1989): the number of times each possible constant-order graph occurs as a subgraph of a Paley graph is (in the limit for large q) the same as for random graphs, and large sets of vertices have approximately the same number of edges as they would in random graphs.
The study of the relationship between constant-order graphs and Paley graphs suggests that as the size of the graph increases, the occurrence of specific types of graphs becomes more like random graphs. This also holds true for sets of vertices with similar sizes, which exhibit comparable edge counts to those found in random graphs.