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.

中文翻译：

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用于特征向量定位的 Jaccard 引导扰动

理解网络在流行病传播中的作用是复杂网络和疾病传播研究中的一个主要问题。最近，许多研究人员已经探索了网络邻接矩阵的主特征向量 (PEV) 的定位。以前的大部分工作都建议通过最大化逆参与率 (IPR) 来定位 PEV。具有最大 IPR 的网络导致最大的 PEV 定位。随机扰动（RP）是最近报道的一种方法，它在原始图中执行随机扰动以获得比原始图更局部化的扰动图，其边数与原始图相同。在本文中，我们提出了一种 Jaccard 引导扰动 (JGP) 方法，该方法通过使用 Jaccard 系数来扰动图。我们在实验中考虑了随机和无标度网络。SIS模型用于实现流行病的传播。结果表明，所提出的 JGP 方法比现有的 RP 方法实现了更好的 PEV 定位。与 RP 相比，JGP 中的修改次数较少。发现 JGP 中的阈值传播率高于 RP。在无标度网络中，JGP 显示出比 RP 更好地保留无标度属性。