Next Level Message-Passing with Hierarchical Support Graphs
Carlos Vonessen, Florian Grötschla, Roger Wattenhofer
TL;DR
This work tackles the limited receptive field of traditional MPNNs by introducing Hierarchical Support Graphs (HSGs), a flexible, multi-level augmentation created via recursive graph coarsening. HSGs integrate with existing MPNN architectures without modifying core message-passing modules, and are wired back to the original graph through vertical connections, forming a comprehensive graph $G^H$ with levels $H^{(i)}$. Theoretical bounds on the growth and connectivity of HSG-augmented graphs are complemented by extensive experiments showing state-of-the-art performance across several benchmarks, often surpassing virtual-node and certain graph-transformer baselines while maintaining scalable computation. Ablation studies reveal how coarsening choices, feature imputation, and adaptation of the prediction head influence performance, providing practical guidance for employing HSGs in diverse graph-learning tasks. Overall, HSGs offer a robust, scalable approach to enhance information flow in graphs, improving long-range communication with modest overhead and broad compatibility with standard GNN pipelines.
Abstract
Message-Passing Neural Networks (MPNNs) are extensively employed in graph learning tasks but suffer from limitations such as the restricted scope of information exchange, by being confined to neighboring nodes during each round of message passing. Various strategies have been proposed to address these limitations, including incorporating virtual nodes to facilitate global information exchange. In this study, we introduce the Hierarchical Support Graph (HSG), an extension of the virtual node concept created through recursive coarsening of the original graph. This approach provides a flexible framework for enhancing information flow in graphs, independent of the specific MPNN layers utilized. We present a theoretical analysis of HSGs, investigate their empirical performance, and demonstrate that HSGs can surpass other methods augmented with virtual nodes, achieving state-of-the-art results across multiple datasets.