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

Many real systems can be represented as networks, and their studycan unveil hidden information and provide an extra insight to ourunderstanding of the systems. However, finding the right modelfor a system is a challenging and fundamental task, as the use of abiased or approximated model can lead to wrongful conclusions.In this thesis we focus on maximum entropy network models. Inparticular, we focus on bipartite networks, that are networks inwhich there are two types of nodes and interactions are allowedonly between two nodes of different type. In the first part ofthe thesis, we describe a new algorithm for the computation ofmaximum entropy models and we introduce a Python packagewe developed implementing it. In the second part of the thesis,we show how maximum entropy models can be used to analysevarious types of real-world systems. In three separate chapters, wepresent the application of maximum entropy bipartite networksmethods to financial, ecological and social systems. For everyapplication, we are able to find non-trivial insights using ournovel methods, showing that the maximum entropy bipartiteconfiguration model can be the standard tool used to analyzemost kinds of two-mode networks.