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ConnectedComponents

ConnectedComponents[g]
gives the connected components of the graph g.
ConnectedComponents
gives the connected components that include at least one of the vertices , , ....
  • 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.
Give the connected components for a complete graph:
For a disconnected graph:
Give the connected components for a complete graph:
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For a disconnected graph:
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ConnectedComponents works with undirected graphs:
Directed graphs:
The strongly connected components are computed:
Use UndirectedGraph to get the weakly connected components:
Works with large graphs:
An undirected graph which is connected has exactly one connected component:
Every graph with vertices and edges has at least components:
An undirected tree has only one connected component:
A directed tree has as many connected components as it has vertices:
An undirected path has only one connected component:
New in 8