Graph entropies-graph energies indices for quantifying network structural irregularity

Quantifying similarities/dissimilarities among different graph models and studying the irregularity (heterogeneity) of graphs in graphs and complex networks are one of the fundamental issues as well as a challenge of scientific and practical importance in many fields of science and engineering. This paper has been motivated by the necessity to establish novel and efficient entropy-based methods to quantify the structural irregularity properties of graphs, measure structural complexity, classify, and compare complex graphs and networks. In particular, we explore how criteria such as Shannon entropy, Von Newman, and generalized graph entropies, already defined for graphs, can be used to evaluate and measure irregularities in complex graphs and networks. To do so, we use some results obtained from graph spectral theory related to the construction of matrices obtained from graphs. We show how to use these irregularity indices based on graph entropies and demonstrate the usefulness and efficiency of each of these complexity measures on both synthetic networks and real-world data sets.