KEdgeConnectedComponents

KEdgeConnectedComponents[g,k]
gives the k-edge-connected components of the graph g.

KEdgeConnectedComponents[g,k,{v1,v2,}]
gives the k-edge-connected components that include at least one of the vertices , , .

DetailsDetails

  • KEdgeConnectedComponents is also known as k-edge components.
  • KEdgeConnectedComponents returns a list of components , where each component is given as a list of vertices.
  • The component generates a maximal k-edge-connected subgraph of g.
  • For an undirected graph, the vertices u and v are in the same component if there are at least k edge-disjoint paths from u to v.
  • For a directed graph, the vertices u and v are in the same component if there are at least k edge-disjoint directed paths from u to v and from v to u.

ExamplesExamplesopen allclose all

Basic Examples  (2)Basic Examples  (2)

Find 3-edge-connected components of a graph:

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Show the 3-edge-connected components:

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Find the 4-edge-connected components in a social network:

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Introduced in 2014
(10.0)