Stochastic block model for multilevel networks unravels structural interdependence between the social and economic networks in a TV program trade fair

Saint-Clair Chabert-Liddell, Pierre Barbillon, Sophie Donnet, Emmanuel Lazega


This work is motivated by the analysis of multilevel networks. We define a multilevel network as the junction of two interaction networks, one level representing the interactions between individuals and the other one the interactions between organizations. The levels are linked by an affiliation relationship, each individual belonging to a unique organization. We extend the Stochastic block model (SBM) to multilevel networks. SBM is a latent variable model for networks, where the connections between nodes depend on a latent clustering (blocks) which accounts for heterogeneity of connection. We develop for multilevel SBM a criterion to select the number of blocks and to detect whether the two levels (inter-individual and inter-organizational) are interdependent or not. In a comprehensive simulation study, we exhibit the benefit of considering our approach, illustrate the robustness of our parameter estimation and highlight the reliability of our model selection criterion. Our approach is applied on a sociological dataset collected during a television program trade fair. The inter-organizational level is the trade network between companies and the inter-individual level is the advice network between their representatives. Our results exhibit the structural interdependence between the two levels and in particular the heterogeneity of individuals who replicate to different extent their organizations's ties.

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