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

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.

17 pages, 9 figures, submitted to Proc. Royal Soc. A (Lond.)

References in corpus (5)

• Network Synchronization, Diffusion, and the Paradox of Heterogeneity
• The entropy of network ensembles
• Analytical framework for recurrence-network analysis of time series
• Complex network based techniques to identify extreme events and (sudden) transitions in spatio-temporal systems
• Uniform framework for the recurrence-network analysis of chaotic time series

Cited by in corpus (6)

• Complex network approaches to nonlinear time series analysis
• Normalised Degree Variance
• Parameterizing Network Graph Heterogeneity using a Modified Weibull Distribution
• Quantifying information loss on chaotic attractors through recurrence networks
• Interplay of network structure and talent configuration on wealth dynamics
• Degree weighted recurrence networks for the analysis of time series data