Detecting the optimal number of communities in complex networks

TL;DR

This paper introduces a new statistic based on normalized mutual information to accurately determine the optimal number of communities in complex networks, improving community detection methods.

Contribution

It proposes the statistic Ω(c) for identifying the optimal community number and measuring community structure significance, validated through numerical and empirical tests.

Findings

Ω(c) peaks at the optimal community number

Effective in artificial and real-world networks

Measures community structure significance

Abstract

To obtain the optimal number of communities is an important problem in detecting community structure. In this paper, we extend the 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 \emph{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.