On the Degree Sequence and its Critical Phenomenon of an Evolving Random Graph Process
نویسندگان
چکیده
Abstract: 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 α1, a new vertex xt and m edges incident with xt are added; or, with probability α− α1, m edges are added; or finally, with probability 1 − α, 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 αc satisfying: 1) if α1 < αc, then the model has power law degree sequence; 2) if α1 > αc, then the model has exponential degree sequence; and 3) if α1 = αc, then the model has a degree sequence lying between the above two cases.
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