  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.
