Canonical fitness model for simple scale-free graphs

F. Flegel and I. M. Sokolov
Phys. Rev. E 87, 022806 – Published 13 February 2013

Abstract

We consider a fitness model assumed to generate simple graphs with a power-law heavy-tailed degree sequence, P(k)k1α with 0<α<1, in which the corresponding distributions do not possess a mean. We discuss the situations in which the model is used to produce a multigraph and examine what happens if the multiple edges are merged to a single one and thus a simple graph is built. We give the relation between the (normalized) fitness parameter r and the expected degree ν of a node and show analytically that it possesses nontrivial intermediate and final asymptotic behaviors. We show that the model produces P(k)k2 for large values of k independent of α. Our analytical findings are confirmed by numerical simulations.

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  • Received 19 November 2012

DOI:https://doi.org/10.1103/PhysRevE.87.022806

©2013 American Physical Society

Authors & Affiliations

F. Flegel and I. M. Sokolov

  • Institut für Physik, Humboldt-Universität zu Berlin, D-12489 Berlin, Germany

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Issue

Vol. 87, Iss. 2 — February 2013

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