title: 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 (SF)) and real-world networks with its value normalized in the interval [Formula: see text]. 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 networkNtends to infinity. We numerically study the variation of heterogeneity for random graphs (as a function ofpandN) and for SF networks withγandNas 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 attractors, thereby providing a single index to compare the structural complexity of chaotic attractors.
authors.affiliation: Department of Physics , The Cochin College , Cochin 682 002 , India.
authors.forename: Rinku
authors.initials: R
authors.lastname: Jacob
authors.affiliation: Department of Physics , The Cochin College , Cochin 682 002 , India.
authors.forename: K P
authors.identifier: 0000-0001-9209-5921
authors.initials: KP
authors.lastname: Harikrishnan
authors.affiliation: Inter University Centre for Astronomy and Astrophysics , Pune 411 007 , India.
authors.forename: R
authors.initials: R
authors.lastname: Misra
authors.affiliation: Indian Institute of Science Education and Research , Pune 411 008 , India.
authors.forename: G
authors.identifier: 0000-0001-7303-9692
authors.initials: G
authors.lastname: Ambika
keywords: complex networks; heterogeneity measure; recurrence network analysis