  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 node's degree, node's degree
correlation, node's redundancy coefficient, and/or the hyperedge's 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.
