A spectral algorithm of community identification

¹ Temasek Laboratories, National University of Singapore - Singapore 117508
² Beijing-Hong Kong-Singapore Joint Center of Nonlinear and Complex Systems (Singapore), National University of Singapore - Singapore 117508
³ Department of Physics, National University of Singapore - Singapore 117542
⁴ Centre for Quantum Technologies, National University of Singapore - Singapore 117543
⁵ Yale-NUS College - Singapore

Received: 24 September 2012
Accepted: 7 February 2013

Abstract

A novel spectral algorithm utilizing multiple eigenvectors is proposed to identify the communities in networks based on the modularity Q. We investigate the reduced modularity on low-rank approximations of the original modularity matrix consisting of leading eigenvectors. By exploiting the rotational invariance of the reduced modularity, near-optimal partitions of the network can be found. This approach generalizes the conventional spectral network partitioning algorithms which usually use only one eigenvector, and promises better results because more spectral information is used. The algorithm shows excellent performance on various real-world and computer-generated benchmark networks, and outperforms the most known community detection methods.