[Math] Simple Directed Graph

Question

In graph theory, would a graph with edges $(u, v)$ and $(v, u)$ connecting vertices $v$ and $u$ be considered a directed simple graph? For example: would this graph be considered a simple directed graph?

Thanks for your help.

Answer 1

Yes, that is a simple directed graph (it has neither loops nor multiple arrows with the same source and target). However it is not a directed acyclic graph, because $u,v$ (or $1,3$ in your picture) form a directed cycle. See here for a description of many directed graph types.