The Degree Sequence of a Scale-Free Random Graph Process with Hard Copying
نویسندگان
چکیده
In this paper we consider a simple model of random graph process with hard copying as follows: At each time step t, with probability 0 < α ≤ 1 a new vertex vt is added and m edges incident with vt are added in the manner of preferential attachment; or with probability 1−α an existing vertex is copied uniformly at random. In this way, while a vertex with large degree is copied, the number of added edges is its degree and thus the number of added edges is not upper bounded. We prove that, in the case of α being large enough, the model possesses a mean degree sequence as dk ∼ Ck −(1+2α), where dk is the limit mean proportion of vertices of degree k. AMS classification: 60K 35; 05C 80.
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