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

作　　者：李旲 曹宏铎 山秀明 任勇 袁坚 

机构地区：[1]School of Business,SUN YAT-SEN University [2]Department of Electronic Engineering,Tsinghua University

出　　处：《Chinese Physics B》2009年第5期1721-1724,共4页中国物理B（英文版）

基　　金：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)

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 （k） and （l）, we are able to find the statistical characteristics of the optimal structure. There is a critical power law exponent ac 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 ac is approximately 2.1.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 （k） and （l）, we are able to find the statistical characteristics of the optimal structure. There is a critical power law exponent ac 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 ac is approximately 2.1.

关 键 词：INTERNET the evolving principle the optimal structure power law 

分 类 号：TP393.02[自动化与计算机技术—计算机应用技术]