  Community detection has been well studied recent years, but the more
realistic case of mixed membership community detection remains a challenge.
Here, we develop an efficient spectral algorithm Mixed-ISC based on applying
more than K eigenvectors for clustering given K communities for estimating the
community memberships under the degree-corrected mixed membership (DCMM) model.
We show that the algorithm is asymptotically consistent. Numerical experiments
on both simulated networks and many empirical networks demonstrate that
Mixed-ISC performs well compared to a number of benchmark methods for mixed
membership community detection. Especially, Mixed-ISC provides satisfactory
performances on weak signal networks.
