Essays on statistical methods for the analysis of social networks

The present work is a collection of articles [133, 134, 135] that, in broad terms, are dedicated to the development of statistical models for the analysis of social networks. Two main approaches are adopted throughout this manuscript that, despite being substantially different in their nature, are also complementary and accompanied by an active and relevant scientific background. From one side, following the statistical physics literature regarding the study of networks, we develop models based on the topology of the observed graphs: these methods are built starting from the activity of each node, i.e. its degree, and this information is preserved on average in the benchmark structure. Therefore any successive analysis that compares observed and expected quantities to detect relevant behaviours is, indeed, identifying quantities that cannot be simply reproduced by a model built on the information regarding solely network topology. On the other side, we also analyse the stream of literature that focuses on generative models. In this framework, the network topology plays a role in the definition of the temporal evolution of the node-related link probability, synthesized in the preferential attachment rule that is a function of nodes’ degrees. We enrich this formulation in order to take into account also some individual features of the nodes, not related to the network structure. This addition gives a fundamental contribution in reproducing the evolution of the considered network. Which of the two approaches provides a more accurate benchmark is often argument of debate. In this work we have developed theoretical tools and tested them with real-world applications, for both the presented cases. The results of our analyses show that the information provided by these two complementary methodologies can reveal equally valuable in reproducing different aspects of the systems object of study