感染扩散至P.A.边插入随机图
Spread of Infection over P.A. random graphs with edge insertion
摘要：
在这项工作中，我们研究了一个随机图模型，它结合了优先连接和先前存在的顶点之间的边插入所产生的随机图的自举渗流过程。添加新顶点或在先前添加的顶点之间添加新连接的概率是不定常的，并且由称为边-阶梯函数的函数$f$给出。我们表明，在可积条件下的边缘阶梯函数的图是非常容易受到感染的传播，这只需要$3$步骤感染整个图的正分数。为了证明这一结果，我们依赖于一个定量的下界的最大程度，可能是独立的利益。
英文摘要：
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.
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。
