Super-Resolution (SR) reconstructs high-resolution images from low-resolution ones. CNNs and window-attention methods are two major categories of canonical SR models. However, these measures are rigid: in both operations, each pixel gathers the same number of neighboring pixels, hindering their effectiveness in SR tasks. Alternatively, we leverage the flexibility of graphs and propose the Image Processing GNN (IPG) model to break the rigidity that dominates previous SR methods. Firstly, SR is unbalanced in that most reconstruction efforts are concentrated to a small proportion of detail-rich image parts. Hence, we leverage degree flexibility by assigning higher node degrees to detail-rich image nodes. Then in order to construct graphs for SR-effective aggregation, we treat images as pixel node sets rather than patch nodes. Lastly, we hold that both local and global information are crucial for SR performance. In the hope of gathering pixel information from both local and global scales efficiently via flexible graphs, we search node connections within nearby regions to construct local graphs; and find connections within a strided sampling space of the whole image for global graphs. The flexibility of graphs boosts the SR performance of the IPG model. Experiment results on various datasets demonstrates that the proposed IPG outperforms State-of-the-Art baselines. Codes are available at https://github.com/huawei-noah/Efficient-Computing/tree/master/LowLevel/IPG.