Abstract
This chapter describes two graphs. The notion of a regular two-graph was proposed by G. Higman as a setting for the 2-transitive representation for certain simple groups. This idea was worked out by Taylor. It turned out that strong relations exist with the switching of graphs. A two-graph (V, ) consists of a set V (the vertices) and a collection of triples of vertices (the odd triples), such that for each 4 vertices the number of odd triples is even. In a regular two-graph, each pair of vertices is in a constant number of odd triples.
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