关于发展随机图过程的度序列及其临界现象
On the Degree Sequence and its Critical Phenomenon of an Evolving Random Graph Process
摘要：
本文主要研究随机图过程的度序列问题。在任何时间步$t$，执行以下三个子步骤之一：以概率$α_1$，添加新顶点$x_t$和与$x_t$关联的$m$边;或者以概率$α-α_1$，添加$m$边;或者最后，以概率$1-\a$，删除$m$随机边。请注意，在任何情况下，边都是以优先连接的方式添加的。证明了存在一个临界点$α_c$满足：1）如果$α_1<α_c$，则模型具有幂律度序列; 2）如果$α_1>α_c$，则模型具有指数度序列; 3）如果$α_1=α_c$，则模型具有介于上述两种情况之间的度序列。
英文摘要：
In this paper we focus on the problem of the degree sequence for the following random graph process. At any time-step $t$, one of the following three substeps is executed: with probability $α_1$, a new vertex $x_t$ and $m$ edges incident with $x_t$ are added; or, with probability $α-α_1$, $m$ edges are added; or finally, with probability $1-\a$, $m$ random edges are deleted. Note that in any case edges are added in the manner of preferential attachment. we prove that there exists a critical point $α_c$ satisfying: 1) if $α_1<α_c$, then the model has power law degree sequence; 2) if $α_1>α_c$, then the model has exponential degree sequence; and 3) if $α_1=α_c$, then the model has a degree sequence lying between the above two cases.
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。
