Uniformly sampling random directed hypergraphs with fixed degrees
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917188044062720 |
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| author | Kraakman, Yanna J. Stegehuis, Clara |
| author_facet | Kraakman, Yanna J. Stegehuis, Clara |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_06466 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Uniformly sampling random directed hypergraphs with fixed degrees Kraakman, Yanna J. Stegehuis, Clara Combinatorics 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. |
| title | Uniformly sampling random directed hypergraphs with fixed degrees |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2402.06466 |