Regularization has appeared explicitly in hyperspectral image (HSI) classification community, which serves as a promising paradigm for leveraging labeled and unlabeled information, computer's automation and user's interaction, spectral and spatial information, and so on. Graph-based regularization is capable of modeling the nonlinear structures embedded in high-dimensional space, with the great potential for HSI classification. However, traditional methods exhibit low capacity when facing noisy and large-scale data, thus posing a big challenge for their successful use in this community. In this paper, we present two novel sparse graph regularization methods, SGR and SGR with total variation (TV-SGR). In SGR, the labels of large unknown data are propagated based on the fraction matrix and the prediction function, where the fraction matrix is obtained using an effective sparse representation (SR) algorithm with respect to the dictionary, and the prediction function is estimated by optimizing a typical graph-based regularization problem. In contrast, TV-SGR is an extension of SGR by considering spatial information modeled by total variation in SR. Propagating the prediction function from dictionary to large unknown data using the fraction matrix is the essence of the paradigm. SGR and TV-SGR can be equipped with semisupervised learning, active learning, and spectral-spatial classification with large flexibility. The experimental results with two popular hyperspectral data sets indicate that the proposed methods outperform some state-of-the-art approaches in terms of computational efficacy, classification accuracy, and robustness to noise.