ConnectedComponents

ConnectedComponents[g]
gives the connected components of the graph g.

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

ConnectedComponents[g,patt]
gives the connected components that include a vertex that matches the pattern patt.

DetailsDetails

  • ConnectedComponents returns a list of components , where each component is given as a list of vertices.
  • For an undirected graph, the vertices u and v are in the same component if there is a path from u to v.
  • For a directed graph, the vertices u and v are in the same component if there is a directed path from u to v and from v to u.
  • For directed graphs, strongly connected components are computed.
  • For undirected graphs, the components are ordered by their length, with the largest component first.
  • For directed graphs, the components are given in an order such that there are no edges from to , , etc.
  • ConnectedComponents works with undirected graphs, directed graphs, multigraphs, and mixed graphs.
Introduced in 2010
(8.0)
| Updated in 2014
(10.0)