A branching process approach to the identification of influential nodes in complex networks

We live in a world surrounded by networks. They are ubiquitous. Be it social media networks linking us to our friends, transportation networks interconnecting locations around the globe, or the metabolic network breaking down food in our bodies. The study of networks is an interdisciplinary field spanning from fields of mathematics, psychology, sociology, biology, computer science, physics, and many other areas. The field of Network Science has greatly profited from the contributions of such diverse scientific communities. However, there are still remaining challenges that are open for further research and discussion. The identification of influential nodes in a network is a constant challenge faced by researchers. Regardless of the specific field of study the solution to this problem is constantly in demand. In this thesis, we present a new measure for the identification of influential nodes in complex networks. It is based on a mathematical model which uses a branching process approach. Unlike a lot of existing measures, it is based on a mathematical model that takes into account not only the structure of the network but also the dynamics taking place on the network. We present the mathematical theory behind the model and explain from this where the measure will return accurate results, and when it should return inaccurate predications. Throughout this work, we provide a considerable amount of results on a range of networks. We do this to support our proposal and recommendations for the usage of this new centrality metric.