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
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