An oriented graph is a directed graph having no symmetric pair of directed edges. A complete oriented graph is called a tournament.

The numbers of oriented graphs on , 2, ... nodes are 1, 2, 7, 42, 582, ... (OEIS A001174).

The numbers of connected oriented graphs on , 2, ... nodes are 1, 1, 5, 34, 535 ... (OEIS A086345).

More things to try:

Weisstein, Eric W. "Oriented Graph." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/OrientedGraph.html