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Strong Connectivity

Explore the concept of strong connectivity in directed graphs by learning how two vertices can mutually reach each other, and how to identify maximal strongly connected components using depth-first search. Understand the algorithmic approach to find these components efficiently, the role of graph reversals, and how the component graph forms a directed acyclic graph, critical for advanced graph analysis.

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 ...