  Community detection was a hot topic on network analysis, where the main aim
is to perform unsupervised learning or clustering in networks. Recently,
semi-supervised learning has received increasing attention among researchers.
In this paper, we propose a new algorithm, called weighted inverse Laplacian
(WIL), for predicting labels in partially labeled networks. The idea comes from
the first hitting time in random walk, and it also has nice explanations both
in information propagation and the regularization framework. We propose a
partially labeled degree-corrected block model (pDCBM) to describe the
generation of partially labeled networks. We show that WIL ensures the
misclassification rate is of order $O(\frac{1}{d})$ for the pDCBM with average
degree $d=\Omega(\log n),$ and that it can handle situations with greater
unbalanced than traditional Laplacian methods. WIL outperforms other
state-of-the-art methods in most of our simulations and real datasets,
especially in unbalanced networks and heterogeneous networks.
