Optimal network structure to induce the maximal small-world effect

doi:10.1088/1674-1056/23/2/028902

Abstract In this paper, the general efficiency, which is the average of the global efficiency and the local efficiency, is defined to measure the communication efficiency of a network. The increasing ratio of the general efficiency of a small-world network relative to that of the corresponding regular network is used to measure the small-world effect quantitatively. The more considerable the small-world effect, the higher the general efficiency of a network with a certain cost is. It is shown that the small-world effect increases monotonically with the increase of the vertex number. The optimal rewiring probability to induce the best small-world effect is approximately 0.02 and the optimal average connection probability decreases monotonically with the increase of the vertex number. Therefore, the optimal network structure to induce the maximal small-world effect is the structure with the large vertex number (>500), the small rewiring probability (≈ 0.02) and the small average connection probability (<0.1). Many previous research results support our results.

Keywords: small-world network communication efficiency optimal network structure

Received: 25 February 2013
Revised: 24 May 2013
Accepted manuscript online:

PACS:	89.75.Fb	(Structures and organization in complex systems)
	89.75.Hc	(Networks and genealogical trees)
	89.70.Cf	(Entropy and other measures of information)
	89.70.Hj	(Communication complexity)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 61101117, 61171099, and 61362008), the National Key Scientific and Technological Project of China (Grant No. 2012ZX03004005002), the Fundamental Research Funds for the Central Universities, China (Grant No. BUPT2012RC0112), and the Natural Science Foundation of Jiangxi Province, China (Grant No. 20132BAB201018).

Corresponding Authors: Lin Jia-Ru
E-mail: jrlin@bupt.edu.cn

About author: 89.75.Fb; 89.75.Hc; 89.70.Cf; 89.70.Hj

Cite this article:

Zhang Zheng-Zhen (张争珍), Xu Wen-Jun (许文俊), Zeng Shang-You (曾上游), Lin Jia-Ru (林家儒) Optimal network structure to induce the maximal small-world effect 2014 Chin. Phys. B 23 028902

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