Graph is a popular technique to explore the structure of data. Many related algorithms directly construct graphs based on the original data. Actually, the samples collected in real life usually contain noise. Besides, some unimportant features probably exist in high-dimensional data. Therefore, this way cannot assure a high-quality graph and furthermore brings some adverse influence to the following tasks. In this paper, we incorporate robust graph learning and dimensionality reduction into a unified framework which also seamlessly integrates the clustering task. On the basis of the framework, Euclidean distance-based robust graph (EDBRG) and self-expressiveness-based robust graph (SEBRG) are presented. Both EDBRG and SEBRG contain clustering information from which the clustering results can be obtained directly. By projecting the original data into a discriminative subspace where the negative effect of redundant features and noise is removed, EDBRG and SEBRG are informative, robust, and sparse. During the whole mapping process, the main energy of data is preserved. Finally, some data sets are adopted to test the performances of EDBRG and SEBRG. Extensive experiments illustrate that the proposed methods have many advantages for the task of clustering, comparing with the state-of-the-art algorithms.