Convolutional neural networks (CNNs) have been widely applied to hyperspectral image classification (HSIC). However, traditional convolutions can not effectively extract features for objects with irregular distributions. Recent methods attempt to address this issue by performing graph convolutions on spatial topologies, but fixed graph structures and local perceptions limit their performances. To tackle these problems, in this article, different from previous approaches, we perform the superpixel generation on intermediate features during network training to adaptively produce homogeneous regions, obtain graph structures, and further generate spatial descriptors, which are served as graph nodes. Besides spatial objects, we also explore the graph relationships between channels by reasonably aggregating channels to generate spectral descriptors. The adjacent matrices in these graph convolutions are obtained by considering the relationships among all descriptors to realize global perceptions. By combining the extracted spatial and spectral graph features, we finally obtain a spectral-spatial graph reasoning network (SSGRN). The spatial and spectral parts of SSGRN are separately called spatial and spectral graph reasoning subnetworks. Comprehensive experiments on four public datasets demonstrate the competitiveness of the proposed methods compared with other state-of-the-art graph convolution-based approaches.