Band selection is an effective means to alleviate the curse of dimensionality in hyperspectral data. Many methods select a compact and low redundant band subset, which is inadequate as it may degrade the classification performance. Instead, more emphasis shall be put on selecting representative bands. In this article, we propose a robust unsupervised band selection method to address this issue. Our method reveals bandwise representativeness based on the comprehensive interband neighborhood structure. It incorporates an interband neighborhood graph into a sparse self-contained regression model in order to provide a reasonable measure for bandwise representativeness. The derived coefficient matrix not only uncovers bandwise importance values but also is coherent to the generalized interband local neighborhood structure. For constructing the interband neighboring structural graph, an integrated multigraph model is employed to achieve better generalization performance. It combines the benefit of multiple graphs but is insusceptible to the defects of a single one. To enhance the reliability of this model, a joint trace minimum and nonnegative constraint is imposed on the coefficient matrix. Accordingly, a multigraph integrated embedding and robust self-contained regression model (MGRSR) is formulated. In addition, an iterative update algorithm is developed to solve the problem. Comparative experiments on three hyperspectral data sets illustrate that MGRSR is robust to various data and has superior performance compared with several state-of-the-art methods.