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Submodular Hypergraphs: p-Laplacians, Cheeger Inequalities and Spectral Clustering

arXiv 1803.03833 ↗First posted 10 Mar 2018cs.LG cs.DM cs.DScited by 25

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Abstract (arXiv)

We introduce submodular hypergraphs, a family of hypergraphs that have different submodular weights associated with different cuts of hyperedges. Submodular hypergraphs arise in clustering applications in which higher-order structures carry relevant information. For such hypergraphs, we define the notion of p-Laplacians and derive corresponding nodal domain theorems and k-way Cheeger inequalities. We conclude with the description of algorithms for computing the spectra of 1- and 2-Laplacians that constitute the basis of new spectral hypergraph clustering methods.

Key facts. Cited by 25 papers in the map (data through 14 Oct 2026). First posted on arXiv 10 Mar 2018.

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Citing papers per year: 2021: 6; 2022: 8; 2023: 5; 2024: 3; 2025: 1; 2026: 2.

25 papers.

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  1. 2021You are AllSet: A Multiset Function Framework for Hypergraph Neural Networkscited by 127
  2. 2021Signal Processing on Higher-Order Networks: Livin' on the Edge ... and Beyondcited by 82
  3. 2022DiffWire: Inductive Graph Rewiring via the Lov'asz Boundcited by 79
  4. 2021Generative hypergraph clustering: from blockmodels to modularitycited by 49
  5. 2022Equivariant Hypergraph Diffusion Neural Operatorscited by 47
  6. 2022I'm Me, We're Us, and I'm Us: Tri-directional Contrastive Learning on Hypergraphscited by 21
  7. 2023Dynamic Hypergraph Structure Learning for Traffic Flow Forecastingcited by 14
  8. 2021A nonlinear diffusion method for semi-supervised learning on hypergraphscited by 11
  9. 2021Local Hyper-Flow Diffusioncited by 8
  10. 2023CAT-Walk: Inductive Hypergraph Learning via Set Walkscited by 6
  11. 2022Finding Bipartite Components in Hypergraphscited by 4
  12. 2024Ada-HGNN: Adaptive Sampling for Scalable Hypergraph Neural Networkscited by 4
13 more
  1. 2024Hypergraphs as Weighted Directed Self-Looped Graphs: Spectral Properties, Clustering, Cheeger Inequalitycited by 4
  2. 2022Sparsification of Decomposable Submodular Functionscited by 3
  3. 2022Cheeger Inequalities for Directed Graphs and Hypergraphs Using Reweighted Eigenvaluescited by 3
  4. 2026Hypergraph Neural Diffusion: A PDE-Inspired Framework for Hypergraph Message Passingcited by 3
  5. 2021Approximate Decomposable Submodular Function Minimization for Cardinality-Based Componentscited by 1
  6. 2022Hypergraph Modeling via Spectral Embedding Connection: Hypergraph Cut, Weighted Kernel k-means, and Heat Kernelcited by 1
  7. 2022Hypergraphs with Edge-Dependent Vertex Weights: p-Laplacians and Spectral Clusteringcited by 1
  8. 2023Exact Inference in High-order Structured Predictioncited by 1
  9. 2023Seven open problems in applied combinatoricscited by 1
  10. 2023Hypergraphs with Edge-Dependent Vertex Weights: Spectral Clustering based on the 1-Laplaciancited by 1
  11. 2024Hypergraph p-Laplacian regularization on point clouds for data interpolationcited by 1
  12. 2025Higher-Order Regularization Learning on Hypergraphscited by 1
  13. 2026The WidthWall: A Strict Expressivity Hierarchy for Hypergraph Neural Networkscited by 0