Berlin 2008 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 3: Statistical physics of complex networks I
DY 3.6: Talk
Monday, February 25, 2008, 11:45–12:00, A 053
Modelling Paradigms for Random Movements on complex networks: How "anti-hubs" control dispersa — •Vasily Yu. Zaburdaev1,2, Marc Timme2,3, and Dirk Brockmann2,4 — 1Technische Universit"at, Berlin — 2Max-Planck-Institute for Dynamics and Self-Organization, Göttingen — 3Bernstein Center for Computational Neuroscience, Göttingen — 4Northwestern University, Evanston IL, USA
Recently a huge number of studies focused on dynamical properties of stochastic processes evolving on networks of complex topology. Very often, researchers strive to understand whether, how and why highly connected nodes (hubs) in scale free networks accelerate relaxation and change the dynamics qualitatively. In all models of physical dispersal phenomena, the topology of the network as defined by a weight matrix wij is translated into transition probability rates pij=wij/∑i wij that define the random process such that waiting times are independent of node degree (system A).
This relationship between topology and dynamics, appealing as it may seem, is by no means unique. In fact for a number of physical systems it is appropriate to interpret weights directly as probability rates, i.e. pij=wij (system B). Here we show that both systems exhibit drastically different dynamical properties: Contrary to the common notion that hubs are the key players in dispersal facilitation, nodes with few connections determine the relaxation properties more strongly, an effect that generically arises in type B systems.