I am trying to do some experiments involving random regular digraphs. After a bit of poking around
and
Computational Discrete Mathematics: Combinatorics and Graph Theory with Mathematica
the quickest thing I am coming up with is
DirectedGraph[
RandomGraph[DegreeGraphDistribution[{4, 4, 4, 4, 4, 4, 4, 4}]]]
This is almost what I need. The caveat is that DirectedGraph function is producing a directed graph from an undirected graph which makes output alway symmetric. I would like to avoid this limitation.
I have no problems producing random asymmetric digraphs from more primitive objects (list of vertices) but then I have a hard time with regularity condition.
Long story short. Can somebody give me some lead on this problem? Problem in its own right is probably trivial for a seasoned graph theorist but I am actually interested in dynamical systems which can be numerically simulated with random regular digraphs. I would like to get some kind numerical intuition about them.