带边插入的P.A.随机图上的感染传播

IF 0.6 4区 数学 Q4 STATISTICS & PROBABILITY
C. Alves, Rodrigo Ribeiro
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引用次数: 1

摘要

在这项工作中,我们研究了由随机图模型生成的随机图上的自举渗流过程,该模型结合了先前存在的顶点之间的优先附着和边插入。添加新顶点或先前添加的顶点之间的新连接的概率是时间相关的,并且由称为边阶函数的函数f给出。我们证明了在边阶函数上的可积条件下,图对感染的传播非常敏感,这只需要3个步骤就可以感染整个图的正部分。为了证明这一结果,我们依赖于可能独立感兴趣的最大程度的定量下限。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Spread of Infection over P.A. random graphs with edge insertion
In this work we investigate a bootstrap percolation process on random graphs generated by a random graph model which combines preferential attachment and edge insertion between previously existing vertices. The probabilities of adding either a new vertex or a new connection between previously added vertices are time dependent and given by a function $f$ called the edge-step function. We show that under integrability conditions over the edge-step function the graphs are highly susceptible to the spread of infections, which requires only $3$ steps to infect a positive fraction of the whole graph. To prove this result, we rely on a quantitative lower bound for the maximum degree that might be of independent interest.
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来源期刊
CiteScore
1.10
自引率
0.00%
发文量
48
期刊介绍: ALEA publishes research articles in probability theory, stochastic processes, mathematical statistics, and their applications. It publishes also review articles of subjects which developed considerably in recent years. All articles submitted go through a rigorous refereeing process by peers and are published immediately after accepted. ALEA is an electronic journal of the Latin-american probability and statistical community which provides open access to all of its content and uses only free programs. Authors are allowed to deposit their published article into their institutional repository, freely and with no embargo, as long as they acknowledge the source of the paper. ALEA is affiliated with the Institute of Mathematical Statistics.
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