Analysis of Multiple Relations in Multilayer and Higher-Order Networks

Network modelling has gained increasing attention in data science, as many real world systems can be explored by analyzing the interaction among their constituents. Therefore, there is a demand for the developement of methodologies that allow to capture the structure and dynamics of such complex systems. Recent advances in network theory have highlighted that classical networks, which model a single type of pairwise relation between objects, do not fully capture the complex nature of a system. The scope of this thesis is to present and discuss methodologies and applications to extend the paradigm of classical networks, following two directions: (i) modelling the existence of multiple types of interactions among the entities in a system; (ii) modelling higher-order interactions, i.e. simultaneous interactions among more than two entities. Concerning (i), the use of multilayer networks to model several types of interactions among a fixed set of entities is discussed. In particular, different methods to collapse a multiplex similarity network into a single graph exploiting the original multiplex structure are analysed. The proposed techniques are applied to two different domains. A first application regards the study of cell phenotype differentiation in human haematopoiesis based on multiple types of histone modification profiles of cells. The second application regards the area of “science of science”, and consists in the identification of communities of scientific journals based on their similarity in terms of common editors, common authors and common references. Regarding (ii), the use of weighted simplicial complexes to model higher order interactions among objects is proposed. The focus here is on the representation power of simplicial complexes; indeed, although they are often seen as a less general object with respect to generic higher order networks, their use allows to borrow concepts from algebraic topology to explore structural geometric properties of the network. The aim here is to show that with a suitably defined weight assignment to the simplices, the original information about the higher order interactions in the system can be fully reconstructed. The proposed weight assignment is tested both on a simplicial complex network model, namely Network Geometry with Flavor, and on a real world collaboration network. In particular, we focus on the higherorder extension of the Von Neumann spectral entropy to study the higher order diffusion properties of the considered simplicial complexes.