Berlin 2012 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 20: Networks III

DY 20.3: Talk

Wednesday, March 28, 2012, 15:30–15:45, MA 004

Network evolution towards optimal dynamical performance — •Steffen Karalus and Markus Porto — Institut für Theoretische Physik, Universität zu Köln, Germany

The functionality of a large number of real world networks is associated with dynamical processes based on the network in the sense that the network structure defines the local interaction pattern between the individual elements of the system. A deeper understanding of the interplay between the network topology and the behavior of the dynamical process in such cases is, however, still missing. As the ‘fitness’ of these networks is primarily determined by their functionality, we presume that they are driven into ‘fitter’ structures by an evolutionary process with mutation acting on topology and selection acting on dynamical properties. We propose a simple optimization scheme in which the latter are determined by the eigenvalue spectrum of the associated time evolution operator. Exemplifying this approach with the graph Laplacian, the relevant operator for fundamental processes such as random walks on a network, we show that our algorithm is able to successfully evolve networks into states with a given eigenvalue spectrum and corresponding dynamical behavior.