  Motivated by social network analysis and network-based recommendation
systems, we study a semi-supervised community detection problem in which the
objective is to estimate the community label of a new node using the network
topology and partially observed community labels of existing nodes. The network
is modeled using a degree-corrected stochastic block model, which allows for
severe degree heterogeneity and potentially non-assortative communities. We
propose an algorithm that computes a `structural similarity metric' between the
new node and each of the $K$ communities by aggregating labeled and unlabeled
data. The estimated label of the new node corresponds to the value of $k$ that
maximizes this similarity metric. Our method is fast and numerically
outperforms existing semi-supervised algorithms. Theoretically, we derive
explicit bounds for the misclassification error and show the efficiency of our
method by comparing it with an ideal classifier. Our findings highlight, to the
best of our knowledge, the first semi-supervised community detection algorithm
that offers theoretical guarantees.
