We propose a new graph-based semisupervised learning (SSL) algorithm and demonstrate its application to document categorization. Each document is represented by a vertex within a weighted undirected graph and our proposed framework minimizes the weighted Kullback-Leibler divergence between distributions that encode the class membership probabilities of each vertex. The proposed objective is convex with guaranteed convergence using an alternating minimization procedure. Further, it generalizes in a straightforward manner to multi-class problems. We present results on two standard tasks, namely Reuters-21578 and WebKB, showing that the proposed algorithm significantly outperforms the state-of-the-art.