{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/higher-order-graph-convolutional-network-with","title":"Higher-order Graph Convolutional Network with Flower-Petals Laplacians on Simplicial Complexes","arxiv_id":"2309.12971","date":"2023-09-22","proceeding":null,"authors":["Yiming Huang","Yujie Zeng","Qiang Wu","Linyuan Lü"],"abstract":"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.","url_abs":"https://arxiv.org/abs/2309.12971v2","url_pdf":"https://arxiv.org/pdf/2309.12971v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"higher-order-graph-convolutional-network-with","repo_url":"https://github.com/yiminghh/higcn","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[{"task_slug":"node-classification","task_name":"Node Classification"},{"task_slug":"node-property-prediction","task_name":"Node Property Prediction"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[{"leaderboard":"/sota/node-classification-on-actor","task":"Node Classification","dataset":"Actor","model":"2-HiGCN","rank_in_archive_order":3,"of":62,"metrics":{"Accuracy":"41.81±0.52"},"uses_additional_data":false},{"leaderboard":"/sota/node-classification-on-chameleon","task":"Node Classification","dataset":"Chameleon","model":"2-HiGCN","rank_in_archive_order":37,"of":61,"metrics":{"Accuracy":"68.47±0.45"},"uses_additional_data":false},{"leaderboard":"/sota/node-classification-on-texas","task":"Node Classification","dataset":"Texas","model":"2-HiGCN","rank_in_archive_order":4,"of":62,"metrics":{"Accuracy":"92.45±0.73"},"uses_additional_data":false},{"leaderboard":"/sota/node-classification-on-wisconsin","task":"Node Classification","dataset":"Wisconsin","model":"5-HiGCN","rank_in_archive_order":1,"of":63,"metrics":{"Accuracy":"94.99±0.65"},"uses_additional_data":false},{"leaderboard":"/sota/node-property-prediction-on-ogbn-arxiv","task":"Node Property Prediction","dataset":"ogbn-arxiv","model":"3-HiGCN","rank_in_archive_order":86,"of":86,"metrics":{"Validation Accuracy":"0.7641±0.0053"},"uses_additional_data":false}],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2309.12971","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2309.12971"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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