Directed Strongly Regular Graph
A directed strongly regular graph is a simple directed graph with adjacency matrix A such that the span of A, the identity matrix I, and the unit matrix J is closed under matrix multiplication.
See also
Regular Graph, Simple Directed Graph, Simple Graph, Strongly Regular GraphExplore with Wolfram|Alpha
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Weisstein, Eric W. "Directed Strongly Regular Graph." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/DirectedStronglyRegularGraph.html