgeNoteMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_BridgeNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to bridge note.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_BridgeNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Bridge Note [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_BridgeNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Bridge note</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_FirstBridgeNoteMember" xlink:label="cntm_FirstBridgeNoteMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FirstBridgeNoteMember" xlink:to="cntm_FirstBridgeNoteMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FirstBridgeNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to first bridge note.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FirstBridgeNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">First Bridge Note [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FirstBridgeNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">First Bridge Note</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_SecondBridgeNoteMember" xlink:label="cntm_SecondBridgeNoteMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_SecondBridgeNoteMember" xlink:to="cntm_SecondBridgeNoteMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_SecondBridgeNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to second bridge note.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_SecondBridgeNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Second Bridge Note [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_SecondBridgeNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Second Bridge Note</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_ThirdBridgeNoteMember" xlink:label="cntm_ThirdBridgeNoteMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ThirdBridgeNoteMember" xlink:to="cntm_ThirdBridgeNoteMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ThirdBridgeNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to third bridge note.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ThirdBridgeNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Third Bridge Note [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ThirdBridgeNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Third Bridge Note</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_NumberOfPromissoryNote" xlink:label="cntm_NumberOfPromissoryNote" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_NumberOfPromissoryNote" xlink:to="cntm_NumberOfPromissoryNote_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_NumberOfPromissoryNote_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of promissory note issued during the period.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_NumberOfPromissoryNote_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number Of Promissory Note</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DebtInstrumentFacilitationFeeAmount" xlink:label="cntm_DebtInstrumentFacilitationFeeAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentFacilitationFeeAmount" xlink:to="cntm_DebtInstrumentFacilitationFeeAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentFacilitationFeeAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of facilitation fee payable to lender.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentFacilitationFeeAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Facilitation Fee, Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentFacilitationFeeAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Facilitation fee, amount</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DebtInstrumentFacilitationFeePercentage" xlink:label="cntm_DebtInstrumentFacilitationFeePercentage" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentFacilitationFeePercentage" xlink:to="cntm_DebtInstrumentFacilitationFeePercentage_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentFacilitationFeePercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of facilitation fee payable to lender.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentFacilitationFeePercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Facilitation Fee, Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentFacilitationFeePercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Facilitation fee, percent</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DebtInstrumentDebtDefaultInterestRatePercentage" xlink:label="cntm_DebtInstrumentDebtDefaultInterestRatePercentage" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentDebtDefaultInterestRatePercentage" xlink:to="cntm_DebtInstrumentDebtDefaultInterestRatePercentage_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentDebtDefaultInterestRatePercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of interest rate on the debt instrument in the event of default.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentDebtDefaultInterestRatePercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Debt Default, Interest Rate, Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentDebtDefaultInterestRatePercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest rate on default</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DebtInstrumentDebtDefaultLatePaymentFeePercentage" xlink:label="cntm_DebtInstrumentDebtDefaultLatePaymentFeePercentage" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentDebtDefaultLatePaymentFeePercentage" xlink:to="cntm_DebtInstrumentDebtDefaultLatePaymentFeePercentage_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentDebtDefaultLatePaymentFeePercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of late payment fee charged on the outstanding amount upon occurrence of default.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentDebtDefaultLatePaymentFeePercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Debt Default, Late Payment Fee, Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentDebtDefaultLatePaymentFeePercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Late payment fee, percent</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DebtInstrumentPurchasePriceNetOfIssueDiscount" xlink:label="cntm_DebtInstrumentPurchasePriceNetOfIssueDiscount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentPurchasePriceNetOfIssueDiscount" xlink:to="cntm_DebtInstrumentPurchasePriceNetOfIssueDiscount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentPurchasePriceNetOfIssueDiscount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of purchase price of debt instrument, net of issue discount.