  Based on the classical Degree Corrected Stochastic Blockmodel (DCSBM) model
for network community detection problem, we propose two novel approaches:
principal component clustering (PCC) and normalized principal component
clustering (NPCC). Without any parameters to be estimated, the PCC method is
simple to be implemented. Under mild conditions, we show that PCC yields
consistent community detection. NPCC is designed based on the combination of
the PCC and the RSC method (Qin & Rohe 2013). Population analysis for NPCC
shows that NPCC returns perfect clustering for the ideal case under DCSBM. PCC
and NPCC is illustrated through synthetic and real-world datasets. Numerical
results show that NPCC provides a significant improvement compare with PCC and
RSC. Moreover, NPCC inherits nice properties of PCC and RSC such that NPCC is
insensitive to the number of eigenvectors to be clustered and the choosing of
the tuning parameter. When dealing with two weak signal networks Simmons and
Caltech, by considering one more eigenvectors for clustering, we provide two
refinements PCC+ and NPCC+ of PCC and NPCC, respectively. Both two refinements
algorithms provide improvement performances compared with their original
algorithms. Especially, NPCC+ provides satisfactory performances on Simmons and
Caltech, with error rates of 121/1137 and 96/590, respectively.
