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We propose a novel measure of degree heterogeneity, for unweighted andundirected complex networks, which requires only the degree distribution of thenetwork for its computation. We show that the proposed measure can be appliedto all types of network topology with ease and increases with the diversity ofnode degrees in the network. The measure is applied to compute theheterogeneity of synthetic (both random and scale free) and real world networkswith its value normalized in the interval [0, 1]. To define the measure, weintroduce a limiting network whose heterogeneity can be expressed analyticallywith the value tending to 1 as the size of the network N tends to infinity. Wenumerically study the variation of heterogeneity for random graphs (as afunction 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 beused to compare the heterogeneity of recurrence networks constructed from thetime series of several low dimensional chaotic attractors9thereby providing asingle index to compare the structural complexity of chaotic attractors.

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