简易广义合作网络度分布的稳定性

The degree distribution of simple generalized collaboration networks

本文对简易广义合作网络的三类特殊情形(择优连接、随机连接、混合连接)进行了研究.基于马氏链理论,给出它们度分布稳定性存在的严格证明,并且得到相应网络度分布和度指数的精确表达式.特别地,对于混合连接情况,说明在连线方式中只要存在择优成分,网络度分布就服从幂律分布,即所得网络为无标度网络.

We study three special cases of simple generalized collaboration networks,namely the preferential attachment,random attachment and mixed attachment networks.Based on Markov chain theory,we provide a rigorous proof for the existence of the steady-state degree distribution of the network generated by this model and obtain its corresponding exact formula.In particular,for mixed attachment,if it has preferential attachment,degree distribution of the network obeys power-law distribution,and it is a scale-free network.