On the Maximum-Entropy Approach to Random Graphs

One issue in network modelling is describing the properties of a real-world network from the partial information available. In this thesis, we present the maximum-entropy principle as a criterion to determine the probability distribution associated to a graph ensemble subject to the available information on a network whose behaviour we aim to analyze and predict. This is formalised for a generic system with a finite number of states and then applied to infer the so-called exponential random graphs: we highlight their potential and limitations through examples. For some of them it is possible to explicit the probability distribution; the last one, instead, requires drawing an analogy with the Ising model and introducing the additional mean-field hypothesis in order to discuss its solutions.