  Many complex systems show non-pairwise interactions, which can be captured by
hypergraphs. In this work, we establish configuration models in which both the
vertex and the hyperarc degrees are preserved for different classes of directed
hypergraphs (containing self-loops, degenerate hyperarcs and/or multiple
hyperarcs). We propose an edge-swapping method to uniformly sample from these
configuration models and prove that this method indeed samples uniformly from
the classes with self-loops and multiple hyperarcs, and that the method does
not sample uniformly from classes without self-loops, or with self-loops and
degenerate hyperarcs but without multiple hyperarcs. We present a partial
result on the class with self-loops, but without degenerate hyperarcs or
multiple hyperarcs.
