Spectral clustering is a widely used method for community detection in networks. We focus on a semi-supervised community detection scenario in the Partially Labeled Stochastic Block Model (PL-SBM) with two balanced communities, where a fixed portion of labels is known. Our approach leverages random walks in which the revealed nodes in each community act as absorbing states. By analyzing the quasi-stationary distributions associated with these random walks, we construct a classifier that distinguishes the two communities by examining differences in the associated eigenvectors. We establish upper and lower bounds on the error rate for a broad class of quasi-stationary algorithms, encompassing both spectral and voting-based approaches. In particular, we prove that this class of algorithms can achieve the optimal error rate in the connected regime. We further demonstrate empirically that our quasistationary approach improves performance on both real-world and simulated
datasets.