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This paper uses the concept of the triad census as developed 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. [ABSTRACT FROM AUTHOR]

Loglinear models are adapted for the analysis of multivariate social networks, a set of sociometric relations among a group of actors. Models that focus on the similarities and differences between the relations and models that concentrate on individual actors are discussed. This approach allows for the partitioning of the actors into blocks or subgroups. Some ideas for combining these models are described, and the various models and computational methods are applied to the analysis of data for a corporate interlock network of the 25 largest organizations in Minneapolis/St. Paul and for a classic network of 18 monks in a cloister. The computational techniques all involve variations on the standard iterative proportional-fitting algorithm used extensively in the analysis of multidimensional contingency tables. [ABSTRACT FROM AUTHOR]