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

On the rich-club effect in dense and weighted networks

¹ 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

Corresponding author: ^a garlaschelli@unisi.it

Received: 29 August 2008
Revised: 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.