Regensburg 2010 – scientific programme
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SOE: Fachverband Physik sozio-ökonomischer Systeme
SOE 19: Networks: From Topology to Dynamics IV (with BP, DY)
SOE 19.3: Talk
Thursday, March 25, 2010, 14:30–14:45, H44
Network evolution driven by spectral profile — •Sebastian Weber1 and Markus Porto2 — 1Freiburg Institute For Advanced Studies (FRIAS), University of Freiburg, Germany — 2Institut für Festkörperphysik, Technische Universität Darmstadt, Germany
A large class of real world networks evolve over time, constantly changing and adapting their topology with respect to criteria imposed on the dynamics they mediate. The properties of the dynamics is ultimately determined by its spectral profile, which is the eigenvalue spectrum of the associated operator. This operator inevitably involves the network’s adjacency matrix, establishing the connection between topology and dynamics. Using the graph Laplacian or Kirchhoff matrix and its spectral profile as an example, the former being central in a wide class of physical processes (random walks, harmonic interaction networks, etc.) on networks, we show that a network evolution scheme recently developed by us is able to successfully evolve networks to display a given spectral profile’s essential features [1].
[1] S. Weber and M. Porto, submitted.