Graph Mediator Networks Bridging Local and Global Semantics via Serial Message Passing

Graph Neural Networks (GNNs) have achieved remarkable success in modeling structured data through local message passing. However, their effectiveness diminishes on graphs with low homophily or irregular structures, where long-range dependencies are hard to capture and features tend to suffer from over-smoothing and noise amplification. To address these limitations, we propose GMN, a novel dual-path Graph Mediator Network that explicitly enhances both global information propagation and spectral stability. In the spatial path, GMN introduces a lightweight Mediator node connected to all graph nodes, allowing long-range communication to occur in a single hop without increasing network depth. In parallel, the spectral path leverages multi-scale Chebyshev filtering along with a spectral energy regularization term that suppresses high-frequency noise, leading to smoother and more stable node embeddings. These two complementary pathways are adaptively integrated via a gated fusion mechanism, which dynamically balances their contributions based on structural context. Final graph-level representations are obtained through task-specific pooling strategies, enabling GMN to generalize effectively across different tasks. Extensive experiments on benchmark datasets with varying homophily levels and structural perturbations demonstrate that GMN consistently achieves state-of-the-art performance in terms of accuracy, robustness, and generalization. Code is available at: https://github.com/sun2017bupt/GMN.