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

Li Ying; Cao Hong-Duo; Shan Xiu-Ming; Ren Yong

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

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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.

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来源
《中国物理：英文版》 |2008年第7期|2327-2332|共6页
作者
Li Ying; Cao Hong-Duo; Shan Xiu-Ming; Ren Yong;
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作者单位

Department of Management Sciences, School of Business, SUN YAT-SEN University, Guangzhou 510275, China;

Department of Electronic Engineering, Tsinghua University, Beijing 100084, China;

Department of Management Sciences, School of Business, SUN YAT-SEN University, Guangzhou 510275, China;

Department of Electronic Engineering, Tsinghua University, Beijing 100084, China;

Department of Electronic Engineering, Tsinghua University, Beijing 100084, China;

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原文格式 PDF
正文语种 chi
中图分类物理学;
关键词
scale free network; power law; small world; power law exponent;

机译：无标度网络幂律小世界幂律指数;

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

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