Dynamical systems on directed hyper-graphs

02/25/2022

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by   Mauro Faccin, et al.

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Networks and graphs provide a simple but effective model to a vast set of systems which building blocks interact throughout pairwise interactions. Such models fail to describe all those systems which building blocks interact at a higher order. Higher order graphs provide us the right tools for the task. We analyze the interplay between the structure of a directed hyper-graph and a dynamical system evolving on it. We connect the dynamical system on the h to a corresponding random walk on an effective graph. Measures of hyper-dynamics correspond to similar measures on the effective dynamics. We can use simple and well tested algorithms on the effective graph.