Optimal network structure to induce the maximal small-world effect |
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| Authors: | Zhang Zheng-Zhen Xu Wen-Jun Zeng Shang-You Lin Jia-Ru |
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| Affiliation: | 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 |
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| 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. |
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| Keywords: | small-world network communication efficiency optimal network structure |
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