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentPurchasePriceNetOfIssueDiscount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt instrument, Purchase Price, Net Of Issue Discount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentPurchasePriceNetOfIssueDiscount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Purchase price</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DebtInstrumentOriginalIssueDiscount" xlink:label="cntm_DebtInstrumentOriginalIssueDiscount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentOriginalIssueDiscount" xlink:to="cntm_DebtInstrumentOriginalIssueDiscount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentOriginalIssueDiscount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The amount of non-cash expense for the original issuance discount incurred on the debt instruments during the reporting period.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentOriginalIssueDiscount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Original Issue Discount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentOriginalIssueDiscount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of non-cash expense for the original issuance discount</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_PaymentsForLegalFeeReimbursement" xlink:label="cntm_PaymentsForLegalFeeReimbursement" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_PaymentsForLegalFeeReimbursement" xlink:to="cntm_PaymentsForLegalFeeReimbursement_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_PaymentsForLegalFeeReimbursement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of cash outflow as legal fees reimbursement in connection with the debt instrument.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_PaymentsForLegalFeeReimbursement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments For Legal Fee Reimbursement</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_PaymentsForLegalFeeReimbursement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments for legal fees reimbursement</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DebtInstrumentRepaymentObligationAmount" xlink:label="cntm_DebtInstrumentRepaymentObligationAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentRepaymentObligationAmount" xlink:to="cntm_DebtInstrumentRepaymentObligationAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentRepaymentObligationAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of repayment obligation of debt instrument, including interest.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentRepaymentObligationAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Repayment Obligation, Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentRepaymentObligationAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Aggregate repayment obligation</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DebtInstrumentRepaymentNumberOfInstallmentsForPeriodicPayments" xlink:label="cntm_DebtInstrumentRepaymentNumberOfInstallmentsForPeriodicPayments" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentRepaymentNumberOfInstallmentsForPeriodicPayments" xlink:to="cntm_DebtInstrumentRepaymentNumberOfInstallmentsForPeriodicPayments_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentRepaymentNumberOfInstallmentsForPeriodicPayments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of installments for periodic payment of debt.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentRepaymentNumberOfInstallmentsForPeriodicPayments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Repayment, Number Of Installments For Periodic Payments</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentRepaymentNumberOfInstallmentsForPeriodicPayments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of installments for periodic payments</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DebtInstrumentRepaymentPaymentDeferralPeriod" xlink:label="cntm_DebtInstrumentRepaymentPaymentDeferralPeriod" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentRepaymentPaymentDeferralPeriod" xlink:to="cntm_DebtInstrumentRepaymentPaymentDeferralPeriod_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentRepaymentPaymentDeferralPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Period during which the payments are temporarily postponed before scheduled repayment begins under the debt instrument.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentRepaymentPaymentDeferralPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Repayment, Payment Deferral Period</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentRepaymentPaymentDeferralPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt instrument, repayment</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DebtInstrumentIntervalFrequencyOfPeriodicPayment" xlink:label="cntm_DebtInstrumentIntervalFrequencyOfPeriodicPayment" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentIntervalFrequencyOfPeriodicPayment" xlink:to="cntm_DebtInstrumentIntervalFrequencyOfPeriodicPayment_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentIntervalFrequencyOfPeriodicPayment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interval frequency of periodic payments of debt.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentIntervalFrequencyOfPeriodicPayment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Interval Frequency of Periodic Payment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentIntervalFrequencyOfPeriodicPayment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt instrument, interval</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_ConvertibleRedeemableFirstJulyNoteMember" xlink:label="cntm_ConvertibleRedeemableFirstJulyNoteMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertibleRedeemableFirstJulyNoteMember" xlink:to="cntm_ConvertibleRedeemableFirstJulyNoteMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertibleRedeemableFirstJulyNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to convertible redeemable first July note.