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FindVertexCut

FindVertexCut[g]

finds a smallest vertex cut of the graph g.

FindVertexCut[g,s,t]

finds a smallest s-t vertex cut of the graph g.

FindVertexCut[{vw,…},…]

uses rules vw to specify the graph g.

Details

A vertex cut is also known as vertex cut set or separating set.
A vertex cut of a graph g is a list of vertices whose deletion from g disconnects g.

The s-t vertex cut is a list of vertices whose deletion from g disconnects g, with s and t in two different connected components.
For a disconnected graph, FindVertexCut will return an empty list {}.

Examples

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Basic Examples (2)

Find a smallest vertex cut:

Highlight a vertex cut:

Find a smallest vertex cut between two vertices:

Scope (6)

FindVertexCut works with undirected graphs:

Directed graphs:

Multigraphs:

Mixed graphs:

Find a smallest s-t vertex cut:

Use rules to specify the graph:

Properties & Relations (1)

Use VertexConnectivity to obtain the size of the vertex cut:

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