Measure for degree heterogeneity in complex networks and its application to recurrence network analysis

TL;DR

This paper introduces a new degree heterogeneity measure for complex networks that is easy to compute, normalized, and applicable to various network types, with practical applications in analyzing recurrence networks from chaotic systems.

Contribution

A novel degree heterogeneity measure based solely on degree distribution, applicable to all network topologies, and demonstrated on synthetic, real-world, and recurrence networks.

Findings

Measure increases with degree diversity in networks.

Normalized heterogeneity values range from 0 to 1.

Application to recurrence networks allows comparison of chaotic attractors.

Abstract

We propose a novel measure of degree heterogeneity, for unweighted and undirected complex networks, which requires only the degree distribution of the network for its computation. We show that the proposed measure can be applied to all types of network topology with ease and increases with the diversity of node degrees in the network. The measure is applied to compute the heterogeneity of synthetic (both random and scale free) and real world networks with its value normalized in the interval [0, 1]. To define the measure, we introduce a limiting network whose heterogeneity can be expressed analytically with the value tending to 1 as the size of the network N tends to infinity. We numerically study the variation of heterogeneity for random graphs (as a function of p and N) and for scale free networks with and N as variables. Finally, as a specific application, we show that the proposed measure can be used to compare the heterogeneity of recurrence networks constructed from the time series of several low dimensional chaotic attractors9thereby providing a single index to compare the structural complexity of chaotic attractors.