Show that in an undirected graph, classifying an edge .u; / as a tree edge or a back edge according to whether .u; / or .; u/ is encountered first during the depth-first search is equivalent to classifying it according to the ordering of the four types in the classification scheme.

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Strongly Connected Components

 A directed graph in which a path exists between all its pairs of vertices is called a strongly connected graph. A portion of the strongly connected directed graph that contains a path to reach from each vertex to other vertices is called a strongly connected component (SCC).