CoChat
Sign Up
Cited by 426Complex Network Analysis TechniquesGraph Theory and AlgorithmsTopological and Geometric Data Analysis

The DOI matches its Crossref record; 304 of the 316 references it cites were found in a registry or an index.

What Are Higher-Order Networks?

Open access
Bick, Christian, Gross, Elizabeth, Harrington, Heather A., Schaub, Michael T.·2023·SIAM Review
DOI 10.1137/21m1414024
Open this paper in CoChat — free account

Abstract

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.

Overview

Integrity signals

Registry

Crossref · 10.1137/21m1414024

Cites

304 of 304 references verified0 citation errors · 0 not checkable

Statistics

Recomputing p-values needs the paper’s full text.

Verification

Claims the paper makes

We couldn’t retrieve this paper’s full text, so its claims and self-check weren’t run. The registry and citation checks still apply.

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

Citations

Cites

Show all 316 references

Research works printed but not linked: 49

  1. Adams H., 2017, J. Mach. Learn. Res., 18, 8
  2. Aukerman A., 2020, 36th International Symposium on Computational Geometry (SoCG 2020
  3. Benson A. R., 1974, Proceedings of the 2015 SIAM International Conference on Data Mining, SIAM, 2015, 118
  4. Bick C., Phase oscillator networks with nonlocal higher-order interactions: Twisted states, stability, and bifurcations
  5. Bick C., 2023, Higher-Order Interactions in Phase Oscillator Networks through Phase Reductions of Oscillators with Phase Dependent Amplitude, preprint, https://doi.org/10.48550/arXiv.2305.04277 · DOI
  6. Bubenik P., 2015, J. Mach. Learn. Res., 16, 77
  7. Byrne H. M., 2019, Math. Today (Southend-on-Sea), 55, 206
  8. Chaplin T., 2021, First Betti Number of the Path Homology of Random Directed Graphs, preprint, https://arxiv.org/abs/2111.13493 · arXiv
  9. Chazal F., 2015, International Conference on Machine Learning, PMLR, 2143
  10. Chazal F., 2021, Frontiers Artificial Intell., 4
  11. Chen Y.-C., 2021, Helmholtzian Eigenmap: Topological Feature Discovery & Edge Flow Learning from Point Cloud Data, preprint, https://arxiv.org/abs/2103.07626 · arXiv
  12. Chien I., 2018, International Conference on Artificial Intelligence and Statistics, 871
  13. Chowdhury S., 2020, International Conference on Complex Networks and Their Applications, 639
  14. Chowdhury S., 1975, Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms, SIAM, 2018, 1152
  15. Chung F. R., 1997, CBMS Reg. Conf. Ser. Math. 92
  16. De Silva V., 2007, Notices Amer. Math. Soc., 54, 10
  17. DeVille L., 2020, Consensus on Simplicial Complexes, or: The Nonlinear Simplicial Laplacian, preprint, https://arxiv.org/abs/2010.07421 · arXiv
  18. 10.1017/CBO9780511761942 · DOI · Paper page
  19. Farber M., 2019, Random Simplicial Complexes, Duality and the Critical Dimension, preprint, https://arxiv.org/abs/1901.09578 · arXiv
  20. Ghoshdastidar D., 2014, Advances in Neural Information Processing Systems, 397
  21. Glaze N., 2021, Principled Simplicial Neural Networks for Trajectory Prediction, preprint, https://arxiv.org/abs/2102.10058 · arXiv
  22. Gross E., 2021, Goodness-of-Fit Tests, and Applications to Biological Networks, preprint, https://arxiv.org/abs/2104.03167 · arXiv
  23. Harer J., 2015, Tech. report
  24. Hein M., 2013, Adv. Neural Inform. Process. Syst., 26
  25. Helm A., 2020, The Growing Topology of the C. Elegans Connectome, preprint, https://arxiv.org/abs/2101.00065 · arXiv
  26. Hickok A., 2021, A Bounded-Confidence Model of Opinion Dynamics on Hypergraphs, preprint, https://arxiv.org/abs/2102.06825 · arXiv
  27. Kaczynski T., 2006, Appl. Math. Sci. 157
  28. Kahle M., 2014, American Mathematical Society, 201
  29. Ke Z. T., 2019, Community Detection for Hypergraph Networks via Regularized Tensor Power Iteration, preprint, https://arxiv.org/abs/1909.06503 · arXiv
  30. Kerber M., 1976, 2021 Proceedings of the Workshop on Algorithm Engineering and Experiments (ALENEX), SIAM, 2021, 207
  31. Kwitt R., 2015, Advances in Neural Information Processing Systems, 3070
  32. Li P., 2018, International Conference on Machine Learning, PMLR, 3014
  33. Matsumoto Y., 2002, Transl. Math. Monogr. 208
  34. Neuhäuser L., 2021, Control and Optimization (NETGCOOP 2021)
  35. 10.1063/5.0093842 · DOI
  36. 10.1137/18M1219977 · DOI
  37. Page L., 1999, Tech. report
  38. Pattison P., 2004, Math. Sci. Hum. Math. Soc. Sci., 168, 11
  39. A. Salova and R. M. D'Souza, Analyzing States beyond Full Synchronization on Hypergraphs Requires Methods beyond Projected Networks , preprint,http://arxiv.org/abs/2107.13712, 2021. · arXiv
  40. A. Salova and R. M. D'Souza, Cluster Synchronization on Hypergraphs , preprint,http://arxiv.org/abs/2101.05464, 2021. · arXiv
  41. Schenck H., 2020, Algebra and Topology for Data Analysis
  42. Spagnuolo C., 2020, Internet Math., 1, 12464
  43. Stasi D., 2014, Proceedings of 21st International Conference on Computational Statistics
  44. Stolz B., 2014, Master's thesis
  45. Taylor D., 2015, Nature Commun., 6, 1
  46. Veldt N., 2020, Hypergraph Cuts with General Splitting Functions, preprint, https://arxiv.org/abs/2001.02817 · arXiv
  47. X. Yang, Social Network Modeling and the Evaluation of Structural Similarity for Community Detection , Ph.D. thesis, Carnegie Mellon University, 2015.
  48. Zheleva E., 2010, NIPS Workshop on Networks Across Disciplines: Theory and Applications, 2
  49. Zhou D., 2006, Adv. Neural Inform. Process. Syst., 19

