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KEdgeConnectedGraphQ[g,k]

yields True if the graph g is k-edge-connected and False otherwise.

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KEdgeConnectedGraphQ

KEdgeConnectedGraphQ[g,k]

yields True if the graph g is k-edge-connected and False otherwise.

Details

  • A graph is k-edge-connected if there are at least k edge-disjoint paths between every pair of vertices.

Examples

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Basic Examples  (2)

Test whether a graph is 2-edge-connected:

Wolfram Language code: Graph[{12, 23, 31}]
Wolfram Language code: KEdgeConnectedGraphQ[%, 2]

A graph with isolated vertices is not k-edge-connected:

Wolfram Language code: Graph[{1, 2, 3, 4, 5}, {12, 23, 31, 45}]
Wolfram Language code: KEdgeConnectedGraphQ[%, 1]

Scope  (5)

Test undirected graphs:

Wolfram Language code: KEdgeConnectedGraphQ[[image], 2]

Directed graphs:

Wolfram Language code: KEdgeConnectedGraphQ[[image], 2]

Multigraphs:

Wolfram Language code: KEdgeConnectedGraphQ[[image], 2]

Mixed graphs:

Wolfram Language code: KEdgeConnectedGraphQ[[image], 2]

KEdgeConnectedGraphQ gives False for anything that is not a k-connected graph:

Wolfram Language code: KEdgeConnectedGraphQ[x, 1]

Properties & Relations  (3)

The complete graph is -edge-connected:

Wolfram Language code: KEdgeConnectedGraphQ[CompleteGraph[4], 3]

An undirected tree is 1-edge-connected:

Wolfram Language code: TreeGraph[{12, 13, 14}]
Wolfram Language code: {KEdgeConnectedGraphQ[%, 1], KEdgeConnectedGraphQ[%, 2]}

A k-edge-connected graph has edge connectivity greater than or equal to k:

Wolfram Language code: g = [image];
Wolfram Language code: EdgeConnectivity[g]
Wolfram Language code: KEdgeConnectedGraphQ[g, 2]
Wolfram Language code: KEdgeConnectedGraphQ[g, 3]
Wolfram Research (2014), KEdgeConnectedGraphQ, Wolfram Language function, https://reference.wolfram.com/language/ref/KEdgeConnectedGraphQ.html.

Text

Wolfram Research (2014), KEdgeConnectedGraphQ, Wolfram Language function, https://reference.wolfram.com/language/ref/KEdgeConnectedGraphQ.html.

CMS

Wolfram Language. 2014. "KEdgeConnectedGraphQ." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/KEdgeConnectedGraphQ.html.

APA

Wolfram Language. (2014). KEdgeConnectedGraphQ. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/KEdgeConnectedGraphQ.html

BibTeX

@misc{reference.wolfram_2026_kedgeconnectedgraphq, author="Wolfram Research", title="{KEdgeConnectedGraphQ}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/KEdgeConnectedGraphQ.html}", note=[Accessed: 12-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_kedgeconnectedgraphq, organization={Wolfram Research}, title={KEdgeConnectedGraphQ}, year={2014}, url={https://reference.wolfram.com/language/ref/KEdgeConnectedGraphQ.html}, note=[Accessed: 12-June-2026]}