Mathematics – Probability
Scientific paper
2008-07-17
Mathematics
Probability
14 pages
Scientific paper
In this paper we consider a simple model of random graph process with {\it hard} copying as follows: At each time step $t$, with probability $0<\alpha\leq 1$ a new vertex $v_t$ is added and $m$ edges incident with $v_t$ are added in the manner of {\it preferential attachment}; or with probability $1-\alpha$ 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 $\alpha$ being large enough, the model possesses a mean degree sequence as $ d_{k}\sim Ck^{-(1+2\alpha)}$, where $d_k$ is the limit mean proportion of vertices of degree $k$.
Cai Kai-Yuan
Ning Gao-Rong
Wu Xian-Yuan
No associations
LandOfFree
The Degree Sequence of a Scale-Free Random Graph Process with Hard Copying does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The Degree Sequence of a Scale-Free Random Graph Process with Hard Copying, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Degree Sequence of a Scale-Free Random Graph Process with Hard Copying will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-42679