Delaunay Graph: Addressing Over-Squashing and Over-Smoothing Using Delaunay Triangulation
Hugo Attali, Davide Buscaldi, Nathalie Pernelle
Abstract
GNNs rely on the exchange of messages to distribute information along the edges of the graph. This approach makes the efficiency of architectures highly dependent on the specific structure of the input graph. Certain graph topologies lead to inefficient information propagation, resulting in a phenomenon known as over-squashing. While the majority of existing methods address oversquashing by rewiring the input graph, our novel approach involves constructing a graph directly from features using Delaunay Triangulation. We posit that the topological properties of the resulting graph prove advantageous for mitigating oversmoothing and over-squashing. Our extensive experimentation demonstrates that our method consistently outperforms established graph rewiring methods.
Ask about this paper
Your agent reads all of it.
Lune indexed this paper to the last equation, along with the top-tier papers that cite it. Ask a question and the answer quotes them.
Your agent calls
Luneget_paper_fulltext
Free to start. No credit card required.
Terminal
Install the CLIlune papers fulltext 45cc4709-2cdf-4950-b10f-e79be44a8fe9Cited by top-tier papers6
- Oversmoothing, "Oversquashing", Heterophily, Long-Range, and more: Demystifying Common Beliefs in Graph Machine LearningAdrián Arnaiz-Rodríguez, Federico ErricaICLR 2026 · 26 citations
- Deeper with Riemannian Geometry: Overcoming Oversmoothing and Oversquashing for Graph Foundation ModelsLi Sun, Zhenhao Huang, Ming Zhang, Philip S. YuNeurIPS 2025 · 10 citations
- Mitigating Over-Squashing in Graph Neural Networks by Spectrum-Preserving SparsificationLangzhang Liang, Fanchen Bu, Zixing Song, Zenglin Xu et al.ICML 2025
- Commute Graph Neural NetworksWei Zhuo, Han Yu, Guang Tan, Xiaoxiao LiICML 2025
- PIORF: Physics-Informed Ollivier-Ricci Flow for Long-Range Interactions in Mesh Graph Neural NetworksYoun-Yeol Yu, Jeongwhan Choi, Jaehyeon Park, Kookjin Lee et al.ICLR 2025
Builds on17
- How Attentive are Graph Attention Networks?Shaked Brody, Uri Alon, Eran YahavICLR 2022 · 1,717 citations
- Beyond Homophily in Graph Neural Networks: Current Limitations and Effective DesignsJiong Zhu, Yujun Yan, Lingxiao Zhao, Mark Heimann et al.NeurIPS 2020 · 1,490 citations
- Geom-GCN: Geometric Graph Convolutional NetworksHongbin Pei, Bingzhe Wei, Kevin Chen-Chuan Chang, Yu Lei et al.ICLR 2020 · 1,445 citations
- Learning to Simulate Complex Physics with Graph NetworksAlvaro Sanchez-Gonzalez, Jonathan Godwin, Tobias Pfaff, Rex Ying et al.ICML 2020 · 1,439 citations
- Measuring and Relieving the Over-Smoothing Problem for Graph Neural Networks from the Topological ViewDeli Chen, Yankai Lin, Wei Li, Peng Li et al.AAAI 2020 · 1,353 citations
Related papers
- FoSR: First-order spectral rewiring for addressing oversquashing in GNNsKedar Karhadkar, Pradeep Kr. Banerjee, Guido MontúfarICLR 2023 · 7 citations
- Understanding over-squashing and bottlenecks on graphs via curvatureJake Topping, Francesco Di Giovanni, Benjamin Paul Chamberlain, Xiaowen Dong et al.ICLR 2022 · 628 citations
- Understanding Oversquashing in GNNs through the Lens of Effective ResistanceMitchell Black, Zhengchao Wan, Amir Nayyeri, Yusu WangICML 2023 · 116 citations
- Locality-Aware Graph Rewiring in GNNsFederico Barbero, Ameya Velingker, Amin Saberi, Michael M. Bronstein et al.ICLR 2024 · 64 citations
- On Over-Squashing in Message Passing Neural Networks: The Impact of Width, Depth, and TopologyFrancesco Di Giovanni, Lorenzo Giusti, Federico Barbero, Giulia Luise et al.ICML 2023 · 190 citations
