  For community detection problem, spectral clustering is a widely used method
for detecting clusters in networks. In this paper, we propose an improved
spectral clustering (ISC) approach under the degree corrected stochastic block
model (DCSBM). ISC is designed based on the k-means clustering algorithm on the
weighted leading K + 1 eigenvectors of a regularized Laplacian matrix where the
weights are their corresponding eigenvalues. Theoretical analysis of ISC shows
that under mild conditions the ISC yields stable consistent community
detection. Numerical results show that ISC outperforms classical spectral
clustering methods for community detection on both simulated and eight
empirical networks. Especially, ISC provides a significant improvement on two
weak signal networks Simmons and Caltech, with error rates of 121/1137 and
96/590, respectively.
