Accurate brain tumor segmentation from MRI is essential for diagnosis and treatment planning. While most exsting graph neural network (GNN)-based approaches use GNNs as the primary segmentation module applied to the full image, we propose a novel hybrid strategy where GNNs act as a targeted refinement of U-Net predictions. By focusing only on regions of uncertainty, the framework combines U-Net’s local spatial precision with GNN-based long-range context, reducing computational overhead. Experiments on the BraTS 2020 dataset show Dice score improvements of 2.63% for whole tumor, 2.18% for tumor core, and 3.71% for enhancing tumor compared to a baseline U-Net. This refinement strategy highlights the potential of graph-enhanced CNNs as an efficient and clinically meaningful alternative for advancing automated brain tumor analysis.