Biconnected Graph Definition/Meaning:
A graph G, either directed or undirected, with the property
that for every three distinct vertices u, v, and w there is a path from u to w
not containing v. For an undirected graph, this is equivalent to the graph
having no cut vertex.
Two edges of an undirected graph are said to be related either if they are
identical or if there is a cycle containing both of them. This is an
equivalence relation and partitions the edges into a set of equivalence classes, E1,
E2... En, say. Let Vi be the set of vertices of the edges of Ei,
for i = 1,2,... n. Then each graph Gi formed from the vertices Vi and the edges
Ei is a biconnected component of G.