Image denoising is a critical problem in industrial information applications since noisy images can have adverse effects on the performance of many industrial tasks. Currently, Transformer structures and graph convolutional networks (GCNs) have been widely employed in image denoising to capture long-range dependencies for the performance promotion. These methods, however, severely suffer from three major problems. Initially, the long-range dependencies captured by Transformers and GCNs are only focused on the pixel level and patch level, respectively. This leads to the coarse retrieved feature, hindering further performance promotion. In addition, due to the limited training data, especially for the noisy images with highly diverse and complex noise, the denoising process may lack sufficient feature for reconstructing denoised images. Eventually, the limited training data may also results in over-fitting, leading to poor generalization in the denoising process. This article first proposes adaptive graph prior network (AGP-Net) using a novel graph construction method to capture the long-range dependencies on both the pixel and patch levels. Then, we propose graph supplementary prior and graph noise prior in AGP-Net to adaptively generate supplementary feature and regularization noise for improving the performance and generalization of image denoising. Extensive ablation and benchmark tests show our AGP-Net achieve the most advanced image denoising performance.