Frank Schweitzer (Zurich):

Complex Networks

Abstract:

Complex Networks have become a quite successful approach to analyse the structure and dynamics of systems with many interacting elements. These elements (often denoted as agents) are represented by the nodes of a network, whereas their interaction is described by the links between nodes. Statistical physics has mostly focused on the topology of such networks, emphasizing the fact that interaction occurs not necessarily via a mean field or on a regular lattice. Instead, the heterogeneity in interaction plays an important role to understand the growth of real networks.

A more refined view on complex networks has to take into account that both interactions and nodes can follow their own dynamics. This has a considerably impact on the systemic properties, in particular on the occurence of phase transitions. The term 'systemic risk' denotes such a phase transition. The breakdown of a whole system can be described as a macroscopic property which emerges from the nonlinear interactions between nodes, conditional on the eigendynamics of the nodes.

The talk will present different examples of growing complex networks ranging from Open Source Software to Economic Networks. It addresses the impact of topology, weighted links, dynamics of links and nodes on the emergence of systemic properties, such as robustness or adaptivity.

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