An estimation formula for the average path length of scale-free networks  

作　　者：李旲 曹宏铎 山秀明 任勇 

机构地区：[1]Department of Management Sciences, School of Business, SUN YAT-SEN University, Guangzhou 510275, China [2]Department of Electronic Engineering, Tsinghua University, Beijing 100084, China

出　　处：《Chinese Physics B》2008年第7期2327-2332,共6页中国物理B（英文版）

基　　金：supported by the National Natural Science Foundation of China (Grant Nos 60672142, 60772053 and 90304005)

摘　　要：A universal estimation formula for the average path length of scale free networks is given in this paper. Different from other estimation formulas, most of which use the size of network, N, as the only parameter, two parameters including N and a second parameter α are included in our formula. The parameter α is the power-law exponent, which represents the local connectivity property of a network. Because of this, the formula captures an important property that the local connectivity property at a microscopic level can determine the global connectivity of the whole network. The use of this new parameter distinguishes this approach from the other estimation formulas, and makes it a universal estimation formula, which can be applied to all types of scale-free networks. The conclusion is made that the small world feature is a derivative feature of a scale free network. If a network follows the power-law degree distribution, it must be a small world network. The power-law degree distribution property, while making the network economical, preserves the efficiency through this small world property when the network is scaled up. In other words, a real scale-free network is scaled at a relatively small cost and a relatively high efficiency, and that is the desirable result of self-organization optimization.A universal estimation formula for the average path length of scale free networks is given in this paper. Different from other estimation formulas, most of which use the size of network, N, as the only parameter, two parameters including N and a second parameter α are included in our formula. The parameter α is the power-law exponent, which represents the local connectivity property of a network. Because of this, the formula captures an important property that the local connectivity property at a microscopic level can determine the global connectivity of the whole network. The use of this new parameter distinguishes this approach from the other estimation formulas, and makes it a universal estimation formula, which can be applied to all types of scale-free networks. The conclusion is made that the small world feature is a derivative feature of a scale free network. If a network follows the power-law degree distribution, it must be a small world network. The power-law degree distribution property, while making the network economical, preserves the efficiency through this small world property when the network is scaled up. In other words, a real scale-free network is scaled at a relatively small cost and a relatively high efficiency, and that is the desirable result of self-organization optimization.

关 键 词：scale free network power law small world power law exponent 

分 类 号：O157.5[理学—数学]