Matrix methods for calculating the triad census

The triad census, T, of a directed network summarizes much of the structural information in a network. Thus, it has been very useful in analyzing structural properties within social networks. This paper presents a set of simple matrix formulas for calculating T. Previous work with the triad census has required enumerating each triad in the graph, which can be time consuming for very large networks. The formulas presented in this paper increase the efficiency of calculating T by an order of magnitude. Thus, these formulas provide researchers with very large networks, or the need to calculate T many times, an efficient tool for studying underlying structural patterns. (C) 1998 Elsevier Science B.V. All rights reserved.