Jacob Rinku, Harikrishnan K P, Misra R, Ambika G
Department of Physics , The Cochin College , Cochin 682 002 , India.
Inter University Centre for Astronomy and Astrophysics , Pune 411 007 , India.
R Soc Open Sci. 2017 Jan 11;4(1):160757. doi: 10.1098/rsos.160757. eCollection 2017 Jan.
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 network tends to infinity. We numerically study the variation of heterogeneity for random graphs (as a function of and ) and for SF networks with and 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 attractors, thereby providing a single index to compare the structural complexity of chaotic attractors.
我们提出了一种针对无权无向复杂网络的度异质性新度量方法，该方法在计算时仅需网络的度分布。我们表明，所提出的度量方法可轻松应用于所有类型的网络拓扑结构，并且会随着网络中节点度的多样性增加而增大。该度量方法用于计算合成网络（包括随机网络和无标度（SF）网络）以及真实世界网络的异质性，其值在区间[公式：见文本]内进行归一化。为了定义该度量方法，我们引入了一个极限网络，其异质性在网络规模趋于无穷大时，可通过解析方式表示，且该值趋于1。我们通过数值研究了随机图（作为 和 的函数）以及以 和 为变量的SF网络的异质性变化。最后，作为一个具体应用，我们表明所提出的度量方法可用于比较由几个低维混沌吸引子的时间序列构建的递归网络的异质性，从而提供一个单一指标来比较混沌吸引子的结构复杂性。
