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A multilevel network is defined as the junction of two interaction networks,one level representing the interactions between individuals and the other theinteractions between organizations. The levels are linked by an affiliationrelationship, each individual belonging to a unique organization. A newStochastic Block Model is proposed as a unified probalistic framework tailoredfor multilevel networks. This model contains latent blocks accounting forheterogeneity in the patterns of connection within each level and introducingdependencies between the levels. The sought connection patterns are notspecified a priori which makes this approach flexible. Variational methods areused for the model inference and an Integrated Classified Likelihood criterionis developed for choosing the number of blocks and also for deciding whetherthe two levels are dependent or not. A comprehensive simulation study exhibitsthe benefit of considering this approach, illustrates the robustness of theclustering and highlights the reliability of the criterion used for modelselection. This approach is applied on a sociological dataset collected duringa television program trade fair, the inter-organizational level being theeconomic network between companies and the inter-individual level being theinformal network between their representatives. It brings a syntheticrepresentation of the two networks unraveling their intertwined structure andconfirms the coopetition at stake.

A Stochastic Block Model Approach for the Analysis of Multilevel Networks: an Application to the Sociology of Organizations