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.
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