Clustering of dyad distributions as a tool in network modeling

A general approach to exploratory analysis and modeling of network data is to investigate dyad distributions. We discuss clustering of dyad distributions when there are several variables defined on the vertices, and these variables interact with the arc values of the network. As an illustration we use data on achievement, race, sex and friendship for children in 48 different school classes. A clustering of the dyad distributions leads to the formulation of a log-linear model for friendship structure explained by achievement, race, and sex parameters. In particular, the example illustrates a way to find and display interaction structures in network data. We comment on how this approach is related to standard use of log-linear network models