Berlin 2012 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 30: Networks IV (with SOE)

DY 30.2: Talk

Friday, March 30, 2012, 10:15–10:30, MA 001

All scale-free networks are sparse — •Charo Del Genio¹, Thilo Gross¹, and Kevin Bassler^2,3 — ¹Max-Planck-Institut für Physik komplexer Systeme, Dresden, Deutschland — ²University of Houston, Houston, TX, USA — ³Texas Center for Superconductivity, Houston, TX, USA

We study the realizability of scale free-networks with a given degree sequence, showing that the fraction of realizable sequences undergoes two first-order transitions at the values 0 and 2 of the power-law exponent. We substantiate this finding by analytical reasoning and by a numerical method, proposed here, based on extreme value arguments, which can be applied to any given degree distribution. Our results reveal a fundamental reason why large scale-free networks without constraints on minimum and maximum degree must be sparse.