Cited by

Sorted by citations

Related

See all

Metadata

Authors
Bick, C., Gross, E., Harrington, H. A., & Schaub, M. T.
Affiliations
  • Vrije Universiteit Amsterdam (NL)
  • University of Hawaiʻi at Mānoa (US)
  • Centre for Human Genetics (GB)
ORCID
Venue
SIAM Review
Publisher
Society for Industrial & Applied Mathematics (SIAM)
Published
2023-08
Volume
65
Issue
3
Pages
686-731
ISSN
  • 0036-1445 (ISSN-L)
  • 1095-7200
DOI
10.1137/21m1414024
OpenAlex
W3158396846
Cited by
420
References
316
Citations by year
2026: 133 · 2025: 141 · 2024: 82 · 2023: 34
FWCI
38.87
Type
journal article
Language
en
Open access
Licence
cc-by
Locations
  • SIAM Review (publishedVersion, cc-by)
  • RWTH Publications (RWTH Aachen) (publishedVersion)
  • VU Research Portal (publishedVersion, other-oa)
  • arXiv (Cornell University) (submittedVersion)
  • arXiv (Cornell University)
Funders
  • H2020 Marie Skłodowska-Curie Actions (702410)
  • Technische Universitat Munchen
  • Ministerium für Innovation, Wissenschaft und Forschung des Landes Nordrhein-Westfalen
  • National Science Foundation (DMS-1945584)
  • Royal Society (RGFnEAn201074, UF150238)
  • Engineering and Physical Sciences Research Council (EP/T013613/1, EP/R018472/1, EP/R005125/1, EP/T001968/1)
Topics
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Complex Network Analysis Techniques
  • Physical Sciences › Computer Science › Computational Theory and Mathematics › Graph Theory and Algorithms
  • Physical Sciences › Computer Science › Computational Theory and Mathematics › Topological and Geometric Data Analysis
Keywords
higher-order networks, hypergraphs, pairwise relationships, graph-based modeling, complex systems, network science

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review