# VertexConnectivity

gives the vertex connectivity of the graph g.

VertexConnectivity[g,s,t]

gives the s-t vertex connectivity of the graph g.

VertexConnectivity[{vw,},]

uses rules vw to specify the graph g.

# Details

• VertexConnectivity is also known as connectivity or point connectivity.
• The vertex connectivity of a graph g is the smallest number of vertices whose deletion from g disconnects g.
• The s-t vertex connectivity is the smallest number of vertices whose deletion from g disconnects g with s and t in two different connected components.
• For a disconnected graph, VertexConnectivity will return 0.
• VertexConnectivity works with undirected graphs, directed graphs, multigraphs, and mixed graphs.

# Examples

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## Basic Examples(2)

Find the vertex connectivity:

Find the vertex connectivity between two vertices:

## Scope(6)

VertexConnectivity works on undirected graphs:

Directed graphs:

Multigraphs:

Mixed graphs:

Use rules to specify the graph:

VertexConnectivity works on large graphs:

## Properties & Relations(1)

Use FindVertexCut to compute the vertex connectivity:

Wolfram Research (2012), VertexConnectivity, Wolfram Language function, https://reference.wolfram.com/language/ref/VertexConnectivity.html (updated 2015).

#### Text

Wolfram Research (2012), VertexConnectivity, Wolfram Language function, https://reference.wolfram.com/language/ref/VertexConnectivity.html (updated 2015).

#### CMS

Wolfram Language. 2012. "VertexConnectivity." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2015. https://reference.wolfram.com/language/ref/VertexConnectivity.html.

#### APA

Wolfram Language. (2012). VertexConnectivity. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/VertexConnectivity.html

#### BibTeX

@misc{reference.wolfram_2024_vertexconnectivity, author="Wolfram Research", title="{VertexConnectivity}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/VertexConnectivity.html}", note=[Accessed: 16-June-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_vertexconnectivity, organization={Wolfram Research}, title={VertexConnectivity}, year={2015}, url={https://reference.wolfram.com/language/ref/VertexConnectivity.html}, note=[Accessed: 16-June-2024 ]}