Dynamics on higher-order networks

XGI does not itself provide solvers for dynamical processes on higher-order networks. Instead, we recommend using one of the maintained companion packages below, all of which either build on XGI directly or interoperate with it via standard formats.

Contagion / spreading

hypercontagion

SIR, SIS, and other epidemic models.

Synchronization (Kuramoto, oscillators)

hypersynchronization

Kuramoto-type synchronization dynamics on hypergraphs, where oscillators are associated with nodes. See Skardal and Skardal (2019) for an example model, or Battiston et al. (2026) for a review.

simplicial-kuramoto

Simplicial Kuramoto dynamics on simplicial complexes, where oscillators are associated with simplices rather than just nodes. See Millán, Torres, and Bianconi (2020) and Arnaudon, Peach, Petri, and Expert (2022) for example models, and Nurisso et al. (2024) for a review.

Contributing

If you maintain a dynamics package that works well with XGI and you’d like it listed here, open an issue or a pull request adding it to this page.

Historical note

Earlier versions of XGI (up to 0.10.x) exposed a xgi.dynamics submodule containing four functions: simulate_kuramoto, compute_kuramoto_order_parameter, simulate_simplicial_kuramoto, and compute_simplicial_order_parameter. These were removed in v1.0 in favor of the companion packages listed above.