Berlin 2008 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 3: Statistical physics of complex networks I

DY 3.6: Vortrag

Montag, 25. Februar 2008, 11:45–12:00, A 053

Modelling Paradigms for Random Movements on complex networks: How "anti-hubs" control dispersa — •Vasily Yu. Zaburdaev^1,2, Marc Timme^2,3, and Dirk Brockmann^2,4 — 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 w_ij is translated into transition probability rates p_ij=w_ij/∑_i w_ij 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. p_ij=w_ij (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.