Bootstrap Percolation in Directed Inhomogeneous Random Graphs
Bootstrap Percolation in Directed Inhomogeneous Random Graphs
复制标题
有向非齐次随机图中的自举渗流
DOI：
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发表时间：
2015
影响因子：
0.7
通讯作者：
K. Panagiotou
中科院分区：
文献类型：
--
作者：
T. Meyer;Nils Detering;K. Panagiotou
Bootstrap渗流是一个用来描述感染在给定图上传播的过程。在这里考虑的模型中，每个顶点都配备了一个单独的阈值。一旦被感染的邻居数量超过该阈值，顶点也会被感染，并永远保持这种状态。我们进行了彻底的分析引导渗透的一种新的模型，有向和非均匀的随机图，其中的边缘的分布是specied通过分配两个不同的权重，每个顶点，描述它的倾向，以接收边缘或发送边缘到其他顶点。在图的极限度分布是可积的温和假设下，我们确定了感染顶点的典型分数。我们的模型允许我们研究各种设置，特别是突出的情况下，度分布具有无界的方差。作为第二个主要贡献，我们量化的概念“系统性风险”，也就是说，我们的特点是在多大程度上微小的初始感染可以传播到大部分的图形通过级联，并发现新的功能，使图形容易/弹性最初小的感染。
Bootstrap percolation is a process that is used to describe the spread of an infection on a given graph. In the model considered here each vertex is equipped with an individual threshold. As soon as the number of infected neighbors exceeds that threshold, the vertex gets infected as well and remains so forever. We perform a thorough analysis of bootstrap percolation on a novel model of directed and inhomogeneous random graphs, where the distribution of the edges is specied by assigning two distinct weights to each vertex, describing the tendency of it to receive edges from or to send edges to other vertices. Under the mild assumption that the limiting degree distribution of the graph is integrable we determine the typical fraction of infected vertices. Our model allows us to study a variety of settings, in particular the prominent case in which the degree distribution has an unbounded variance. As a second main contribution, we quantify the notion of "systemic risk", that is, we characterize to what extent tiny initial infections can propagate to large parts of the graph through a cascade, and discover novel features that make graphs prone/resilient to initially small infections.
影响因子：
1.6
作者：
Amini, Hamed;Fountoulakis, Nikolaos
通讯作者：
Fountoulakis, Nikolaos