Taking the reverse respects going to the strongly connected component graph

Lemma

Let be a directed graph and be its reverse. Then if is strongly connected component graph of then the reverse of is equal the strongly connected component graph of called . I.e. .

Proof

As the strongly connected components are the same in a directed graph and its reverse we know and have the same vertex set.

The edge set for is therefore the edge set for is Which by the definition of reverse could be rephrased as This is exactly the definition of the edge set for giving the required statement.