This course covers the study of the main concepts and algorithms for the analysis of complex networks, the models that summarize their most relevant properties, and the dynamics which take place on top of them. First, we show the presence of complex networks in all kinds of fields (biology, medicine, ecology, social sciences, economy, linguistics, etc.) and the existence of several properties that are common to most of them. We will classify complex networks according to different criteria, and explain their main structural characteristics at three levels of description: microscale, macroscale and mesoscale. These include from descriptors at the level of nodes (e.g., degree, clustering coefficient and centrality measures) to global properties of the network (e.g., degree distributions, small-world property, transitivity and assortativity), and also showing the appearance of intermediate mesoscopic structures (e.g., community structure, rich-club and motifs). We will also study the main models of complex networks, which allow the understanding of the appearance of their distinctive structural properties. Finally, we will describe some of the dynamics on complex networks, such as diffusion, synchronization and epidemics spreading, and the analysis of the robustness of complex networks.

This course is coordinated by Universitat Rovira i Virgili (Dept. Enginyeria informàtica i Matemàtiques) in collaboration with Universitat de Barcelona (Dept. Física de la Matèria Condensada).