  Mixed-SCORE is a recent approach for mixed membership community detection
proposed by Jin et al. (2017) which is an extension of SCORE (Jin, 2015). In
the note Jin et al. (2018), the authors propose SCORE+ as an improvement of
SCORE to handle with weak signal networks. In this paper, we propose a method
called Mixed-SCORE+ designed based on the Mixed-SCORE and SCORE+, therefore
Mixed-SCORE+ inherits nice properties of both Mixed-SCORE and SCORE+. In the
proposed method, we consider K+1 eigenvectors when there are K communities to
detect weak signal networks. And we also construct vertices hunting and
membership reconstruction steps to solve the problem of mixed membership
community detection. Compared with several benchmark methods, numerical results
show that Mixed-SCORE+ provides a significant improvement on the Polblogs
network and two weak signal networks Simmons and Caltech, with error rates
54/1222, 125/1137 and 94/590, respectively. Furthermore, Mixed-SCORE+ enjoys
excellent performances on the SNAP ego-networks.
