An extended formalism for preferential attachment in heterogeneous complex networks

TL;DR

This paper extends the preferential attachment model to heterogeneous networks by incorporating node properties and affinity functions, revealing richer degree distribution behaviors while maintaining power law scaling.

Contribution

It introduces a formal framework for heterogeneous PA models with affinity functions, analyzing their degree distributions and demonstrating robustness of power laws.

Findings

Degree densities show richer scaling behavior.

Power law scaling remains robust despite heterogeneity.

Analytical results on stationary degree distributions.

Abstract

In this paper we present a framework for the extension of the preferential attachment (PA) model to heterogeneous complex networks. We define a class of heterogeneous PA models, where node properties are described by fixed states in an arbitrary metric space, and introduce an affinity function that biases the attachment probabilities of links. We perform an analytical study of the stationary degree distributions in heterogeneous PA 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 presence of heterogeneity.