Regensburg 2007 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 4: Statistical physics of complex networks I
DY 4.3: Vortrag
Montag, 26. März 2007, 12:30–12:45, H3
Generating random networks with arbitrary two-point correlations — •Sebastian Weber and Markus Porto — Institut für Festkörperphysik, Technische Universität Darmstadt, Hochschulstr. 8, 64289 Darmstadt, Germany
Random networks are heavily used as null models to investigate properties of complex networks. We describe a generator of two-point correlated undirected random networks without self- or multiple-connections among vertices [1]. With the goal to systematically investigate the influence of two-point correlations, we develop a formalism to construct a joint degree distribution P(k,k′) which allows to fix an arbitrary degree distribution P(k) and an average nearest neighbor function knn(k) simultaneously. The formalism is demonstrated with scale-free networks (P(k) ∝ k−γ) and empirical complex networks (P(k) taken from graph) as an example. Finally, we introduce the notion of an annealed graph which allows a graph to be represented in a mean-field like manner.
[1] S. Weber and M. Porto, in preparation