In mathematics, a two-graph is a set of unordered triples chosen from a finite vertex set X, such that every unordered quadruple from X contains an even number of triples of the two-graph. A regular two-graph has the property that every pair of vertices lies in the same number of triples of the two-graph. Two-graphs have been studied because of their connection with equiangular lines and, for regular two-graphs, strongly regular graphs, and also finite groups because many regular two-graphs have interesting automorphism groups.
A two-graph is not a graph and should not be confused with other objects called 2-graphs in graph theory, such as 2-regular graphs.