A digraph is said to be strongly connected if for each vertex u of D, any other vertex of D is reachable from u. An equivalent definition is that D is strongly connected if the distance matrix of D has only positive terms in the non-diagonal entries.
i1 : D = digraph({1,2,3,4},{{1,2},{2,3},{3,4},{4,2}});
i2 : isStronglyConnected D
o2 = false
i3 : D' = digraph({1,2,3,4},{{1,2},{2,1},{2,3},{3,4},{4,2}});