mlsanityData to 7 Oct 2026

What are higher-order networks?

arXiv 2104.11329 ↗First posted 20 Apr 2021cs.SI math.CO math.DScited by 66

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Abstract (arXiv)

Network-based modeling of complex systems and data using the language of graphs has become an essential topic across a range of different disciplines. Arguably, this graph-based perspective derives its success from the relative simplicity of graphs: A graph consists of nothing more than a set of vertices and a set of edges, describing relationships between pairs of such vertices. This simple combinatorial structure makes graphs interpretable and flexible modeling tools. The simplicity of graphs as system models, however, has been scrutinized in the literature recently. Specifically, it has been argued from a variety of different angles that there is a need for higher-order networks, which go beyond the paradigm of modeling pairwise relationships, as encapsulated by graphs. In this survey article we take stock of these recent developments. Our goals are to clarify (i) what higher-order networks are, (ii) why these are interesting objects of study, and (iii) how they can be used in applications.

Key facts. Cited by 66 papers in the map (data through 7 Oct 2026). First posted on arXiv 20 Apr 2021.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 5; 2022: 7; 2023: 18; 2024: 10; 2025: 16; 2026: 10.

66 papers.

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  1. 2024Position: Topological Deep Learning is the New Frontier for Relational Learningcited by 65
  2. 2023Graph Neural Networks for temporal graphs: State of the art, open challenges, and opportunitiescited by 60
  3. 2022Graph Filters for Signal Processing and Machine Learning on Graphscited by 53
  4. 2023Convolutional Learning on Simplicial Complexescited by 26
  5. 2023Learning from data with structured missingnesscited by 24
  6. 2024TopoBench: A Framework for Benchmarking Topological Deep Learningcited by 24
  7. 2024A Survey on Hypergraph Neural Networks: An In-Depth and Step-By-Step Guidecited by 22
  8. 2021Bridging the Gap between Spatial and Spectral Domains: A Unified Framework for Graph Neural Networkscited by 18
  9. 2022Simplicial Convolutional Filterscited by 18
  10. 2023Combinatorial Complexes: Bridging the Gap Between Cell Complexes and Hypergraphscited by 15
  11. 2021Latent Space Model for Higher-order Networks and Generalized Tensor Decompositioncited by 13
  12. 2021Signal processing on simplicial complexescited by 12
38 more
  1. 2024Attending to Topological Spaces: The Cellular Transformercited by 11
  2. 2025Copresheaf Topological Neural Networks: A Generalized Deep Learning Frameworkcited by 11
  3. 2023HOT: Higher-Order Dynamic Graph Representation Learning with Efficient Transformerscited by 10
  4. 2023Learning High-Order Relationships of Brain Regionscited by 10
  5. 2023Dirac signal processing of higher-order topological signalscited by 9
  6. 2021Data-Centric AI Requires Rethinking Data Notioncited by 8
  7. 2023Hypergraph Transformer for Semi-Supervised Classificationcited by 7
  8. 2023Topo-MLP : A Simplicial Network Without Message Passingcited by 7
  9. 2024Training-Free Message Passing for Learning on Hypergraphscited by 7
  10. 2021Quantifying Gender Biases Towards Politicians on Redditcited by 5
  11. 2023Recurrences reveal shared causal drivers of complex time seriescited by 5
  12. 2023A Markov Random Field model for Hypergraph-based Machine Learningcited by 5
  13. 2023Hypergraph-MLP: Learning on Hypergraphs without Message Passingcited by 5
  14. 2025Hypergraph Foundation Modelcited by 5
  15. 2025HOPSE: Scalable Higher-Order Positional and Structural Encoder for Combinatorial Representationscited by 5
  16. 2022Nonbacktracking spectral clustering of nonuniform hypergraphscited by 4
  17. 2024Demystifying Higher-Order Graph Neural Networkscited by 4
  18. 2025Topological Schr"odinger Bridge Matchingcited by 4
  19. 2022Hypergraphon Mean Field Gamescited by 3
  20. 2023Interaction Measures, Partition Lattices and Kernel Tests for High-Order Interactionscited by 3
  21. 2023Learning the effective order of a hypergraph dynamical systemcited by 3
  22. 2023Intrinsically motivated graph exploration using network theories of human curiositycited by 3
  23. 2023Learning graphs and simplicial complexes from datacited by 3
  24. 2024Information-Theoretic Measures on Lattices for High-Order Interactionscited by 3
  25. 2024ICML Topological Deep Learning Challenge 2024: Beyond the Graph Domaincited by 3
  26. 2025Matched Topological Subspace Detectorcited by 3
  27. 2022Multiscale methods for signal selection in single-cell datacited by 2
  28. 2023Zoo Guide to Network Embeddingcited by 2
  29. 2024Dirac-Equation Signal Processing: Physics Boosts Topological Machine Learningcited by 1
  30. 2025Information Filtering Networks: Theoretical Foundations, Generative Methodologies, and Real-World Applicationscited by 1
  31. 2025Higher-Order Group Synchronizationcited by 1
  32. 2025Permutation-Free High-Order Interaction Testscited by 1
  33. 2025Chordless cycle filtrations for dimensionality detection in complex networks via topological data analysiscited by 1
  34. 2026Stationarity and Spectral Characterization of Random Signals on Simplicial Complexescited by 1
  35. 2026Attention as Frustrated Synchronizationcited by 1
  36. 2022Topological data analysis of truncated contagion mapscited by 0
  37. 2022Efficient Cavity Searching for Gene Network of Influenza A Viruscited by 0
  38. 2023XFlow: Benchmarking Flow Behaviors over Graphscited by 0

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