An estimation formula for the average path length of scale-free networks
Li Ying(李旲)a)b), Cao Hong-Duo(曹宏铎)a),Shan Xiu-Ming(山秀明)b), and Ren Yong(任勇)b)
aDepartment of Management Sciences, School of Business, SUN YAT-SEN University, Guangzhou 510275, China; b Department of Electronic Engineering, Tsinghua University, Beijing 100084, China
Abstract 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, , as the only parameter, two parameters including and a second parameter are included in our formula. The parameter 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.
Fund: Project supported by the National
Natural Science Foundation of China
(Grant Nos 60672142, 60772053 and 90304005).
Cite this article:
Li Ying(李旲), Cao Hong-Duo(曹宏铎), Shan Xiu-Ming(山秀明), and Ren Yong(任勇) An estimation formula for the average path length of scale-free networks 2008 Chin. Phys. B 17 2327
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