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Applied Mathematics and Mechanics (English Edition) ›› 2009, Vol. 30 ›› Issue (6): 795-802.doi: https://doi.org/10.1007/s10483-009-0614-6

• Articles • 上一篇    下一篇

Markov chain-based analysis of a modified Cooper-Frieze model

童金英1 侯振挺1 史定华1,2     

  1. 1. School of Mathematics, Central South University, Changsha 410075, P. R. China;
    2. Department of Mathematics, Shanghai University, Shanghai 200444, P. R. China
  • 收稿日期:2008-08-19 修回日期:2009-04-22 出版日期:2009-06-01 发布日期:2009-06-01

Markov chain-based analysis of a modified Cooper-Frieze model

Jin-Ying TONG1, Zhen-Ting HOU1, Ding-Hua SHI1,2   

  1. 1. School of Mathematics, Central South University, Changsha 410075, P. R. China;
    2. Department of Mathematics, Shanghai University, Shanghai 200444, P. R. China
  • Received:2008-08-19 Revised:2009-04-22 Online:2009-06-01 Published:2009-06-01

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摘要： From the perspective of probability, the stability of a modified Cooper- Frieze model is studied in the present paper. Based on the concept and technique of the first-passage probability in the Markov theory, we provide a rigorous proof for the existence of the steady-state degree distribution, and derive the explicit formula analytically. Moreover, we perform extensive numerical simulations of the model, including the degree distribution and the clustering.

关键词: growing networks, preferential attachment, power law

Abstract: From the perspective of probability, the stability of a modified Cooper- Frieze model is studied in the present paper. Based on the concept and technique of the first-passage probability in the Markov theory, we provide a rigorous proof for the existence of the steady-state degree distribution, and derive the explicit formula analytically. Moreover, we perform extensive numerical simulations of the model, including the degree distribution and the clustering.

Key words: growing networks, preferential attachment, power law

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