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We will amalgamate the Rash model (for rectangular binary tables) and thenewly introduced $\alpha$-$\beta$ models (for random undirected graphs) in theframework of a semiparametric probabilistic graph model. Our purpose is to givea partition of the vertices of an observed graph so that the generatedsubgraphs and bipartite graphs obey these models, where their stronglyconnected parameters give multiscale evaluation of the vertices at the sametime. In this way, a heterogeneous version of the stochastic block model isbuilt via mixtures of loglinear models and the parameters are estimated with aspecial EM iteration. In the context of social networks, the clusters can beidentified with social groups and the parameters with attitudes of people ofone group towards people of the other, which attitudes depend on the clustermemberships. The algorithm is applied to randomly generated and real-word data.

Estimating parameters of a multipartite loglinear graph model via the EM algorithm