تقرير
A Stochastic Block Hypergraph model
| العنوان: | A Stochastic Block Hypergraph model |
|---|---|
| المؤلفون: | Pister, Alexis, Barthelemy, Marc |
| سنة النشر: | 2023 |
| المجموعة: | Computer Science Condensed Matter Physics (Other) |
| مصطلحات موضوعية: | Physics - Physics and Society, Condensed Matter - Disordered Systems and Neural Networks, Condensed Matter - Statistical Mechanics, Computer Science - Social and Information Networks |
| الوصف: | We propose a simple model for a hypergraph generalization of the stochastic block model, using the clustering connection probability $P_{ij}$ between communities $i$ and $j$, and integrating explicitly the hyperedge formation process. Indeed, hyperedges are groups of nodes and we can expect that different real-world networks correspond to different formation processes of these groups and to different levels of homophily between nodes. We describe a simple model where we can explicitly introduce the hyperedge formation process and study its impact on the composition of hyperedges. We focus on the standard case where $P_{ij}=p\delta_{ij}+q(1-\delta_{ij})$, and when $0\leq q\leq p$, we show that the degree and hyperedge size distributions can be approximated by binomials with effective parameters that depend on the number of communities and on $q/p$. Also, the composition of hyperedges goes for $q=0$ from `pure' hyperedges (comprising nodes belonging to the same community) to `mixed' hyperedges that comprise nodes from different communities for $q=p$. We tested various formation processes and our results suggest that when they depend on the composition of the hyperedge, they tend to favor the dominant community and lead to hyperedges with a smaller diversity. In contrast, for formation processes that are independent from the hyperedge structure, we obtain hyperedges comprising a larger diversity of communities. The advantages of the model proposed here are its simplicity and flexibility that make it a good candidate for testing community-related problems, from their detection to their impact on various dynamics. Comment: 10 pages, 10 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2312.12536 |
| رقم الأكسشن: | edsarx.2312.12536 |
| قاعدة البيانات: | arXiv |
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