Configuration models for random directed hypergraphs

Abstract: 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.