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An optimal self-stabilizing algroithm is presented that ®nds the strongly connected components of a directed graph on an underlying network after OC† rounds, where C is the length of the longest cycle in the graph. Because the algorithm is self-stabilizing, it is resilient to transient faults and does not require initialization. The proposed algorithm can withstand topology changes in the form of addition or removal of edges and vertices. A correctness proof of the algorithm is provided.fatcat:s7dlsfjkajdfpev2vquyjbiq6m