An extended formalism for preferential attachment in heterogeneous complex networks

Grupo de Sistemas Complejos, Departamento de Física y Mecánica, Escuela Técnica Superior de Ingenieros Agrónomos, Universidad Politécnica de Madrid - 28040 Madrid, Spain, EU

Corresponding authors: antonio.santiago@upm.es rosamaria.benito@upm.es

Received: 26 December 2007
Accepted: 15 April 2008

Abstract

In this paper we present a framework for the extension of the Barabási-Albert model to heterogeneous complex networks. We define a class of heterogeneous preferential attachment models where node properties are described by fixed states in an arbitrary space, and introduce an affinity function that biases the attachment probabilities of links. We perform an analytical study of the degree distributions in heterogeneous preferential attachment networks. We show that their degree densities exhibit a richer scaling behavior than their homogeneous counterparts, and that the power law scaling in the degree distribution is robust in the presence of heterogeneity.