OEIS A000273: Unlabeled Simple Digraphs

We explore unlabeled simple directed graphs with n vertices: what "simple" means (no loops, no multiple arrows in the same direction) and what "unlabeled" means (counting up to isomorphism). We discuss why counting non-isomorphic digraphs is hard due to symmetries, and how Burnside's lemma and the Pólya enumeration theorem help. We'll also look at the computational toolbox (Maple, Mathematica, PARI, Python) used to compute terms for bigger n and touch on connections to graphical enumeration in combinatorics and to applications in genetics, information theory, and distributed computing.

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