On the Degree Sequence and its Critical Phenomenon of an Evolving Random Graph Process

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dc.creatorWu, Xian-Yuan
dc.creatorDong, Zhao
dc.creatorLiu, Ke
dc.creatorCai, Kai-Yuan
dc.date2008-06-28
dc.date.accessioned2026-07-07T09:47:22Z
dc.date.available2026-07-07T09:47:22Z
dc.descriptionIn 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.
dc.description18 pages
dc.identifierhttps://arxiv.org/abs/0806.4684
dc.identifierhttp://arxiv.org/abs/0806.4684
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/163848
dc.subjectProbability
dc.subjectHistory and Overview
dc.subject05C07, 05C80
dc.titleOn the Degree Sequence and its Critical Phenomenon of an Evolving Random Graph Process
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