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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:

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

Scope  (5)

Test undirected graphs:

Directed graphs:

Multigraphs:

Mixed graphs:

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

Properties & Relations  (3)

The complete graph is -edge-connected:

An undirected tree is 1-edge-connected:

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

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_2025_kedgeconnectedgraphq, author="Wolfram Research", title="{KEdgeConnectedGraphQ}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/KEdgeConnectedGraphQ.html}", note=[Accessed: 16-August-2025]}

BibLaTeX

@online{reference.wolfram_2025_kedgeconnectedgraphq, organization={Wolfram Research}, title={KEdgeConnectedGraphQ}, year={2014}, url={https://reference.wolfram.com/language/ref/KEdgeConnectedGraphQ.html}, note=[Accessed: 16-August-2025]}