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 correspond...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.展开更多
基金Supported by National Natural Science Foundation of China (Grant No. 10901164)Graduate Research Innovation Projects in Hunan Province (Grant No. CX2009B020)+2 种基金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)
文摘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.
