An energy-based heterogeneity measure for quantifying structural irregularity in complex networks

Abstract

In this article, we propose a novel and efficient measure to quantify the structural heterogeneity characteristics of a graph. This measure is also used for comparing and classifying the complex networks based on the spectral graph theory, by quantifying the difference between the energy and Laplacian energy extracted from the underlying networks. Experimental results captured from simulations on the synthetic and real-world networks imply that for regular graphs and star-like graphs, the proposed measure has lower and upper bound 0 and 1, respectively and in cases in which the graphs are non-isomorphic, the measure returns non-zero values.