Variability Analysis of Complex Networks Measures based on Stochastic Distances

Abstract: Complex networks can model the structure and dynamics of different types of systems. It has been shown that they are characterized by a set of measures. In this work, we evaluate the variability of complex networks measures face to perturbations and, for this purpose, we impose controlled perturbations and quantify their effect. We analyze theoretical models (random, small-world and scale-free) and real networks (a collaboration network and a metabolic networks) along with the shortest path length, vertex degree, local cluster coefficient and betweenness centrality measures. In such analysis, we propose the use of three stochastic quantifiers: the Kullback-Leibler divergence and the Jensen-Shannon and Hellinger distances. The sensitivity of these measures was analyzed with respect to the following perturbations: edge addition, edge removal, edge rewiring and node removal, all of them applied at different intensities. The results reveal that the evaluated measures are influenced by these perturbations. Additionally, hypotheses tests were performed to verify the behavior of the degree distribution to identify the intensity of the perturbations that leads to break this property.