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertibleRedeemableFirstJulyNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Redeemable First July Note [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertibleRedeemableFirstJulyNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">First July note</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_ConvertibleRedeemableSecondJulyNoteMember" xlink:label="cntm_ConvertibleRedeemableSecondJulyNoteMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertibleRedeemableSecondJulyNoteMember" xlink:to="cntm_ConvertibleRedeemableSecondJulyNoteMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertibleRedeemableSecondJulyNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to convertible redeemable second July note.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertibleRedeemableSecondJulyNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Redeemable, Second July Note [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertibleRedeemableSecondJulyNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Second July note</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_ConvertibleRedeemableNoteJuly92026Member" xlink:label="cntm_ConvertibleRedeemableNoteJuly92026Member" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertibleRedeemableNoteJuly92026Member" xlink:to="cntm_ConvertibleRedeemableNoteJuly92026Member_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertibleRedeemableNoteJuly92026Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to 14% convertible redeemable note issued on July 9, 2026.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertibleRedeemableNoteJuly92026Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Redeemable Note July 9, 2026 [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertibleRedeemableNoteJuly92026Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">July 9 Note</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_ConvertiblePromissoryNoteJuly182026Member" xlink:label="cntm_ConvertiblePromissoryNoteJuly182026Member" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertiblePromissoryNoteJuly182026Member" xlink:to="cntm_ConvertiblePromissoryNoteJuly182026Member_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertiblePromissoryNoteJuly182026Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to convertible promissory note issued on July 18, 2026.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertiblePromissoryNoteJuly182026Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Promissory Note July 18, 2026 [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertiblePromissoryNoteJuly182026Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">July 18 Note</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_ConvertiblePromissoryNoteJuly182027Member" xlink:label="cntm_ConvertiblePromissoryNoteJuly182027Member" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertiblePromissoryNoteJuly182027Member" xlink:to="cntm_ConvertiblePromissoryNoteJuly182027Member_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertiblePromissoryNoteJuly182027Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to convertible promissory note issued on July 18, 2027.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertiblePromissoryNoteJuly182027Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Promissory Note July 18, 2027 [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_ConvertiblePromissoryNoteJuly182027Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">July 18</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_ConvertiblePromissoryNoteMember" xlink:label="cntm_ConvertiblePromissoryNoteMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertiblePromissoryNoteMember" xlink:to="cntm_ConvertiblePromissoryNoteMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertiblePromissoryNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to a convertible promissory note.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertiblePromissoryNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Promissory Note [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertiblePromissoryNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible promissory note</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_UnsecuredConvertiblePromissoryNotesIssuedToInvestorsMember" xlink:label="cntm_UnsecuredConvertiblePromissoryNotesIssuedToInvestorsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_UnsecuredConvertiblePromissoryNotesIssuedToInvestorsMember" xlink:to="cntm_UnsecuredConvertiblePromissoryNotesIssuedToInvestorsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_UnsecuredConvertiblePromissoryNotesIssuedToInvestorsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to unsecured convertible promissory notes issued to investors.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_UnsecuredConvertiblePromissoryNotesIssuedToInvestorsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Unsecured Convertible Promissory Notes Issued To Investors [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_UnsecuredConvertiblePromissoryNotesIssuedToInvestorsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Unsecured convertible promissory notes issued to investors</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_SixInstallmentMember" xlink:label="cntm_SixInstallmentMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_SixInstallmentMember" xlink:to="cntm_SixInstallmentMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_SixInstallmentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">It represents the six installments.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_SixInstallmentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Six Installment [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_SixInstallmentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Six Installment</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_ThereafterSeventhInstallmentMember" xlink:label="cntm_ThereafterSeventhInstallmentMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ThereafterSeventhInstallmentMember" xlink:to="cntm_ThereafterSeventhInstallmentMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ThereafterSeventhInstallmentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">It represents thereafter seventh installments.