Optimal network structure to induce the maximal small-world effect

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

中国物理B ›› 2014, Vol. 23 ›› Issue (2): 28902-028902.doi: 10.1088/1674-1056/23/2/028902

• INTERDISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY • 上一篇下一篇

Optimal network structure to induce the maximal small-world effect

张争珍^a, 许文俊^a, 曾上游^b, 林家儒^a

a Key Laboratory of Universal Wireless Communications, Ministry of Education, Beijing University of Posts and Telecommunications, Beijing 100876, China;
b College of Electronic Engineering, Guangxi Normal University, Guilin 541004, China

收稿日期:2013-02-25 修回日期:2013-05-24 出版日期:2013-12-12 发布日期:2013-12-12
基金资助:
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).

Optimal network structure to induce the maximal small-world effect

Zhang Zheng-Zhen (张争珍)^a, Xu Wen-Jun (许文俊)^a, Zeng Shang-You (曾上游)^b, Lin Jia-Ru (林家儒)^a

a Key Laboratory of Universal Wireless Communications, Ministry of Education, Beijing University of Posts and Telecommunications, Beijing 100876, China;
b College of Electronic Engineering, Guangxi Normal University, Guilin 541004, China

Received:2013-02-25 Revised:2013-05-24 Online:2013-12-12 Published:2013-12-12
Contact: Lin Jia-Ru E-mail:jrlin@bupt.edu.cn
About author:89.75.Fb; 89.75.Hc; 89.70.Cf; 89.70.Hj
Supported by:
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).

摘要/Abstract

摘要： 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.

关键词: small-world network, communication efficiency, optimal network structure

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.

Key words: small-world network, communication efficiency, optimal network structure

中图分类号: (Structures and organization in complex systems)

89.75.Fb

89.75.Hc (Networks and genealogical trees) 89.70.Cf (Entropy and other measures of information) 89.70.Hj (Communication complexity)

张争珍, 许文俊, 曾上游, 林家儒. Optimal network structure to induce the maximal small-world effect[J]. 中国物理B, 2014, 23(2): 28902-028902.

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[J]. Chin. Phys. B, 2014, 23(2): 28902-028902.

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Optimal network structure to induce the maximal small-world effect

Optimal network structure to induce the maximal small-world effect

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