Community Detection And Dynamics in Temporal Networks

Many systems of current scientific interest are made of elements in interaction and can be represented as networks. Important examples include the Internet, contact networks, airline routes but also a wide range of biological systems. The capacity to collect large data-sets of relational data has radically changed the way networks are considered and has led to the development of statistical methods allowing for the extraction of significant information from their overall structure. Despite its many successes, standard tools of network science often overlook the intrinsic dynamical nature of networks. In many situations, networks are not static entities but their edges are instead limited in time and can change over time. The concept of temporal networks is used to study such time-dependent networks. The main purpose of this project is to explore how the interplay between the structure and dynamics of networks affects diffusive processes, and to exploit the resulting constraints on diffusion in order to uncover their inner dynamical community structure. This approach searches to strengthen ou understanding of how the dynamics on and of the network are inter-related, and builds on algorithms designed for static networks, such as Markov stability, where diffusion is known to be essential to explore the multi-scale structure of the system, and to help defining the centrality of nodes and the embedding of networks. The project will be tested and inspired by real-world data from a range of disciplines, and will ultimately aim at deepening our mathematical knowledge of temporal networks and their relation to graph signal processing, and at developing novel algorithms to uncover significant structures in networks evolving in time.