A statistical perspective on higher-order interactions modeling
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917368812273664 |
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| author | Matias, Catherine |
| author_facet | Matias, Catherine |
| contents | Modeling higher-order interactions (HOI) has emerged as a crucial challenge in complex systems analysis, as many phenomena cannot be fully captured by pairwise relationships alone. Hypergraphs, which generalize graphs by allowing interactions among more than two entities, provide a powerful framework for representing such intricate dependencies. Adopting a statistical and probabilistic perspective on hypergraph modeling, we propose a guided tour through this emerging research area. We begin by illustrating the ubiquity of HOI in real-world systems, where interactions often involve groups of entities rather than isolated pairs. We then introduce the foundational concepts and notations of hypergraphs, discussing their descriptive statistics, graph-based representations, and the challenges associated with their complexity. We further explore a variety of statistical models for hypergraphs and address the critical task of node clustering. We conclude by outlining some open challenges in the field. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_28273 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A statistical perspective on higher-order interactions modeling Matias, Catherine Applications Modeling higher-order interactions (HOI) has emerged as a crucial challenge in complex systems analysis, as many phenomena cannot be fully captured by pairwise relationships alone. Hypergraphs, which generalize graphs by allowing interactions among more than two entities, provide a powerful framework for representing such intricate dependencies. Adopting a statistical and probabilistic perspective on hypergraph modeling, we propose a guided tour through this emerging research area. We begin by illustrating the ubiquity of HOI in real-world systems, where interactions often involve groups of entities rather than isolated pairs. We then introduce the foundational concepts and notations of hypergraphs, discussing their descriptive statistics, graph-based representations, and the challenges associated with their complexity. We further explore a variety of statistical models for hypergraphs and address the critical task of node clustering. We conclude by outlining some open challenges in the field. |
| title | A statistical perspective on higher-order interactions modeling |
| topic | Applications |
| url | https://arxiv.org/abs/2603.28273 |