"We have a directed graph, G. We say that G is moderately connected if for all vertices u & v of G there is a path from u to v or a path from v to u (but not both).
Show that if G is moderately connected then there is a vertex u in G such that for all other vertex in G there is a path from u to v."
isn't that kind of already proven??? I don't understand what to prove, it's obvious that if G is a moderately connected directed graph, then there is a path from some vertex u to v.