Eur. Phys. J. B (2012) 85: 328
https://doi.org/10.1140/epjb/e2012-21026-3

Regular Article

Random networks with given rich-club coefficient

¹ Queen Mary University of London, School of Electronic Engineering and Computer Science, Mile End Road, E1 4 NS London, UK
² University College London, Department of Computer Science, Gower Street, WC1E 6 BT London, UK

^a e-mail: r.j.mondragon@eecs.qmul.ac.uk

Received: 12 December 2011
Received in final form: 3 May 2012
Published online: 24 September 2012

Abstract

In complex networks it is common to model a network or generate a surrogate network based on the conservation of the number of connections of individual nodes. In this paper we analyse the ensemble of random networks that are defined by the conservation of the rich-club coefficient, which measures the density of connections among a group of nodes. We also present a method to generate such surrogate networks for a given network. We show that by choosing a suitable local linking term, the random networks not only preserve the rich-club coefficient but also closely approximate the degree distribution and the mixing pattern of real networks. Our work provides a different and complementary perspective to the network randomisation problem.