This paper proposes a framework to identify the structure of a financial network and its evolution over time, and presents an application to an interbank market with complete actual data. The framework is based on a methodology popular in the social network literature – stochastic blockmodeling – which, we argue, is more general, transparent and rewarding in terms of results than other proposed methodologies. In particular, it allows us to identify the presence of multiple cores and peripheries as well as the different forms of interaction between them. We find that such a varied core–periphery structure exists in almost all periods for the different instruments analyzed. In the case of term deposits, which account for two-thirds of interbank exposures, we find that, far from being static, the structure underwent a transition in the period 2009–15, with the core increasing its size. We also show that facts revealed by our approach cannot be observed in the metrics commonly used to describe networks. Finally, we describe how the elements identified by our method can be used to single out sources and channels of transmission of systemic risk in a network of banks.