An estimation formula for the average path length of scale-free networks |
| |
Authors: | Li Ying Cao Hong-Duo Shan Xiu-Ming and Ren Yong |
| |
Institution: | 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 |
| |
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. |
| |
Keywords: | scale free network power law small world power law exponent |
|
| 点击此处可从《中国物理 B》浏览原始摘要信息 |
| 点击此处可从《中国物理 B》下载免费的PDF全文 |
|