团体择优广义合作网络的度分布分析

The degree distribution of generalized collaboration network with group preferential attachment

将团体竞争的思想引入到合作网络的研究中,提出了一个团体择优广义合作网络模型,其中,新加入的节点以团体择优概率选择已存在的节点形成一个含有T个节点完全图.利用马尔可夫链的方法,证明了网络的稳态度分布是存在的,且得到了网络度分布的精确解析表达式,并说明了此广义合作网络是一个标度指数γ=T+1的无标度网络.

Inspired by the idea of team competition, a generalized collaboration network with group preferential attachment is proposed, in which the new vertex will join a complete graph with T-1 vertices chosen from the existing network preferentially. Based on the techniques of Markov chain theory, the existence of the steady degree distribution is proved, and the expressions for the degree distribution are obtained. Theoretical results show that this generalized collaboration network is a scale free network with degree exponent γ= T＋ 1.