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Graph-based methods form a main category of semi-supervised learning, offering flexibility and easy implementation in many applications. However, the performance of these methods is often sensitive to the construction of a neighborhood graph, which is non-trivial for many real-world problems. In this paper, we propose a novel framework that builds on learning the graph given labeled and unlabeled data. The paper has two major contributions. Firstly, we use a nonparametric algorithm to learn the entire adjacency matrix of a symmetry-favored k-NN graph, assuming that the matrix is doubly stochastic. The nonparametric algorithm makes the constructed graph highly robust to noisy samples and capable of approximating underlying submanifolds or clusters. Secondly, to address multi-class semi-supervised classification, we formulate a constrained label propagation problem on the learned graph by incorporating class priors, leading to a simple closed-form solution. Experimental results on both synthetic and real-world datasets show that our approach is significantly better than the state-of-the-art graph-based semi-supervised learning algorithms in terms of accuracy and robustness.