Transitivity and the path census in sociometry

This paper develops a method for calculating the tendency towards transitivity while keeping constant the number of choices which are made by each member of the group (U_n(X_I+) distribution) or the number of times each member is chosen (U_N (X_+J) distribution). Such a calculation was suggested by Wasserman, who used the triad census developed by Holland and Leinhardt. This work presents a simpler way. This is accomplished by developing a path census and two supplementary functions. Our technique can be used to calculate the mean and variance of other quantities, such as mutuality and intransitivity. In order to enable researchers to use this technique, we present explicitly the mean and variance of the path census.