Ramanujan Graph Rewiring with Non Negative Resistance Curvature

• URL: http://arxiv.org/abs/2606.21333v2
• Date: Wed, 24 Jun 2026 08:57:15 GMT
• Title: Ramanujan Graph Rewiring with Non Negative Resistance Curvature
• Abstract summary: Graph Neural Networks (GNNs) have emerged as a powerful paradigm for learning on graph-structured data by iteratively propagating and aggregating information across edges.<n>Conventional message passing schemes often suffer from over-squashing, whereby exponentially large neighborhoods are compressed into fixed-dimensional embeddings.
• Score: 1.4323566945483497
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Graph Neural Networks (GNNs) have emerged as a powerful paradigm for learning on graph-structured data by iteratively propagating and aggregating information across edges. However, conventional message passing schemes often suffer from over-squashing, whereby exponentially large neighborhoods are compressed into fixed-dimensional embeddings, impeding effective long-range dependency learning. In this work, we introduce Ramanujan Propagation, a graph rewiring strategy that leverages Ramanujan graphs to alleviate topological bottlenecks in GNNs. We first establish that suitably chosen Ramanujan graphs guarantee non-negative resistance curvature, which mitigates over-squashing and facilitates efficient information flow. We then propose an algorithmic framework to construct a Ramanujan rewired graph that preserves the local connectivity of the original graph. Our experiments demonstrate that our method outperforms nine state-of-the-art rewiring techniques. These results establish Ramanujan graphs as a rigorous structural prior for scalable, topology-aware message passing in GNNs.

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