Modularity and Hierarchy in complex systems: Relating network structure to dynamics [HBNI Th11]

Abstract

Complex systems, whether integrated circuits, food webs, transportation networks, social systems, or the biochemical interactome of a living cell, all behave in ways that cannot be fully explained by analyzing their constituent parts in isolation. Understanding the emergent behavior of such nonlinear systems, which is more than just an aggregate of the properties of their components, require novel integrative approaches. Many of these systems can be represented as networks, consisting of a large number of nodes connected via directed or undirected links. The recent discovery of the existence of universal principles underlying these complex networks that occur across widely differing domains in the biological, social and technological arenas have spurred the interest of physicists in trying to understand such principles using techniques from statistical physics and nonlinear dynamics. This thesis looks at how the structure of a network, as charaterized by the connection topology, governs its dynamical behavior, and conversely, how the dynamical processes taking place on the network affects its structure (eg. stability considerations constraining the evolution of the network towards specific topologies). In particular the focus is on modularity, the existence of groups whose nodes are more densely connected to each other than to nodes in other groups, and hierarchy ie., the nested arrangement of connection topology into several layers. Both of these mesoscopic organizational structures are observed in many complex networks that occur in reality.