Issue Eur. Phys. J. B Volume 67, Number 3, February I 2009 Page(s) 271 - 275 Section Interdisciplinary Physics DOI 10.1140/epjb/e2009-00007-9 Published online 13 January 2009

Eur. Phys. J. B 67, 271-275 (2009)
DOI: 10.1140/epjb/e2009-00007-9

On the rich-club effect in dense and weighted networks

V. Zlatic^{1, 2}, G. Bianconi³, A. Díaz-Guilera⁴, D. Garlaschelli⁵, F. Rao^{6, 7} and G. Caldarelli<sup>1, 4, 8

1</sup>  INFM-CNR Centro SMC and Dipartimento di Fisica, Università di Roma La Sapienza, Piazzale Moro 5, 00185 Roma, Italy
²  Theoretical Physics Division, Rudjer Bošković Institute, P.O. Box 180, 10002 Zagreb, Croatia
³  The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34014 Trieste, Italy
⁴  Dept. de Física Fonamental, Facultat de Física, Universitat de Barcelona Diagonal 647, 08028 Barcelona, Spain
⁵  Dipartimento di Fisica, Università di Siena, Via Roma 56, 53100 Siena, Italy
⁶  Centro Studi e Museo della Fisica Enrico Fermi, Compendio Viminale, 00185 Roma, Italy
⁷  Université “Louis Pasteur” Laboratoire de Chimie Biophysique/ISIS 8, allee Gaspard Monge, 67000 Strasbourg, France
⁸  Linkalab, Center for the Study of Complex Networks, 09100 Cagliari, Sardegna, Italy

garlaschelli@unisi.it

Received 29 August 2008 / Received in final form 20 November 2008 / Published online 13 January 2009

Abstract
For many complex networks present in nature only a single instance, usually of large size, is available. Any measurement made on this single instance cannot be repeated on different realizations. In order to detect significant patterns in a real-world network it is therefore crucial to compare the measured results with a null model counterpart. Here we focus on dense and weighted networks, proposing a suitable null model and studying the behaviour of the degree correlations as measured by the rich-club coefficient. Our method solves an existing problem with the randomization of dense unweighted graphs, and at the same time represents a generalization of the rich-club coefficient to weighted networks which is complementary to other recently proposed ones.

PACS
89.75.Hc - Networks and genealogical trees.
89.75.Fb - Structures and organization in complex systems.

© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2009

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