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, $N$, as the only parameter, two parameters including $N$ and a second parameter $\alpha $ are included in our formula. The parameter $\alpha $ 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.
Received: 12 September 2007
Revised: 26 December 2007
Accepted manuscript online:
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
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
