Fig. 1: Functional reducibility of higher-order networks.
Illustration of our method with an example hypergraph. Given a an original hypergraph with interactions of orders up to \({d}_{\max }\) (=3, here), b we use higher-order diffusion processes to probe the system at a chosen diffusion time τ (e.g., small) that acts as a topological scale. c We then compute the cost function, a trade-off between information loss and model complexity, of the same hypergraph, but considering orders only up to d. We determine the optimal order dopt as the one that minimizes the cost function. Finally, d we reduce the original hypergraph to an optimal version by considering orders up to dopt.
