Detecting the optimal number of communities in complex networks

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 Omega(c) is proposed to detect the optimal number of communities. In general, when Omega(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 Omega(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 Omega(c) is effective in both artificial and real world networks. (C) 2011 Published by Elsevier B.V.