 The Paley digraph is the directed graph with vertex set "V" = F"q" and arc set 

The Paley digraph is a tournament because each pair of distinct vertices is linked by an arc in one and only one direction.The Paley digraph leads to the construction of some antisymmetric conference matrices and biplane geometries.The six neighbors of each vertex in the Paley graph of order 13 are connected in a cycle; that is, the graph is locally cyclic.