Emergence of multiscaling in heterogeneous complex networks

TL;DR

This paper demonstrates that heterogeneous preferential attachment networks exhibit multiscaling in degree distributions, revealing richer connectivity behaviors than homogeneous models, with exponents influenced by heterogeneity.

Contribution

It provides numerical evidence of multiscaling in degree distributions of heterogeneous networks, highlighting the impact of heterogeneity on network structure.

Findings

Degree densities show power-law multiscaling.

Degree distribution exponents depend on heterogeneity.

Heterogeneous networks exhibit richer connectivity behavior.

Abstract

In this paper we provide numerical evidence of the richer behavior of the connectivity degrees in heterogeneous preferential attachment networks in comparison to their homogeneous counterparts. We analyze the degree distribution in the threshold model, a preferential attachment model where the affinity between node states biases the attachment probabilities of links. We show that the degree densities exhibit a power-law multiscaling which points to a signature of heterogeneity in preferential attachment networks. This translates into a power-law scaling in the degree distribution, whose exponent depends on the specific form of heterogeneity in the attachment mechanism.