Community detection and diffusion on complex networks

Abstract

In the last century, network science has found different applications in real world problems, such as social sciences, transportation and epistemology. This system abstraction considers as fundamental elements the nodes and their connections. It has been observed that most real-world networks present a modular structure, i.e., entities are more interconnected within a group than to entities outside the group. Identifying and analyzing such groups represent one fundamental problem in the field. While several different methods are constantly being proposed, less attention has relatively been given to hierarchical approaches. Hierarchical methods generally differ by providing a better explaining of the clustering process and by requiring a few or no parameters. On top of the modular structure, networks may represent virtually any information of a system. For instance, in spatial networks, the elements carry the information from the embedding in a metric space. Instead of studying only the static nature of these structures, one may study the dynamics of physical processes taking place on the network. The diffusion processes represent a class of dynamical processes which are frequently evaluated on networks. Most studies on each of the previous topics assume that the network structure is static. A further complexity factor is added when these network structures are allowed to evolve in time. All these concepts are at the core of our proposal. More specifically, we aim at the following non-exhaustive subjects: dynamical processes on top of spatial networks; new hierachical community detection methods considering the recent advancements in flow-based community detection; and the modelling of the progress of the knowledge networks. (AU)