Uniformly sampling random directed hypergraphs with fixed degrees
Abstract
Many complex systems show non-pairwise interactions, which can be captured by hypergraphs. In this work, we propose an edge-swapping method to sample random directed hypergraphs with fixed vertex and hyperarc degrees, which can be applied to different classes of directed hypergraphs (containing self-loops, degenerate hyperarcs and/or multi-hyperarcs). We prove that this method indeed samples uniformly from the classes with self-loops and multi-hyperarcs, and that the method may not sample uniformly from classes without self-loops, or with self-loops and degenerate hyperarcs but without multi-hyperarcs. We present a partial result on the class with self-loops, but without degenerate hyperarcs or multi-hyperarcs.
Cite
@article{arxiv.2402.06466,
title = {Uniformly sampling random directed hypergraphs with fixed degrees},
author = {Yanna J. Kraakman and Clara Stegehuis},
journal= {arXiv preprint arXiv:2402.06466},
year = {2026}
}
Comments
Version 2: Restructured proof of Theorem 2; clarified model by replacing configuration model terminology with a uniform-sampling formulation; changed title (original title: Configuration models for random directed hypergraphs). The conclusions of the paper remain unchanged