
We do this for every node x
for ( each node "n" ∈ G ) { Find all nodes x that can be reached by a traveral starting in "n"; if ( # nodes reached != N ) return( G is not strongly connected ); } return( G is strongly connected ); 


Observation:

Note:


Select an arbitrary node x; A = set of node reached by a DFS/BFS in the forward path graph starting at x; if ( A ≠ all nodes in graph ) { return ( not strongly connected ); } B = set of node reached by a DFS/BFS in the reverse path graph starting at x; if ( B ≠ all nodes in graph ) { return ( not strongly connected ); } return ( strongly connected ); 