A major challenge in real-world feature matching problems is to tolerate the numerous outliers arising in typical visual tasks. Variations in object appearance, shape, and structure within the same object class make it harder to distinguish inliers from outliers due to clutters. In this pa- per, we propose a max-pooling approach to graph matching, which is not only resilient to deformations but also remarkably tolerant to outliers. The proposed algorithm evaluates each candidate match using its most promising neighbors, and gradually propagates the corresponding scores to update the neighbors. As final output, it assigns a reliable score to each match together with its supporting neighbors, thus providing contextual information for further verification. We demonstrate the robustness and utility of our method with synthetic and real image experiments.