A simple directed graph is a directed graph having no multiple edges or graph loops (corresponding to a binary adjacency matrix with 0s on the diagonal). The number of simple directed graphs of n nodes for n = 1, 2, ... are 1, 3, 16, 218, 9608, ... (OEIS A000273), which is given by NumberOfDirectedGraphs[n] in the Wolfram Language package Combinatoricaˋ . The directed graphs on n nodes can be enumerated as ListGraphs[n, Directed] in the Wolfram Language package Combinatoricaˋ .
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