Hypergraphs and simplicial complexes in focus: a roadmap for future research in higher-order interactions
Journal of Physics Complexity, vol. 7, pp. 022501
Abstract
Abstract Higher-order interactions are increasingly being recognized as fundamental to our understanding of complex systems, networks, and the development of the next generation of AI algorithms. However, modeling 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 34
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Eindhoven University of Technology
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Eindhoven University of Technology, De Zaale 5, Eindhoven, 135, 5600 MB, NETHERLANDS
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Deaprtment d'Enginyeria Informatica i Matematiques, Universitat Rovira i Virgili, Avinguda dels Paisos Catalans 26, Campus Sescelades, 43007 Tarragona, Tarragona, 43007 , SPAIN
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ELTE, 1117 Budapest, Pázmány Péter sétány 1/c., Budapest, Budapest, 1053, HUNGARY
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University of Illinois Chicago
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University of Illinois Chicago, 1200 West Harrison Street, Chicago, 60607, UNITED STATES
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King's College London, Strand, London, WC2R 2LS, UNITED KINGDOM OF GREAT BRITAIN AND NORTHERN IRELAND
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Universita degli Studi di Roma La Sapienza, Piazzale Aldo Moro 5, Rome, 00185, ITALY
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Queen Mary University of London
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School of Mathematics, Queen Mary University of London, Mile End Road, London, E1 4NS, UNITED KINGDOM OF GREAT BRITAIN AND NORTHERN IRELAND
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Department of Mathematics, Vrije Universiteit Amsterdam, De Boelelaan 1111, Amsterdam, 1081 HV, NETHERLANDS
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Vrije Universiteit Amsterdam, De Boelelaan 1109B, Amsterdam, 110, 1081 HV, NETHERLANDS
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Mathematics, Universite de Namur, rue Grafé 2, Namur, 5000, BELGIUM
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Radboud University Nijmegen, Houtlaan 4, Nijmegen, 6500 HC, NETHERLANDS
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University of Catania, Via Santa Sofia, 64, Catania, 95131, ITALY
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Network Science Institute, Northeastern University, 177 Huntington Ave, Boston, MA 02115, UNITED STATES
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Nanyang Technological University
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Nanyang Technological University, 50 Nanyang Avenue, Singapore, Singapore, 639798, SINGAPORE
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University of Amsterdam, Science Park 107, Amsterdam, 1000 GG, NETHERLANDS
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Centre for Bioinformatics, Imperial College London, Division of Molecular Biosciences, Wolfson Building, Imperial College London, South Kensington Campus, SW7 2AY London, London, SW7 2AY, UNITED KINGDOM OF GREAT BRITAIN AND NORTHERN IRELAND
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Max Planck Institute for Mathematics in the Sciences
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Complex systems, Max-Planck-Institut fuer Mathematik in den Naturwissenschaften, Inselstrasse 22-26, D-04103 Leipzig, Leipzig, D-04103, GERMANY
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Physics Department, Boston University, 590 Commonwealth Avenue, Boston MA 02215, USA, Boston, Massachusetts, 02215, UNITED STATES
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University of Cambridge, 15 JJ Thomson Avenue, Cambridge, CB3 0FD, UNITED KINGDOM OF GREAT BRITAIN AND NORTHERN IRELAND
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University of Southampton, Southampton, Southampton, SO17 1BJ, UNITED KINGDOM OF GREAT BRITAIN AND NORTHERN IRELAND
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CENTAI Institute, CORSO INGHILTERRA 3, Turin, 10138, ITALY
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Department of Psychology, University of Cambridge, Department of Psychology, Downing Pl, Cambridge, Cambridgeshire, CB2 3EB, UNITED KINGDOM OF GREAT BRITAIN AND NORTHERN IRELAND
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Institute 'Carlos I' for Theoretical and Computational Physics , University of Granada, Campus Fuente Nueva s/n, Facultad de Ciencias, Granada, Granada, 18071, SPAIN
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Vrije Universiteit Amsterdam, De Boelelaan 1111, Amsterdam, 1081 HV, NETHERLANDS
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Department of Mathematics and Statistics, University of Vermont, 82 University Place, Burlington, Vermont, 05405-0160, UNITED STATES
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Institute for Scientific Interchange
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ISI Foundation, Institute for Scientific Interchange, Via Chisola 5, Torino, 10126 Torino, ITALY
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University of KwaZulu-Natal, Mazisi Kunene Road, Durban, 4041, SOUTH AFRICA
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KTH Royal Institute of Technology
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KTH Royal Institute of Technology, Lindstedtsvägen 3, Stockholm, 100 44, SWEDEN
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Michael T. Schaub Aachen
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RWTH Aachen University, Templergraben 55, Aachen, 52062 Aachen, GERMANY
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Nordic Institute for Theoretical Physics · Stockholm University · KTH Royal Institute of Technology
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NORDITA, NORDITA, Nordita, KTH Royal Institute of Technology and Stockholm University, Hannes Alfvéns väg 12, Stockholm, 106 91, SWEDEN
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Center for Systems Biology Dresden
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Center for Systems Biology Dresden, Pfotenhauerstr. 108, Dresden, 01307, GERMANY
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Politecnico di Torino, Corso Duca degli Abruzzi, 24, Torino, 10129 Torino, ITALY
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