中国物理B ›› 2009, Vol. 18 ›› Issue (5): 1721-1724.doi: 10.1088/1674-1056/18/5/001

• •    下一篇

The principle of the Internet evolving and the conjecture of the optimal structure of Internet

曹宏铎1, 山秀明1, 任勇1, 袁坚1, 李旲2   

  1. (1)Department of Electronic Engineering, Tsinghua University, Beijing 100084, China; (2)School of Business, SUN YAT-SEN University, Guangzhou 510275, China;Department of Electronic Engineering, Tsinghua University, Beijing 100084, China
  • 收稿日期:2008-04-14 修回日期:2008-11-20 出版日期:2009-05-20 发布日期:2009-05-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos 70801066, 60674048, 60772053 and 60672142); the National Basic Research Program of China (Grant Nos 2007CB307100 and 2007CB307105).

The principle of the Internet evolving and the conjecture of the optimal structure of Internet

Li Ying(李旲)a)b)†, Cao Hong-Duo(曹宏铎)a)‡, Shan Xiu-Ming(山秀明)b), Ren Yong(任勇)b), and Yuan Jian(袁坚)b)   

  1. a School of Business, SUN YAT-SEN University, Guangzhou 510275, China;Department of Electronic Engineering, Tsinghua University, Beijing 100084, China; b Department of Electronic Engineering, Tsinghua University, Beijing 100084, China
  • Received:2008-04-14 Revised:2008-11-20 Online:2009-05-20 Published:2009-05-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos 70801066, 60674048, 60772053 and 60672142); the National Basic Research Program of China (Grant Nos 2007CB307100 and 2007CB307105).

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摘要： In this paper we will give the statistical characteristics and general principles of an optimal structure of the Internet, which is a scale-free network. Since the purpose of the Internet is to allow fast and easy communication, the average path length is used to measure the performance of the network, and the number of edges of the network is used as a metric of its cost. Based on this, the goal of this Internet optimization problem is to obtain the highest performance with the lowest cost. A multi goal optimization problem is proposed to model this problem. By using two empirical formulas of and , we are able to find the statistical characteristics of the optimal structure. There is a critical power law exponent α c for the Internet with power law degree distribution, at which the Internet can obtain a relatively good performance with a low cost. We find that this α c is approximately 2.1.

关键词: Internet, the evolving principle, the optimal structure, power law

Abstract: In this paper we will give the statistical characteristics and general principles of an optimal structure of the Internet, which is a scale-free network. Since the purpose of the Internet is to allow fast and easy  communication, the average path length is used to measure the performance of the network, and the number of edges of the network is used as a metric of its cost. Based on this, the goal of this Internet optimization problem is  to obtain the highest performance with the lowest cost. A multi goal optimization problem is proposed to model this problem. By using two empirical formulas of $\langle k\rangle $ and $\langle l\rangle$, we are able to find the  statistical characteristics of the optimal structure. There is a critical power law exponent $\alpha _{\rm c}$ for the Internet with power law degree distribution, at which the Internet can obtain a relatively good performance  with a low cost. We find that this $\alpha _{\rm c}$ is approximately 2.1.

Key words: Internet, the evolving principle, the optimal structure, power law

中图分类号:  (World Wide Web, Internet)

  • 89.20.Hh
02.50.Ng (Distribution theory and Monte Carlo studies) 02.60.Pn (Numerical optimization)