  Community detection in network analysis is an attractive research area
recently. Here, under the degree-corrected mixed membership (DCMM) model, we
propose an efficient approach called mixed regularized spectral clustering
(Mixed-RSC for short) based on the regularized Laplacian matrix. Mixed-RSC is
designed based on an ideal cone structure of the variant for the
eigen-decomposition of the population regularized Laplacian matrix. We show
that the algorithm is asymptotically consistent under mild conditions by
providing error bounds for the inferred membership vector of each node. As a
byproduct of our bound, we provide the theoretical optimal choice for the
regularization parameter {\tau}. To demonstrate the performance of our method,
we apply it with previous benchmark methods on both simulated and real-world
networks. To our knowledge, this is the first work to design spectral
clustering algorithm for mixed membership community detection problem under
DCMM model based on the application of regularized Laplacian matrix.
