Higher-order network modelling

Higher-order networks — including hypergraphs, simplicial complexes, and networks with triadic interactions — encode the group interactions present in real-world complex systems. While percolation has been well studied on pairwise networks, little was known about how higher-order interactions affect critical phenomena. My work addresses this from several complementary angles.

Percolation on higher-order structures

On pseudofractal simplicial and cell complexes, I showed that percolation displays two distinct critical thresholds and an unusual critical exponent, in contrast to standard percolation on dyadic networks.

I introduced multiplex hypergraphs as a general framework to study percolation on higher-order structures, characterising how hyperedge organisation such as hyperedge correlation affects critical behaviour.

Networks with triadic interactions

I proposed a novel higher-order network model called networks with triadic interactions and developed a percolation theory on these structures, showing that triadic regulation can turn percolation into a fully dynamical process displaying periodic oscillations and chaos. I further extended this framework to spatial networks, random hypergraphs, and multilayer networks, and explored its implications for neuronal dynamics.

Related publications

• Criticality and universality in network dismantling, arXiv, 2026 — L. Cirigliano, C. Castellano, M. Kim, F. Radicchi, H. Sun^†
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• Triadic percolation on multilayer networks, Physical Review E, 2026 — H. Sun^†, F. Radicchi, G. Bianconi (Editors' Suggestion)
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• Spatio-temporal activity patterns induced by triadic interactions in an in silico neural medium, Journal of Physics: Complexity, 2025 — A. P. Millán, H. Sun, J. J. Torres
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• Topology shapes dynamics of higher-order networks, Nature Physics, 2025 — A. P. Millán, H. Sun, L. Giambagli, R. Muolo, T. Carletti, J. J. Torres, F. Radicchi, J. Kurths, G. Bianconi
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• Higher-order triadic percolation on random hypergraphs, Physical Review E, 2024 — H. Sun^†, G. Bianconi
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• Triadic percolation induces dynamical topological patterns in higher-order networks, PNAS Nexus, 2024 — A. P. Millán, H. Sun^*, J. J. Torres, G. Bianconi
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• The dynamic nature of percolation on networks with triadic interactions, Nature Communications, 2023 — H. Sun, F. Radicchi, J. Kurths, G. Bianconi
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• Higher-order percolation processes on multiplex hypergraphs, Physical Review E, 2021 — H. Sun, G. Bianconi
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• Renormalization group theory of percolation on pseudofractal simplicial and cell complexes, Physical Review E, 2020 — H. Sun, R. M. Ziff, G. Bianconi
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