Random Directed Graph Distributions in the Triad Census in Social Networks

Abstract

This paper uses the concept of the triad census first introduced by Holland and Leinhardt, and describes several distributions on directed graphs. Methods are presented for calculating the mean and the covariance matrix of the triad census for the uniform distribution that conditions on the number of choices made by each individual in the social network. Several complex distributions on digraphs are approximated, and an application of these methods to a sociogram is given.