A graph is called connected if every pair of distinct vertices in the graph is connected (directly or indirectly). A connected component is a maximal connected subgraph of G. Each vertex belongs to exactly one connected component, as does each edge. A directed graph is called weakly connected if replacing all of its directed edges with undirected edges produces a connected (undirected) graph. It is strongly connected or strong if it contains a directed path from u to v and a directed path from v to u for every pair of vertices u,v. The strong components are the maximal strongly connected subgraphs. See http://en.wikipedia.org/wiki/Connectivity_(graph_theory) We will only check for a connected un-directed graph or a weakly connected directed graph (same logic).

public virtual bool IsConnected()

Public Overridable Function IsConnected As Boolean