# KVertexConnectedComponents

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

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

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

# Details

• KVertexConnectedComponents is also known as k-connected components.
• KVertexConnectedComponents 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-vertex-connected subgraph of g.
• For an undirected graph, the vertices u and v are in the same component if there are at least k vertex-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 vertex-disjoint directed paths from u to v and from v to u.

# Examples

open allclose all

## Basic Examples(2)

Find 2-connected components of a graph:

Show the 2-connected components:

Find the 2-connected components in a social network:

## Scope(4)

KVertexConnectedComponents works with undirected graphs:

Select 2-connected components that include at least one of the specified vertices:

Use patterns to select components:

Works with large graphs:

## Applications(1)

Highlight the k-connected components of a graph:

## Properties & Relations(1)

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

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

#### Text

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

#### CMS

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

#### APA

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

#### BibTeX

@misc{reference.wolfram_2024_kvertexconnectedcomponents, author="Wolfram Research", title="{KVertexConnectedComponents}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/KVertexConnectedComponents.html}", note=[Accessed: 21-July-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_kvertexconnectedcomponents, organization={Wolfram Research}, title={KVertexConnectedComponents}, year={2014}, url={https://reference.wolfram.com/language/ref/KVertexConnectedComponents.html}, note=[Accessed: 21-July-2024 ]}