What's the name for a digraph such that for each pair of vertices $u,v$, there is either a path from $u$ to $v$ or a path from $v$ to $u$? I'd call it just connected, since this is an intermediate property between weak and strong connectivity, and is in fact equivalent to the existence of a path containing all vertices. However, I'm not an expert of the subject, and I was unable to find any reference about this, so far.



Digraph intermediate connectivity
Just `connected' is fine. For example, [Wikipedia](http://en.wikipedia.org/wiki/Connectivity_%28graph_theory%29) and [Tutte](http://books.google.com/books?id=uTGhooU37h4C&lpg=PP1&dq=graph%2520theory&pg=PA132#v=onepage&q&f=false) agree. However, since "the number of systems of terminology presently used in graph theory is equal, to a close approximation, to the number of graph theorists," (R.P. Stanley, 1986) you might want to include the definition anyway.


