Simple Directed Graph?

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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.

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1 Answer

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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.

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