标题： 相关随机网络上的渗透现象 显示英文标题

标题： Percolation on correlated random networks

摘要： 我们考虑一类随机加权网络，这些网络通过重新定义类似Hopfield模型中的模式获得，并通过进行渗流过程，可以了解网络本身的拓扑结构和鲁棒性特性。 由于图的加权性质，可以研究不同类型的键渗流：随机（随机删除链接）和确定性（基于权重等级删除链接），每种都模仿不同的物理过程。 网络的演化因此不同，这由最大组件大小和簇大小分布的行为所证明。 特别是，我们可以得出结论，弱连接对于保持图的连通性至关重要，而且当它们最容易发生故障时，巨组件通常会逐渐缩小而不会突然分裂；这些结果最近在多种社会网络中得到了证实。 显示英文摘要

摘要： We consider a class of random, weighted networks, obtained through a redefinition of patterns in an Hopfield-like model and, by performing percolation processes, we get information about topology and resilience properties of the networks themselves. Given the weighted nature of the graphs, different kinds of bond percolation can be studied: stochastic (deleting links randomly) and deterministic (deleting links based on rank weights), each mimicking a different physical process. The evolution of the network is accordingly different, as evidenced by the behavior of the largest component size and of the distribution of cluster sizes. In particular, we can derive that weak ties are crucial in order to maintain the graph connected and that, when they are the most prone to failure, the giant component typically shrinks without abruptly breaking apart; these results have been recently evidenced in several kinds of social networks.