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Paley graph

In mathematics, Paley graphs are undirected graphs constructed from the members of a suitable finite field by connecting pairs of elements that differ by a quadratic residue. The Paley graphs form an infinite family of conference graphs, which... Wikipedia
Diameter: 2
Edges: q(q − 1)/4
Properties: Strongly regular; Conference graph; Self-complementary
Vertices: q ≡ 1 mod 4, q prime power