# 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 • 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.

# 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:

Introduced in 2012
(9.0)
|
Updated in 2015
(10.3)