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ThereafterSeventhInstallmentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Thereafter, Seventh Installment [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ThereafterSeventhInstallmentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Seventh Installments</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_GrossProceedsFromConvertibleDebt" xlink:label="cntm_GrossProceedsFromConvertibleDebt" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_GrossProceedsFromConvertibleDebt" xlink:to="cntm_GrossProceedsFromConvertibleDebt_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_GrossProceedsFromConvertibleDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of gross proceeds from convertible debt.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_GrossProceedsFromConvertibleDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gross Proceeds From Convertible Debt</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DebtInstrumentAccompaniedCommitmentShares" xlink:label="cntm_DebtInstrumentAccompaniedCommitmentShares" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentAccompaniedCommitmentShares" xlink:to="cntm_DebtInstrumentAccompaniedCommitmentShares_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentAccompaniedCommitmentShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of commitment shares accompanied with the debt issuance.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentAccompaniedCommitmentShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Accompanied Commitment Shares</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentAccompaniedCommitmentShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance commitment shares</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DebInstrumentNumberOfConvertibleDebtFinancing" xlink:label="cntm_DebInstrumentNumberOfConvertibleDebtFinancing" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebInstrumentNumberOfConvertibleDebtFinancing" xlink:to="cntm_DebInstrumentNumberOfConvertibleDebtFinancing_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebInstrumentNumberOfConvertibleDebtFinancing_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of convertible debt financing entered.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebInstrumentNumberOfConvertibleDebtFinancing_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Deb Instrument, Number Of Convertible Debt Financing</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebInstrumentNumberOfConvertibleDebtFinancing_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of convertible debt financing</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DebtInstrumentPrepaymentNoticePeriod" xlink:label="cntm_DebtInstrumentPrepaymentNoticePeriod" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentPrepaymentNoticePeriod" xlink:to="cntm_DebtInstrumentPrepaymentNoticePeriod_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentPrepaymentNoticePeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of trading days' prior written notice required before voluntary prepayment of the debt instrument pursuant to the terms of the debt agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentPrepaymentNoticePeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument Prepayment Notice Period</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentPrepaymentNoticePeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of trading days of debt agreement</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DebtInstrumentPrepaymentAmountPercentage" xlink:label="cntm_DebtInstrumentPrepaymentAmountPercentage" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentPrepaymentAmountPercentage" xlink:to="cntm_DebtInstrumentPrepaymentAmountPercentage_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentPrepaymentAmountPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of outstanding principal and accrued interest required upon voluntary prepayment of the debt instrument.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentPrepaymentAmountPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Prepayment Amount Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentPrepaymentAmountPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of outstanding principal</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DebtInstrumentPrepaymentAdministrativeFeeAmount" xlink:label="cntm_DebtInstrumentPrepaymentAdministrativeFeeAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentPrepaymentAdministrativeFeeAmount" xlink:to="cntm_DebtInstrumentPrepaymentAdministrativeFeeAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentPrepaymentAdministrativeFeeAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Administrative fee required to be paid upon voluntary prepayment of the debt instrument in accordance with the terms of the debt agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentPrepaymentAdministrativeFeeAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument Prepayment Administrative Fee Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentPrepaymentAdministrativeFeeAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accrued interest plus</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DebtInstrumentDebtDefaultInterestRate" xlink:label="cntm_DebtInstrumentDebtDefaultInterestRate" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentDebtDefaultInterestRate" xlink:to="cntm_DebtInstrumentDebtDefaultInterestRate_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentDebtDefaultInterestRate_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contractual interest rate for funds borrowed, under the debt agreement in the event of default.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentDebtDefaultInterestRate_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Debt Default, Interest Rate</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentDebtDefaultInterestRate_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt instrument - interest rate in case of default</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DebtInstrumentIncreaseInNotePrincipalUponLossOfDepositoryTrustCompanyEligibility" xlink:label="cntm_DebtInstrumentIncreaseInNotePrincipalUponLossOfDepositoryTrustCompanyEligibility" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentIncreaseInNotePrincipalUponLossOfDepositoryTrustCompanyEligibility" xlink:to="cntm_DebtInstrumentIncreaseInNotePrincipalUponLossOfDepositoryTrustCompanyEligibility_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentIncreaseInNotePrincipalUponLossOfDepositoryTrustCompanyEligibility_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of increase in the note balance triggered by loss of DTC eligibility.