PEV网络定位的轮图策略
Wheel graph strategy for PEV localization of networks
摘要：
研究复杂网络的特征向量局部化性质不仅对于深入了解网络中心性度量、谱划分、近似算法的发展等基本网络问题具有重要意义，而且对于理解疾病传播、脑网络动力学中的临界性等现实世界中的许多现象也具有重要意义。对于一个网络来说，当一个特征向量的大部分分量取接近于零的值，而少数分量取非常高的值时，这个特征向量被称为局部化的。在这篇文章中，我们设计了一种方法来构建一个主特征向量（PEV）本地化网络从一个给定的输入网络。该方法依赖于将具有轮图的小组件添加到给定的输入网络。通过大量的数值模拟和分析公式的基础上的最大特征值的输入网络，我们计算的大小的车轮图本地化的组合网络的PEV。使用易感染-易感染模型，我们证明了这种方法的成功，各种模型和现实世界的网络视为输入网络。我们表明，在这样的PEV本地化网络，疾病得到本地化的网络结构的一个小区域内爆发之前。该研究对于控制以网络为代表的复杂系统的传播过程具有重要意义。
英文摘要：
Investigation of eigenvector localization properties of complex networks is not only important for gaining insight into fundamental network problems such as network centrality measure, spectral partitioning, development of approximation algorithms, but also is crucial for understanding many real-world phenomena such as disease spreading, criticality in brain network dynamics. For a network, an eigenvector is said to be localized when most of its components take value near to zero, with a few components taking very high values. In this article, we devise a methodology to construct a principal eigenvector (PEV) localized network from a given input network. The methodology relies on adding a small component having a wheel graph to the given input network. By extensive numerical simulation and an analytical formulation based on the largest eigenvalue of the input network, we compute the size of the wheel graph required to localize the PEV of the combined network. Using the susceptible-infected-susceptible model, we demonstrate the success of this method for various models and real-world networks consider as input networks. We show that on such PEV localized networks, the disease gets localized within a small region of the network structure before the outbreaks. The study is relevant in controlling spreading processes on complex systems represented by networks.
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