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VertexConnectivity

VertexConnectivity[g]

gives the vertex connectivity of the graph g.

VertexConnectivity[g,s,t]

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

VertexConnectivity[{vw,…},…]

uses rules vw 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 either disconnects g or reduces it to a single vertex graph.

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 (2)

The connectivity of a complete graph is :

Use FindVertexCut to compute the vertex connectivity:

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