Detecting the optimal number of communities in complex networks |
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Authors: | Zhifang LiYanqing Hu Beishan XuZengru Di Ying Fan |
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Institution: | a Department of Systems Science, School of Management and Center for Complexity Research, Beijing Normal University, Beijing 100875, Chinab School of Mathematics, Southwest Jiaotong University, Chengdu 610031, China |
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Abstract: | To obtain the optimal number of communities is an important problem in detecting community structures. In this paper, we use the extended measurement of community detecting algorithms to find the optimal community number. Based on the normalized mutual information index, which has been used as a measure for similarity of communities, a statistic Ω(c) is proposed to detect the optimal number of communities. In general, when Ω(c) reaches its local maximum, especially the first one, the corresponding number of communities c is likely to be optimal in community detection. Moreover, the statistic Ω(c) can also measure the significance of community structures in complex networks, which has been paid more attention recently. Numerical and empirical results show that the index Ω(c) is effective in both artificial and real world networks. |
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Keywords: | Complex network Community structure Optimal community number |
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