Hypergraphs and simplicial complexes in focus: A roadmap for future research in higher-order interactions

Aida Abiad, Alex Arenas, Agnes Backhausz, Jozsef Balogh, Christopher R. S. Banerji, Sergio Barbarossa, Ginestra Bianconi, Christian Bick, Magnus Bakke B Botnan, Timoteo Carletti, Lucia Cavallaro, Andrea Civilini, Tina Eliassi-Rad, Xue Gong, Krystal Guo, Heather Harrington, Juergen Jost, Paul L Krapivsky, Pietro Liò, Ben MacArthur, Carolina Mattsson, Pedro Mediano, Ana Paula Millán, Raffaella Mulas, Alice Patania, Giovanni Petri, Cerene Rathilal, Ruben Jose Sanchez Garcia, Martina Scolamiero, Michael T Schaub, Hanlin Sun, Yu Tian, Francesco Vaccarino, Xia Kelin
January, 2026
DOI paper

Abstract

This roadmap surveys mathematical and scientific challenges for hypergraphs and simplicial complexes, including spectral theory, discrete topology, higher-order dynamics, and applications across complex systems.

Type
Journal article
Publication
In Journal of Physics: Complexity
Hypergraphs Simplicial complexes Higher-order interactions
Hanlin Sun
Hanlin Sun
Wallenberg Initiative on Networks and Quantum Information (WINQ) Research Fellow