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
- The dynamic nature of percolation on networks with triadic interactions — Nature Communications
- Topology shapes dynamics of higher-order networks — Nature Physics
- Triadic percolation induces dynamical topological patterns in higher-order networks — PNAS Nexus
- Triadic percolation on multilayer networks — Physical Review E (Editors’ Suggestion)
- Higher-order triadic percolation on random hypergraphs — Physical Review E
- Spatio-temporal activity patterns induced by triadic interactions in an in silico neural medium — Journal of Physics: Complexity
- Higher-order percolation processes on multiplex hypergraphs — Physical Review E
- Renormalization group theory of percolation on pseudofractal simplicial and cell complexes — Physical Review E
