The Paley graph of order q with q a prime power is a graph on q nodes with two nodes adjacent if their difference is a square in the finite field GF(q). This graph is undirected when q congruent 1 (mod 4). Simple Paley graphs therefore exist for orders 5, 9, 13, 17, 25, 29, 37, 41, 49, 53, 61, 73, 81, 89, 97, 101, 109, 113, 121, 125, 137, 149, 157, 169, ... (OEIS A085759). Paley graphs are commonly denoted P(q) or Q R(q) , where "QR" stands for quadratic residue. Cyclotomic graphs are cubic analogs of the Paley graphs.

Brouwer-Haemers graph | conference graph | cyclotomic graph | finite field | Hadamard graph | Hadamard matrix | Paley construction | Paley's theorem | Paulus graphs | strongly regular graph