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For community detection problem, spectral clustering is a widely used methodfor detecting clusters in networks. In this paper, we propose an improvedspectral clustering (ISC) approach under the degree corrected stochastic blockmodel (DCSBM). ISC is designed based on the k-means clustering algorithm on theweighted leading K + 1 eigenvectors of a regularized Laplacian matrix where theweights are their corresponding eigenvalues. Theoretical analysis of ISC showsthat under mild conditions the ISC yields stable consistent communitydetection. Numerical results show that ISC outperforms classical spectralclustering methods for community detection on both simulated and eightempirical networks. Especially, ISC provides a significant improvement on twoweak signal networks Simmons and Caltech, with error rates of 121/1137 and96/590, respectively.

An improved spectral clustering method for community detection under the degree-corrected stochastic blockmodel