Reducibility of higher-order to pairwise interactions: Social impact models on hypergraphs
We show that a general class of node-update social impact models on hypergraphs can be mapped exactly onto pairwise dynamics on a weighted projected network, preserving the microscopic transition probabilities. We apply this mapping to hypergraph-voter models and characterize their ordering dynamics. For the hypergraph-linear voter model, the projected weights are static, allowing us to develop a pair approximation that accurately describes the evolution of macroscopic observables. These observables are independent of the weights, making the macroscopic dynamics equivalent to that of the standard voter model on the unweighted projected network. For the hypergraph-nonlinear voter model, the weights depend on the instantaneous system configuration. Nevertheless, for well-connected hypergraphs, the nonlinear voter model on the unweighted projected network reproduces the main macroscopic trends. We conclude with general reflections on the reducibility of higher-order interactions.
This IFISC Seminar will be broadcasted in the following zoom link: https://us06web.zoom.us/j/89466064429?pwd=po9p99eAEYVPaNI8xIIGoOIz0hOqaF.1
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