# KEdgeConnectedComponents

gives the k-edge-connected components of the graph g.

KEdgeConnectedComponents[g,k,{v1,v2,}]

gives the k-edge-connected components that include at least one of the vertices v1, v2, .

KEdgeConnectedComponents[{vw,},]

uses rules vw to specify the graph g.

# Details

• KEdgeConnectedComponents is also known as k-edge components.
• KEdgeConnectedComponents returns a list of components {c1,c2,}, where each component ci is given as a list of vertices.
• The component ci generates a maximal k-edge-connected subgraph of g.
• For an undirected graph, the vertices u and v are in the same component if there are at least k edge-disjoint paths from u to v.
• For a directed graph, the vertices u and v are in the same component if there are at least k edge-disjoint directed paths from u to v and from v to u.

# Examples

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## Basic Examples(2)

Find 3-edge-connected components of a graph:

Show the 3-edge-connected components:

Find the 4-edge-connected components in a social network:

## Scope(8)

KEdgeConnectedComponents works with undirected graphs:

Directed graphs:

Multigraphs:

Mixed graphs:

Select 3-edge-connected components that include at least one of the specified vertices:

Use rules to specify the graph:

Use patterns to select components:

Works with large graphs:

## Applications(1)

Highlight the k-edge-connected components of a graph:

## Properties & Relations(1)

A k-edge-connected graph has a k-edge-connected component as itself:

Wolfram Research (2014), KEdgeConnectedComponents, Wolfram Language function, https://reference.wolfram.com/language/ref/KEdgeConnectedComponents.html (updated 2015).

#### Text

Wolfram Research (2014), KEdgeConnectedComponents, Wolfram Language function, https://reference.wolfram.com/language/ref/KEdgeConnectedComponents.html (updated 2015).

#### CMS

Wolfram Language. 2014. "KEdgeConnectedComponents." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2015. https://reference.wolfram.com/language/ref/KEdgeConnectedComponents.html.

#### APA

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

#### BibTeX

@misc{reference.wolfram_2024_kedgeconnectedcomponents, author="Wolfram Research", title="{KEdgeConnectedComponents}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/KEdgeConnectedComponents.html}", note=[Accessed: 22-May-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_kedgeconnectedcomponents, organization={Wolfram Research}, title={KEdgeConnectedComponents}, year={2015}, url={https://reference.wolfram.com/language/ref/KEdgeConnectedComponents.html}, note=[Accessed: 22-May-2024 ]}