Applications of dual regularized Laplacian matrix for community detection

Spectral clustering is widely used for detecting clusters in networks for community detection, while a small change on the graph Laplacian matrix could bring a dramatic improvement. In this paper, we propose a dual regularized graph Laplacian matrix and then employ it to the classical spectral clustering approach under the degree-corrected stochastic block model. If the number of communities is known as K, we consider more than K leading eigenvectors and weight them by their corresponding eigenvalues in the spectral clustering procedure to improve the performance. The improved spectral clustering method is dual regularized spectral clustering (DRSC). Theoretical analysis of DRSC shows that under mild conditions it yields stable consistent community detection. Meanwhile, we develop a strategy by taking advantage of DRSC and Newman’s modularity to estimate the number of communities K. We compare the performance of DRSC with several spectral methods and investigate the behaviors of our strategy for estimating K by substantial simulated networks and real-world networks. Numerical results show that DRSC enjoys satisfactory performance and our strategy on estimating K performs accurately and consistently, even in cases where there is only one community in a network.