A graph G is connected if for each pair of vertices u and v in G there exists a path from u to v in G (if G is undirected), or in the underlying graph of G (if G is directed).

IsConnected returns true if the input graph is a connected graph or false otherwise. If G is a directed graph then the directions of edges are ignored. Use the IsStronglyConnected command to test whether each pair of vertices is connected by a directed path.

ConnectedComponents returns the components of the graph as a list of lists of vertices.  Each sublist is a list of vertices for a connected component.