中国物理B ›› 2007, Vol. 16 ›› Issue (5): 1239-1245.doi: 10.1088/1009-1963/16/5/012

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The classification and analysis of dynamic networks

郭进利   

  1. Business School, University of Shanghai for Science and Technology, Shanghai 200093, China
  • 收稿日期:2006-04-12 修回日期:2006-11-27 出版日期:2007-05-20 发布日期:2007-05-20
  • 基金资助:
    Project supported by the Shanghai Leading Academic Discipline Project, China (Grant No T0502) and by the Shanghai Municipal Education Commission Natural Science Foundation, China (Grant No 05EZ35).

The classification and analysis of dynamic networks

Guo Jin-Li(郭进利)   

  1. Business School, University of Shanghai for Science and Technology, Shanghai 200093, China
  • Received:2006-04-12 Revised:2006-11-27 Online:2007-05-20 Published:2007-05-20
  • Supported by:
    Project supported by the Shanghai Leading Academic Discipline Project, China (Grant No T0502) and by the Shanghai Municipal Education Commission Natural Science Foundation, China (Grant No 05EZ35).

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摘要： In this paper we, firstly, classify the complex networks in which the nodes are of the lifetime distribution. Secondly, in order to study complex networks in terms of queuing system and homogeneous Markov chain, we establish the relation between the complex networks and queuing system, providing a new way of studying complex networks. Thirdly, we prove that there exist stationary degree distributions of M--G--P network, and obtain the analytic expression of the distribution by means of Markov chain theory. We also obtain the average path length and clustering coefficient of the network. The results show that M--G--P network is not only scale-free but also of a small-world feature in proper conditions.

Abstract: In this paper we, firstly, classify the complex networks in which the nodes are of the lifetime distribution. Secondly, in order to study complex networks in terms of queuing system and homogeneous Markov chain, we establish the relation between the complex networks and queuing system, providing a new way of studying complex networks. Thirdly, we prove that there exist stationary degree distributions of M--G--P network, and obtain the analytic expression of the distribution by means of Markov chain theory. We also obtain the average path length and clustering coefficient of the network. The results show that M--G--P network is not only scale-free but also of a small-world feature in proper conditions.

Key words: complex network, lifetime of nodes, BA model, scale-free network, small-world network

中图分类号:  (Networks and genealogical trees)

  • 89.75.Hc
02.50.Cw (Probability theory) 02.50.Ga (Markov processes)