  A multilevel network is defined as the junction of two interaction networks,
one level representing the interactions between individuals and the other the
interactions between organizations. The levels are linked by an affiliation
relationship, each individual belonging to a unique organization. A new
Stochastic Block Model is proposed as a unified probalistic framework tailored
for multilevel networks. This model contains latent blocks accounting for
heterogeneity in the patterns of connection within each level and introducing
dependencies between the levels. The sought connection patterns are not
specified a priori which makes this approach flexible. Variational methods are
used for the model inference and an Integrated Classified Likelihood criterion
is developed for choosing the number of blocks and also for deciding whether
the two levels are dependent or not. A comprehensive simulation study exhibits
the benefit of considering this approach, illustrates the robustness of the
clustering and highlights the reliability of the criterion used for model
selection. This approach is applied on a sociological dataset collected during
a television program trade fair, the inter-organizational level being the
economic network between companies and the inter-individual level being the
informal network between their representatives. It brings a synthetic
representation of the two networks unraveling their intertwined structure and
confirms the coopetition at stake.
