数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (1): 221-228.doi: 10.1016/S0252-9602(11)60222-1

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MARKOV CHAIN-BASED ANALYSIS OF THE DEGREE DISTRIBUTION FOR A GROWING NETWORK

侯振挺1|童金英3|史定华1,2   

  1. 1. School of Mathematical Science and Computing Technology, Central South University, Changsha |410075, China;
    2. Department of Mathematics, Shanghai University, Shanghai 200444, China;
    3. School of Sciences, Donghua University, Shanghai 201620, China
  • 收稿日期:2008-07-09 修回日期:2008-11-25 出版日期:2011-01-20 发布日期:2011-01-20
  • 基金资助:

    This research is supported by the National Natural Science Foundation (11071258, 60874083, 10872119, 10901164)

MARKOV CHAIN-BASED ANALYSIS OF THE DEGREE DISTRIBUTION FOR A GROWING NETWORK

 HOU Zhen-Ting1, TONG Jin-Ying3, SHI Ding-Hua1,2   

  1. 1. School of Mathematical Science and Computing Technology, Central South University, Changsha |410075, China;
    2. Department of Mathematics, Shanghai University, Shanghai 200444, China;
    3. School of Sciences, Donghua University, Shanghai 201620, China
  • Received:2008-07-09 Revised:2008-11-25 Online:2011-01-20 Published:2011-01-20
  • Supported by:

    This research is supported by the National Natural Science Foundation (11071258, 60874083, 10872119, 10901164)

摘要:

In this article, we focus on discussing the degree distribution of the DMS model from the perspective of probability. On the basis of  the concept and technique of first-passage probability in Markov theory, we provide a rigorous proof for existence of the steady-state degree distribution, mathematically re-deriving the exact formula of the distribution. The approach based on Markov chain theory is universal and performs well in a large class of growing networks.

关键词: Growing networks, preferential attachment, power law 

Abstract:

In this article, we focus on discussing the degree distribution of the DMS model from the perspective of probability. On the basis of  the concept and technique of first-passage probability in Markov theory, we provide a rigorous proof for existence of the steady-state degree distribution, mathematically re-deriving the exact formula of the distribution. The approach based on Markov chain theory is universal and performs well in a large class of growing networks.

Key words: Growing networks, preferential attachment, power law

中图分类号: 

  • 05C80