A minimum vertex cut of a graph is a vertex cut of smallest possible size. A vertex cut set of size 1 in a connected graph corresponds to an articulation vertex. The size of a minimum vertex cut in a connected graph G gives the vertex connectivity κ(G). Complete graphs have no vertex cuts since there is no subset of vertices whose removal disconnected a complete graph. A single minimum vertex cut of a connected graph G can be found in the Wolfram Language using the function FindVertexCut[G].

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FindVertexCut