I am trying to do some experiments involving random regular digraphs. After a bit of poking around

https://www.math.cmu.edu/~af1p/BOOK.pdf

and

Computational Discrete Mathematics: Combinatorics and Graph Theory with Mathematica

https://www.amazon.com/Computational-Discrete-Mathematics-Combinatorics-Mathematica/dp/0521121469

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.