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentIncreaseInNotePrincipalUponLossOfDepositoryTrustCompanyEligibility_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument , Increase in Note Principal Upon Loss of Depository Trust Company Eligibility</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentIncreaseInNotePrincipalUponLossOfDepositoryTrustCompanyEligibility_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">DTC eligibility principal balance increases</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DebtInstrumentLiquidatedDamagesPerDayForFailureToDeliverConversionShares" xlink:label="cntm_DebtInstrumentLiquidatedDamagesPerDayForFailureToDeliverConversionShares" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentLiquidatedDamagesPerDayForFailureToDeliverConversionShares" xlink:to="cntm_DebtInstrumentLiquidatedDamagesPerDayForFailureToDeliverConversionShares_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentLiquidatedDamagesPerDayForFailureToDeliverConversionShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of daily penalty payable for late delivery of conversion shares under the convertible note agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentLiquidatedDamagesPerDayForFailureToDeliverConversionShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Liquidated Damages Per Day for Failure to Deliver Conversion Shares</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentLiquidatedDamagesPerDayForFailureToDeliverConversionShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Conversion shares triggers liquidated damages</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DebtInstrumentConversionPriceAsPercentageOfMarketPrice" xlink:label="cntm_DebtInstrumentConversionPriceAsPercentageOfMarketPrice" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentConversionPriceAsPercentageOfMarketPrice" xlink:to="cntm_DebtInstrumentConversionPriceAsPercentageOfMarketPrice_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentConversionPriceAsPercentageOfMarketPrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of the market price used to determine the conversion price under debt agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentConversionPriceAsPercentageOfMarketPrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Conversion Price as Percentage of Market Price</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentConversionPriceAsPercentageOfMarketPrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Conversion price percentage</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DebtInstrumentBeneficialOwnershipLimitationPercentage" xlink:label="cntm_DebtInstrumentBeneficialOwnershipLimitationPercentage" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentBeneficialOwnershipLimitationPercentage" xlink:to="cntm_DebtInstrumentBeneficialOwnershipLimitationPercentage_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentBeneficialOwnershipLimitationPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the percentage of the issuer's outstanding common stock that the holder may beneficially own following conversion of the convertible debt instrument.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentBeneficialOwnershipLimitationPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Beneficial Ownership Limitation Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentBeneficialOwnershipLimitationPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Beneficial ownership limitation</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DebtInstrumentOneTimeInterestChargeAmount" xlink:label="cntm_DebtInstrumentOneTimeInterestChargeAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentOneTimeInterestChargeAmount" xlink:to="cntm_DebtInstrumentOneTimeInterestChargeAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentOneTimeInterestChargeAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of one-time interest charge on the debt instrument.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentOneTimeInterestChargeAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, One Time Interest Charge, Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentOneTimeInterestChargeAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">One time interest amount</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_PercentageOfConvertibleBeneficialOwnershipLimitation" xlink:label="cntm_PercentageOfConvertibleBeneficialOwnershipLimitation" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_PercentageOfConvertibleBeneficialOwnershipLimitation" xlink:to="cntm_PercentageOfConvertibleBeneficialOwnershipLimitation_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_PercentageOfConvertibleBeneficialOwnershipLimitation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of conversion notice, subject to beneficial ownership limitation.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_PercentageOfConvertibleBeneficialOwnershipLimitation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage Of Convertible Beneficial Ownership Limitation</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_PercentageOfConvertibleBeneficialOwnershipLimitation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Beneficial ownership limitation</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DebtInstrumentConversionRestrictionPeriod" xlink:label="cntm_DebtInstrumentConversionRestrictionPeriod" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentConversionRestrictionPeriod" xlink:to="cntm_DebtInstrumentConversionRestrictionPeriod_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentConversionRestrictionPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the period from issuance during which the holder may not convert the convertible note into common stock.