ConnectedComponents

ConnectedComponents[g] gives the connected components of graph g as lists of vertices.

Examples

Find connected components:

g = Graph[{1 <-> 2, 2 <-> 3, 4 <-> 5}]
ConnectedComponents[g]
(* {{1, 2, 3}, {4, 5}} *)

Single connected graph:

ConnectedComponents[CompleteGraph[5]]
(* {{1, 2, 3, 4, 5}} *)

Number of components:

Length[ConnectedComponents[g]]
(* 2 *)

Please visit the official Wolfram Language Reference for more details.