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Strong Connectivity

Explore the concept of strong connectivity in directed graphs and learn how to use depth-first search (DFS) to identify strongly connected components. Understand the equivalence relation of connectivity, how to implement DFS for this purpose, and analyze the structure of the strong component graph. Gain skills in efficiently computing strong connectivity and improving algorithm performance in graph problems.

Let’s go back to the proper definition of connectivity in directed graphs. Recall that one vertex uu can reach another vertex vv in a directed graph GG if GG contains a directed path from uu to vv, and that reach(u)reach(u) denotes the set of all vertices that uu can reach. Two vertices uu and vv are strongly connected if uu can reach ...