Many complex systems involve direct interactions among more than two entities and can be represented by hypergraphs, in which hyperedges encode higher-order interactions among an arbitrary number of nodes. To analyze structures and dynamics of given hypergraphs, a solid practice is to compare them with those for randomized hypergraphs that preserve some specific properties of the original hypergraphs. In the present study, we propose a family of such reference models for hypergraphs, called the hyper dK-series, by extending the so-called dK-series for dyadic networks to the case of hypergraphs. The hyper dK-series preserves up to the individual nodes degree, nodes degree correlation, nodes redundancy coefficient, and/or the hyperedges size depending on the parameter values. We also apply the hyper dK-series to numerical simulations of epidemic spreading and evolutionary game dynamics on empirical hypergraphs.
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