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# vertexConnectivity -- computes the vertex connectivity of a graph

- Usage:
    `C = vertexConnectivity G`
- Inputs:
  - G, a graph,
- Outputs:
  - C, an integer, the vertex connectivity of a graph

## Description

The vertex connectivity of a graph is the smallest amount of vertices that need be removed from a graph to make it not connected or have one vertex. This corresponds to the size of the smallest vertex cut. A not connected graph has connectivity equal to 0.

    i1 : G = graph({{1,2},{2,3},{3,1},{3,4},{4,5},{5,3}},EntryMode=>"edges");

    i2 : vertexConnectivity G

    o2 = 1

## See also

- minimalVertexCuts -- finds the minimal vertex cuts of a graph
- vertexCuts -- lists all the vertex cuts of a graph
- edgeConnectivity -- computes the edge connectivity of a graph

## Ways to use vertexConnectivity:

- `vertexConnectivity(Graph)`

## For the programmer

The object vertexConnectivity is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/Graphs.m2:2986:0.