Optimal network structure to induce the maximal small-world effect  

作　　者：张争珍 许文俊 曾上游 林家儒 

机构地区：[1]Key Laboratory of Universal Wireless Communications,Ministry of Education,Beijing University of Posts and Telecommunications [2]College of Electronic Engineering,Guangxi Normal University

出　　处：《Chinese Physics B》2014年第2期623-627,共5页中国物理B（英文版）

基　　金：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);the Natural Science Foundation of Jiangxi Province,China (Grant No.20132BAB201018)

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.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 

分 类 号：O157.5[理学—数学]