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentConversionRestrictionPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Conversion Restriction Period</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentConversionRestrictionPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Lock up period for conversion</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DebtInstrumentConversionPricePercentageDuringDepositoryTrustCompany" xlink:label="cntm_DebtInstrumentConversionPricePercentageDuringDepositoryTrustCompany" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentConversionPricePercentageDuringDepositoryTrustCompany" xlink:to="cntm_DebtInstrumentConversionPricePercentageDuringDepositoryTrustCompany_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentConversionPricePercentageDuringDepositoryTrustCompany_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the conversion price percentage applied to the lowest trading price of the issuer's common stock during a DTC chill.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentConversionPricePercentageDuringDepositoryTrustCompany_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Conversion Price Percentage During Depository Trust Company</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentConversionPricePercentageDuringDepositoryTrustCompany_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Conversion price percentage subject to DTC</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DebtInstrumentBeneficialOwnershipLimitationIncreasePeriod" xlink:label="cntm_DebtInstrumentBeneficialOwnershipLimitationIncreasePeriod" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentBeneficialOwnershipLimitationIncreasePeriod" xlink:to="cntm_DebtInstrumentBeneficialOwnershipLimitationIncreasePeriod_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentBeneficialOwnershipLimitationIncreasePeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the advance notice period required to increase the beneficial ownership limitation under the convertible debt instrument.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentBeneficialOwnershipLimitationIncreasePeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Beneficial Ownership Limitation, Increase Period</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentBeneficialOwnershipLimitationIncreasePeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Beneficial ownership limitation increase period</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DebtInstrumentPrepaymentPremiumPercentage" xlink:label="cntm_DebtInstrumentPrepaymentPremiumPercentage" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentPrepaymentPremiumPercentage" xlink:to="cntm_DebtInstrumentPrepaymentPremiumPercentage_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentPrepaymentPremiumPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the percentage of outstanding principal and accrued interest required to be paid upon prepayment of the convertible debt instrument.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentPrepaymentPremiumPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Prepayment Premium Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentPrepaymentPremiumPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Prepayment premium percentage</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DebtInstrumentPrepaymentRightExpirationPeriod" xlink:label="cntm_DebtInstrumentPrepaymentRightExpirationPeriod" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentPrepaymentRightExpirationPeriod" xlink:to="cntm_DebtInstrumentPrepaymentRightExpirationPeriod_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentPrepaymentRightExpirationPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the period after issuance during which early redemption of the convertible debt instrument is permitted.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentPrepaymentRightExpirationPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Prepayment Right Expiration Period</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentPrepaymentRightExpirationPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Prepayment premium expiration period</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DebtInstrumentSharesReservedForConversion" xlink:label="cntm_DebtInstrumentSharesReservedForConversion" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentSharesReservedForConversion" xlink:to="cntm_DebtInstrumentSharesReservedForConversion_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentSharesReservedForConversion_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of common shares required to be reserved by the company for issuance upon conversion of the debt instrument.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentSharesReservedForConversion_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Shares Reserved For Conversion</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentSharesReservedForConversion_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of shares reserved for conversion</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DebtInstrumentNumberOfCommitmentSharesIssued" xlink:label="cntm_DebtInstrumentNumberOfCommitmentSharesIssued" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentNumberOfCommitmentSharesIssued" xlink:to="cntm_DebtInstrumentNumberOfCommitmentSharesIssued_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentNumberOfCommitmentSharesIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of commitment shares issued in connection with the debt instrument.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentNumberOfCommitmentSharesIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Number Of Commitment Shares Issued</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentNumberOfCommitmentSharesIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of commitment shares issued</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DebtInstrumentConversionHolderFeeAmount" xlink:label="cntm_DebtInstrumentConversionHolderFeeAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentConversionHolderFeeAmount" xlink:to="cntm_DebtInstrumentConversionHolderFeeAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentConversionHolderFeeAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of fee deducted by the note holder from the conversion amount upon conversion of outstanding principal and interest into common stock.