BUILT-IN MATHEMATICA SYMBOL

# ConnectedComponents

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.

## ExamplesExamplesopen allclose all

### Basic Examples (2)Basic Examples (2)

Give the connected components for a complete graph:

 Out[1]=

Find connected components for a disconnected graph:

 Out[2]=

Highlight connected components:

 Out[3]=