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[{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:

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Find the vertex connectivity between two vertices:

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Scope  (6)

Properties & Relations  (1)

See Also

EdgeConnectivity  ConnectedComponents  HararyGraph

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