Jaccard Guided Perturbation for Eigenvector Localization

Abstract

Understanding the role of network for epidemic spread is a major concern in the study of complex network and disease spread. Localization of Principal EigenVector (PEV) of the network’s adjacency matrix has been explored in recent past by many researchers. Most of the previous works suggest the localization of PEV through maximization of inverse participation ratio (IPR). The network with maximum IPR leads to maximum PEV localization. Random perturbation (RP) is one of the methods reported recently that performs the random perturbation in the original graph to obtain a perturbed graph that is more localized than the original graph, with same number of edges as the original graph. In this paper, we propose a Jaccard Guided Perturbation (JGP) method that perturbs the graph by using Jaccard’s coefficient. We consider both random and scale-free networks for the experiment. SIS model is used to implement the spread of epidemic. The results show that the proposed JGP approach achieve better PEV localization than the existing RP method. The number of modifications is found to be less in JGP in comparison to RP. The threshold rate of spread is found to be more in JGP than RP. In scale-free networks, JGP shows a better preservation of scale-free property than that of RP.