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

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What Are Higher-Order Networks?

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Bick, Christian, Gross, Elizabeth, Harrington, Heather A., Schaub, Michael T.·2023·SIAM Review
DOI 10.1137/21m1414024
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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.

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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

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