# The properties of almost all directed graphs

A mathematician on the forum previously requested a reference on human brains modelled as directed graphs. This makes sense as neurons are mostly unidirectional and I have been thinking about similar things recently.

In the same vein, might there be a good reference on random directed graphs that includes a section on the properties of almost all directed graphs? I must add that I'm looking for a text that is self-contained.

• Just one result, so not an answer to your question: Almost every $r$-regular digraph is Hamiltonian for $r \ge 3$. Cooper, Colin, Alan Frieze, and Michael Molloy. "Hamilton cycles in random regular digraphs." Combinatorics, Probability and Computing 3, no. 1 (1994): 39-49. Jul 30 '19 at 14:22