Linear-time graph triples census algorithm under assumptions typical of social networks

Abstract

A graph triples census is a histogram of all possible sets of three vertici (called a triple) from a graph. Graph triples census have been in active use in sociology for over 50 years. The earliest paper using this approach is by Holland and Leinhardt [1]. This gives a general description of the structure of directed graphs in a fixed length vector. Since this time, this analytic tool has been widely used in social network analysis. A summary of important papers using this approach, both as end product and as a component of further analysis, are in[2].