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentConversionHolderFeeAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Conversion Holder Fee Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentConversionHolderFeeAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Beneficial ownership limitation</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DebtInstrumentConversionShareReserveMultiplier" xlink:label="cntm_DebtInstrumentConversionShareReserveMultiplier" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentConversionShareReserveMultiplier" xlink:to="cntm_DebtInstrumentConversionShareReserveMultiplier_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentConversionShareReserveMultiplier_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Multiplier applied to the number of shares issuable upon full conversion of the debt instrument to determine the required share reserve amount.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentConversionShareReserveMultiplier_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Conversion Share Reserve Multiplier</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentConversionShareReserveMultiplier_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of shares issuable upon full conversion</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DebtInstrumentAnnualInterestPayment" xlink:label="cntm_DebtInstrumentAnnualInterestPayment" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentAnnualInterestPayment" xlink:to="cntm_DebtInstrumentAnnualInterestPayment_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentAnnualInterestPayment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of annual interest payment for debt instrument.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentAnnualInterestPayment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Annual Interest Payment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentAnnualInterestPayment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Guaranteed and issuance interest payment</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentPeriodicPaymentPrincipal" xlink:label="us-gaap_DebtInstrumentPeriodicPaymentPrincipal" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentPeriodicPaymentPrincipal" xlink:to="us-gaap_DebtInstrumentPeriodicPaymentPrincipal_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentPeriodicPaymentPrincipal_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Periodic Payment, Principal</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DebtInstrumentPeriodicPaymentPrincipal_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Principle payments of debt instrument</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DebtInstrumentThresholdPeriodForInitiatingRepaymentPeriodicPayment" xlink:label="cntm_DebtInstrumentThresholdPeriodForInitiatingRepaymentPeriodicPayment" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentThresholdPeriodForInitiatingRepaymentPeriodicPayment" xlink:to="cntm_DebtInstrumentThresholdPeriodForInitiatingRepaymentPeriodicPayment_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentThresholdPeriodForInitiatingRepaymentPeriodicPayment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Threshold period for initiating repayment of periodic payment.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentThresholdPeriodForInitiatingRepaymentPeriodicPayment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Threshold Period for Initiating Repayment Periodic Payment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentThresholdPeriodForInitiatingRepaymentPeriodicPayment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Repayment threshold period</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsidiarySaleOfStockAxis" xlink:label="us-gaap_SubsidiarySaleOfStockAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SubsidiarySaleOfStockAxis" xlink:to="us-gaap_SubsidiarySaleOfStockAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SubsidiarySaleOfStockAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Sale of Stock [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SaleOfStockNameOfTransactionDomain" xlink:label="us-gaap_SaleOfStockNameOfTransactionDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SaleOfStockNameOfTransactionDomain" xlink:to="us-gaap_SaleOfStockNameOfTransactionDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SaleOfStockNameOfTransactionDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Sale of Stock [Domain]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PrivatePlacementMember" xlink:label="us-gaap_PrivatePlacementMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PrivatePlacementMember" xlink:to="us-gaap_PrivatePlacementMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PrivatePlacementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Private Placement [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PrivatePlacementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Private Placement</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_NumberOfAccreditedInvestors" xlink:label="cntm_NumberOfAccreditedInvestors" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_NumberOfAccreditedInvestors" xlink:to="cntm_NumberOfAccreditedInvestors_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_NumberOfAccreditedInvestors_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of accredited investors participated in the stock transaction.