基于自我中心网络的社会和通信网络中病毒传播过程的结构分析
Structural Analysis of Viral Spreading Processes in Social and Communication Networks Using Egonets
AI总结：
提出基于代数图论和凸优化的数学框架，利用自我中心网络（egonets）约束网络邻接矩阵最大特征值的可能区间，从而分析局部结构对病毒传播动力学的影响。
摘要：
我们研究病毒传播过程的行为如何受其传播网络局部结构特性的影响。对于多种传播过程，网络邻接矩阵的最大特征值对其全局动力学行为起着关键作用。对于许多现实世界的大规模网络，精确获取完整的网络结构以计算其最大特征值是不可行的。相反，我们通常只能获得网络结构的近视、自我中心视图，也称为自我中心网络。在本文中，我们提出了一个基于代数图论和凸优化的数学框架，研究网络局部结构特性如何约束最大特征值必须位于的区间。基于该框架，我们提出了一种计算高效的方法，从一组自我中心网络中找到该区间。我们的数值模拟表明，对于几个社会和通信网络，网络的局部结构特性强烈约束了最大特征值的位置以及由此产生的传播动力学。从实际角度来看，我们的结果可用于制定免疫策略以抑制病毒的传播，或设计有利于信息病毒式传播的网络拓扑。
英文摘要：
We study how the behavior of viral spreading processes is influenced by local structural properties of the network over which they propagate. For a wide variety of spreading processes, the largest eigenvalue of the adjacency matrix of the network plays a key role on their global dynamical behavior. For many real-world large-scale networks, it is unfeasible to exactly retrieve the complete network structure to compute its largest eigenvalue. Instead, one usually have access to myopic, egocentric views of the network structure, also called egonets. In this paper, we propose a mathematical framework, based on algebraic graph theory and convex optimization, to study how local structural properties of the network constrain the interval of possible values in which the largest eigenvalue must lie. Based on this framework, we present a computationally efficient approach to find this interval from a collection of egonets. Our numerical simulations show that, for several social and communication networks, local structural properties of the network strongly constrain the location of the largest eigenvalue and the resulting spreading dynamics. From a practical point of view, our results can be used to dictate immunization strategies to tame the spreading of a virus, or to design network topologies that facilitate the spreading of information virally.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
