Regensburg 2013 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 24: Networks, From Topology to Dynamics (joint session BP/DY/SOE)
DY 24.1: Talk
Wednesday, March 13, 2013, 15:45–16:00, H37
Eigenvector centrality as a measure of influence in dynamics on networks — •Konstantin Klemm1, M. Angeles Serrano2, Victor M. Eguiluz3, Maxi San Miguel3, and Fakhteh Ghanbarnejad4 — 1Bioinformatics, Institute for Computer Science, Leipzig University, Germany — 2Fisica Fonamental, University of Barcelona, Spain — 3Institute for Cross-Disciplinary Physics and Complex Systems, Palma de Mallorca, Spain — 4MPI for Physics of Complex Systems, Dresden, Germany
Definitions of centrality aim at quantifying the importance of a node in a given graph. Among many others, the degree, the betweenness and the closeness are examples of frequently used measures of centrality. Here we ask which notion of centrality is best suited for predicting the influence a node has on dynamics. The concept of dynamical influence is made rigorous for a class of dynamical rules that asymptotically lead the system to a stationary state y(∞) from any initial condition y(0). Then the influence of node v is the dependence of the asymptotic state on the initial condition yv(0) at node v. We find that the principal eigenvector of the coupling matrix is an accurate predictor of influence for various kinds of dynamics [1,2], including critical epidemic and Ising models, Boolean networks, the voter model as well as Kuramoto and Rössler oscillators.
[1] Klemm et al., Scientific Reports 2, 292 (2012).
[2] Ghanbarnejad and Klemm, EPL 99:58006 (2012).