Markov Chain-based Degree Distributions of Evolving Networks  

作　　者：Xiang Xing KONG Zhen Ting HOU Ding Hua SHI Quan Rong CHEN Qing Gui ZHAO 

机构地区：[1]School of Mathematics,Central South University [2]Department of Mathematics,Shanghai University [3]Department of Electronic Engineering,City University of Hong Kong,P.R.China [4]Department of Mathematics and Science,Hunan First Normal University

出　　处：《Acta Mathematica Sinica,English Series》2012年第10期1981-1994,共14页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China (Grant No. 10901164);Graduate Research Innovation Projects in Hunan Province (Grant No. CX2009B020);Graduate Degree Thesis Innovation Foundation of Central South University (Grant No. 2009ybfz11);supported by Natural Science Foundation of China (Grant Nos. 11071258, 90820302);Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20090162110058)

摘　　要：In this paper, we study a class of stochastic processes, called evolving network Markov chains, in evolving networks. Our approach is to transform the degree distribution problem of an evolving network to a corresponding problem of evolving network Markov chains. We investigate the evolving network Markov chains, thereby obtaining some exact formulas as well as a precise criterion for determining whether the steady degree distribution of the evolving network is a power-law or not. With this new method, we finally obtain a rigorous, exact and unified solution of the steady degree distribution of the evolving network.In this paper, we study a class of stochastic processes, called evolving network Markov chains, in evolving networks. Our approach is to transform the degree distribution problem of an evolving network to a corresponding problem of evolving network Markov chains. We investigate the evolving network Markov chains, thereby obtaining some exact formulas as well as a precise criterion for determining whether the steady degree distribution of the evolving network is a power-law or not. With this new method, we finally obtain a rigorous, exact and unified solution of the steady degree distribution of the evolving network.

关 键 词：Evolving network Markov chain scale-free network degree distribution 

分 类 号：O211.62[理学—概率论与数理统计] TN943.6[理学—数学]