compute edge connectivity of a graph
compute vertex connectivity of a graph
EdgeConnectivity returns the edge connectivity of a graph, that is the minimum number of edges whose removal disconnects the graph. A set of such edges is called an edge-cut. You can use the IsCutSet command to test whether a set of edges is an edge-cut.
VertexConnectivity returns the vertex connectivity of a graph, that is the minimum number of vertices whose removal disconnects the graph.
By an elementary theorem of graph theory, the vertex connectivity of a graph is less than or equal to the edge connectivity, which is less than or equal to the minimum degree.
G ≔ Graph⁡1,2,1,3,2,3,1,4,3,4,4,5,5,6,4,6
G≔Graph 1: an undirected graph with 6 vertices and 8 edge(s)
P ≔ PetersenGraph⁡
P≔Graph 2: an undirected graph with 10 vertices and 15 edge(s)
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