Papers › Higher-order Graph Convolutional Network with Flower-Petals Laplacians on Simplicial Complexes
Higher-order Graph Convolutional Network with Flower-Petals Laplacians on Simplicial Complexes
Yiming Huang, Yujie Zeng, Qiang Wu, Linyuan Lü
Despite the recent successes of vanilla Graph Neural Networks (GNNs) on various tasks, their foundation on pairwise networks inherently limits their capacity to discern latent higher-order interactions in complex systems. To bridge this capability gap, we propose a novel approach exploiting the rich mathematical theory of simplicial complexes (SCs) - a robust tool for modeling higher-order interactions. Current SC-based GNNs are burdened by high complexity and rigidity, and quantifying higher-order interaction strengths remains challenging. Innovatively, we present a higher-order Flower-Petals (FP) model, incorporating FP Laplacians into SCs. Further, we introduce a Higher-order Graph Convolutional Network (HiGCN) grounded in FP Laplacians, capable of discerning intrinsic features across varying topological scales. By employing learnable graph filters, a parameter group within each FP Laplacian domain, we can identify diverse patterns where the filters' weights serve as a quantifiable measure of higher-order interaction strengths. The theoretical underpinnings of HiGCN's advanced expressiveness are rigorously demonstrated. Additionally, our empirical investigations reveal that the proposed model accomplishes state-of-the-art performance on a range of graph tasks and provides a scalable and flexible solution to explore higher-order interactions in graphs. Codes and datasets are available at https://github.com/Yiminghh/HiGCN.
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Tasks
Results from the paper archive 2025-07-28
| Task | Dataset | Model | Metric | Value | Rank at snapshot | Leaderboard | Report |
|---|---|---|---|---|---|---|---|
| Node Classification | Actor | 2-HiGCN | Accuracy | 41.81±0.52 | #3 of 62 | Archive leaderboard | report |
| Node Classification | Chameleon | 2-HiGCN | Accuracy | 68.47±0.45 | #37 of 61 | Archive leaderboard | report |
| Node Classification | Texas | 2-HiGCN | Accuracy | 92.45±0.73 | #4 of 62 | Archive leaderboard | report |
| Node Classification | Wisconsin | 5-HiGCN | Accuracy | 94.99±0.65 | #1 of 63 | Archive leaderboard | report |
| Node Property Prediction | ogbn-arxiv | 3-HiGCN | Validation Accuracy | 0.7641±0.0053 | #86 of 86 | Archive leaderboard | report |
Ranks are positions in the archive's leaderboards as they stood at the 2025-07-28 snapshot. Results published since then are not among these rows, so a rank here is not a current standing.
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