Recently, graph convolutional network (GCN) has progressed significantly and gained increasing attention in hyperspectral image (HSI) classification due to its impressive representation power. However, existing GCN-based methods do not give full consideration to the multiscale spatial information, since the convolution operations are governed by fixed neighborhood. As a result, their performances can be limited, particularly in the regions with diverse land cover appearances. In this article, we develop a new dual interactive GCN (DIGCN) which introduces the dual GCN branches to capture spatial information at different scales. More significantly, the dual interactive module is embedded across the GCN branches, so that the correlation of multiscale spatial information can be leveraged to refine the graph information. To be concrete, the edge information contained in one GCN branch can be refined by incorporating the feature representations from the other branch. Analogously, improved feature representations can be generated in one GCN branch by fusing the edge information from the other branch. As such, the refined graph information can help enhance the representation power of the model. Furthermore, to avoid the negative effects of the manually constructed graph, our proposed model adaptively learns a discriminative region-induced graph, which also accelerates the convolution operation. We comprehensively evaluate the proposed method on four commonly used HSI benchmark data sets, and the state-of-the-art results can be achieved when compared with several typical HSI classification methods.