Random Networks with Macroscopic Structures: Inference, Detectability and Belief Propagation

A network is a good representation of a system with many interacting agents and networks with macroscopic structures (communities, hierarchies, cores, ...) naturally emerge from interactions regularities at a microscopic level. In many applications ( financial networks, biological networks, social networks) much of the information hidden in the data can be extracted from the detection of macroscopic structures wich are robust against microscopic noise. Starting from motivations and possible applications I will introduce the inference framework based on the Stochastic Block Model and the statistical mechanics approach to the associated detectability problem. This approach at the same time allows to depict the problem complexity in terms of detectability phase transitions and offers an efficient solution through a Belief Propagation algorithm.