Hypergraphs and simplicial complexes in focus: A roadmap for future research in higher-order interactions
Abstract Higher-order interactions are increasingly being recognised as fundamental to our understanding of complex systems, networks, and the development of the next generation of AI algorithms. However, modelling higher-order interactions requires us to go beyond graphs and networks, which can only encode pairwise interactions, and so demands a new theory. Hypergraphs and simplicial complexes (also called higher-order networks), which arise as natural mathematical representations of higher-order complex systems, are therefore attracting increasing attention. The mathematics of higher-order networks is already providing important insights, yet many fundamental mathematical questions remain unsolved; for instance, in spectral graph theory, discrete topology, and higher-order network dynamics. This roadmap summarizes the scientific discussions that took place on these topics between pure mathematicians, theoretical physicists, computer and network scientists at the Newton Institute Satellite meeting on `Hypergraphs: Theory and Applications'. We survey the current state-of-the-art in higher-order network research, and propose some trajectories for future research, including in areas such as extremal and spectral hypergraph theory, discrete topology, higher-order dynamics, higher-order machine learning, and applications in the brain and social sciences.
Authors
- Xia Kelin
- Cerene. Rathilal (ORCID: https://orcid.org/0000-0002-9026-7547)
- Andrea Civilini (ORCID: https://orcid.org/0009-0001-3795-0910)
- P. L. Krapivsky (ORCID: https://orcid.org/0000-0003-3470-5095)
- Christopher R. S. Banerji (ORCID: https://orcid.org/0000-0002-4373-7657)
- Raffaella Mulas (ORCID: https://orcid.org/0000-0003-4995-6479)
- Carolina E. S. Mattsson (ORCID: https://orcid.org/0000-0002-9160-7523)
- Alice Patania (ORCID: https://orcid.org/0000-0002-3047-4376)
- Pedro A. M. Mediano (ORCID: https://orcid.org/0000-0003-1789-5894)
- Tina Eliassi‐Rad (ORCID: https://orcid.org/0000-0002-1892-1188)
- Christian Bick (ORCID: https://orcid.org/0000-0002-5238-1146)
- Sergio Barbarossa (ORCID: https://orcid.org/0000-0001-9846-8741)
- Krystal Guo (ORCID: https://orcid.org/0000-0001-8776-537X)
- Pietro Liò
- Juergen Jost
- Aida Abiad
- Alex Arenas (ORCID: https://orcid.org/0000-0003-0937-0334)
- Ben D. MacArthur
- Lucia Cavallaro
- Jozsef Balogh
- Timoteo Carletti
- Martina Scolamiero
- Francesco Vaccarino
- Yu Tian
- Magnus Bakke B Botnan
- Michael T Schaub
- Ruben Jose Sanchez Garcia
- Hanlin Sun
- Agnes Backhausz
- Xue Gong
- Ana Paula Millán
- Heather Harrington
- Ginestra Bianconi
Institutions
- Eötvös Loránd University (HU)
- Boston University (US)
- University of Vermont (US)
- Nordic Institute for Theoretical Physics (SE)
- Northeastern University (US)
- Institute for Scientific Interchange (IT)
- Radboud University Nijmegen (NL)
- University of Namur (BE)
- Queen Mary University of London (GB)
- Nanyang Technological University (SG)
- Universidad de Granada (ES)
- Politecnico di Torino (IT)
- King's College London (GB)
- University of Cambridge (GB)
- Pázmány Péter Catholic University (HU)
- University of Catania (IT)
- University of Illinois Chicago (US)
- Max Planck Institute for Mathematics in the Sciences (DE)
- Bridge University (SS)
- Center for Systems Biology Dresden (DE)
- GGD Amsterdam (NL)
- Ospedale Santa Corona (IT)
- University of Southampton (GB)
- Imperial College London (GB)
- Universitat Rovira i Virgili (ES)
- Eindhoven University of Technology (NL)
- Sapienza University of Rome (IT)
- Vrije Universiteit Amsterdam (NL)
- KTH Royal Institute of Technology (SE)
- University of Amsterdam (NL)
- RWTH Aachen University (DE)
- University of KwaZulu-Natal (ZA)
Publication Details
- Journal
- Journal of Physics Complexity
- Published
- 2026-01-22
- DOI
- https://doi.org/10.1088/2632-072x/ae3c4e
- Citations
- 1
- Primary Topic
- Topological and Geometric Data Analysis
- Type
- article
- Field-Weighted Citation Impact
- 45.17