Maximum entropy methods for the statistical analysis of bipartite networks: fast computation and applications

Many real systems can be represented as networks, and their study can unveil hidden information and provide an extra insight to our understanding of the systems. However, finding the right model for a system is a challenging and fundamental task, as the use of a biased or approximated model can lead to wrongful conclusions. In this thesis we focus on maximum entropy network models. In particular, we focus on bipartite networks, that are networks in which there are two types of nodes and interactions are allowed only between two nodes of different type. In the first part of the thesis, we describe a new algorithm for the computation of maximum entropy models and we introduce a Python package we developed implementing it. In the second part of the thesis, we show how maximum entropy models can be used to analyse various types of real-world systems. In three separate chapters, we present the application of maximum entropy bipartite networks methods to financial, ecological and social systems. For every application, we are able to find non-trivial insights using our novel methods, showing that the maximum entropy bipartite configuration model can be the standard tool used to analyze most kinds of two-mode networks.