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_NumberOfAccreditedInvestors_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number Of Accredited Investors</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_NumberOfAccreditedInvestors_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of accredited investors</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SharesIssuedPricePerShare" xlink:label="us-gaap_SharesIssuedPricePerShare" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SharesIssuedPricePerShare" xlink:to="us-gaap_SharesIssuedPricePerShare_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SharesIssuedPricePerShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Shares Issued, Price Per Share</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_SharesIssuedPricePerShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Purchase price, per unit</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromIssuanceOfCommonStock" xlink:label="us-gaap_ProceedsFromIssuanceOfCommonStock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ProceedsFromIssuanceOfCommonStock" xlink:to="us-gaap_ProceedsFromIssuanceOfCommonStock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ProceedsFromIssuanceOfCommonStock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from Issuance of Common Stock</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ProceedsFromIssuanceOfCommonStock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from issuance of common stock</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_ConnectmBabioneLlcAndBourqueHeatingCoolingCoIncMember" xlink:label="cntm_ConnectmBabioneLlcAndBourqueHeatingCoolingCoIncMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConnectmBabioneLlcAndBourqueHeatingCoolingCoIncMember" xlink:to="cntm_ConnectmBabioneLlcAndBourqueHeatingCoolingCoIncMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConnectmBabioneLlcAndBourqueHeatingCoolingCoIncMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information pertaining to ConnectM Babione LLC and Bourque Heating &amp; Cooling Co., Inc.,</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConnectmBabioneLlcAndBourqueHeatingCoolingCoIncMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">ConnectM Babione LLC and Bourque Heating &amp; Cooling Co Inc [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConnectmBabioneLlcAndBourqueHeatingCoolingCoIncMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Purchase order financing advance</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentFeeAmount" xlink:label="us-gaap_DebtInstrumentFeeAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentFeeAmount" xlink:to="us-gaap_DebtInstrumentFeeAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentFeeAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Fee Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DebtInstrumentFeeAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Origination fees</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DebtInstrumentAccruedFee" xlink:label="cntm_DebtInstrumentAccruedFee" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentAccruedFee" xlink:to="cntm_DebtInstrumentAccruedFee_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentAccruedFee_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of fee payable in association with debt instrument.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentAccruedFee_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Accrued Fee</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentAccruedFee_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of fee payable</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DebtInstrumentPercentageOfSalesReceiptsToBeRemitted" xlink:label="cntm_DebtInstrumentPercentageOfSalesReceiptsToBeRemitted" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentPercentageOfSalesReceiptsToBeRemitted" xlink:to="cntm_DebtInstrumentPercentageOfSalesReceiptsToBeRemitted_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentPercentageOfSalesReceiptsToBeRemitted_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The percentage of sales receipts to be remitted by the entity as per the terms of the debt instrument.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentPercentageOfSalesReceiptsToBeRemitted_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Percentage Of Sales Receipts To Be Remitted</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentPercentageOfSalesReceiptsToBeRemitted_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of sales receipts to be remitted</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DebtInstrumentSalesReceiptsToBeRemittedDaily" xlink:label="cntm_DebtInstrumentSalesReceiptsToBeRemittedDaily" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentSalesReceiptsToBeRemittedDaily" xlink:to="cntm_DebtInstrumentSalesReceiptsToBeRemittedDaily_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentSalesReceiptsToBeRemittedDaily_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The amount of sales receipts to be remitted daily by the entity as per the terms of the debt instrument.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentSalesReceiptsToBeRemittedDaily_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Sales Receipts To Be Remitted Daily</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentSalesReceiptsToBeRemittedDaily_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of initial estimated daily remittance</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DebtInstrumentSalesReceiptsToBeRemittedWeekly" xlink:label="cntm_DebtInstrumentSalesReceiptsToBeRemittedWeekly" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentSalesReceiptsToBeRemittedWeekly" xlink:to="cntm_DebtInstrumentSalesReceiptsToBeRemittedWeekly_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentSalesReceiptsToBeRemittedWeekly_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The amount of sales receipts to be remitted weekly by the entity as per the terms of the debt instrument.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentSalesReceiptsToBeRemittedWeekly_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Sales Receipts To Be Remitted Weekly</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentSalesReceiptsToBeRemittedWeekly_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of initial estimated weekly remittance</label>
    <loc xlink:type="locator" xlink:href="cntm-20260630.xsd#cntm_DebtInstrumentAnnualPercentageRate" xlink:label="cntm_DebtInstrumentAnnualPercentageRate" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentAnnualPercentageRate" xlink:to="cntm_DebtInstrumentAnnualPercentageRate_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentAnnualPercentageRate_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Annual interest rate for funds borrowed, under the debt agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentAnnualPercentageRate_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Annual Percentage Rate</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentAnnualPercentageRate_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Annual interest rate for funds borrowed</label>
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