论文标题
复杂网络的随机节点增强和$ k $ - 核心结构
Random node reinforcement and $K$-core structure of complex networks
论文作者
论文摘要
为了增强复杂网络系统的鲁棒性，一种简单的方法正在引入加强节点，这些节点在失败传播过程中始终发挥作用。随机的节点增强方案可以被视为找到最佳加固解决方案的基准。然而，仍然缺乏对节点增强如何在失败后在介观级别影响网络结构的系统评估。在这里，我们通过$ k $ cores网络的镜头研究此问题。基于一个分析渗透框架，我们首先表明，在不相关的随机图上，具有临界的增强节点大小，突然出现$ k $ cores的曲线被平滑至连续的零件，并得出了详细的相图。然后，我们表明，通过对随机增强的成本效益分析，对于恒定和增加边际成本的成本函数的适当重量因素，增益函数表明了单程性，因此我们可以通过定位最大增益来分析地找到最佳的增强分数。总的来说，我们的框架为设计强大的互连系统提供了面向增益的分析观点。
To enhance robustness of complex networked systems, a simple method is introducing reinforced nodes which always function during failure propagation. A random scheme of node reinforcement can be considered as a benchmark for finding an optimal reinforcement solution. Yet there still lacks a systematic evaluation on how node reinforcement affects network structure at a mesoscopic level upon failures. Here we study this problem through the lens of $K$-cores of networks. Based on an analytical percolation framework, we first show that, on uncorrelated random graphs, with a critical size of reinforced nodes, an abrupt emergence of $K$-cores is smoothed out to a continuous one, and a detailed phase diagram is derived. We then show that, with a cost-benefit analysis on random reinforcement, for proper weight factors in cost functions with constant and increasing marginal costs, a gain function shows a unimodality, thus we can analytically find an optimal reinforcement fraction by locating the maximal gain. In all, our framework offers a gain-oriented analytical perspective to designing robust interconnected systems.
