The nestedness of higher-order networks
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arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866918509287571456 |
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| author | LaRock, Timothy Zhang, Yanting Young, Jean-Gabriel Eikmeier, Nicole Lambiotte, Renaud Landry, Nicholas W. |
| author_facet | LaRock, Timothy Zhang, Yanting Young, Jean-Gabriel Eikmeier, Nicole Lambiotte, Renaud Landry, Nicholas W. |
| contents | In contrast to dyadic interactions, higher-order interactions may contain one another, with subgroups naturally embedded within larger groups. These containment patterns arise empirically in ecology, sociology, computer science and the science of science, and have been studied under the names nestedness, simpliciality, encapsulation, and inclusion. In this chapter, we review each of these measures and unify them through a mathematical object known as the encapsulation directed acyclic graph, formulating each measure as a function of its properties. We demonstrate that nested structure is prevalent in social systems across several domains, show that different measures capture complementary aspects of this structure, and find that the absence of nestedness can itself be a powerful indicator of the mesoscale organization of a system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_18420 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The nestedness of higher-order networks LaRock, Timothy Zhang, Yanting Young, Jean-Gabriel Eikmeier, Nicole Lambiotte, Renaud Landry, Nicholas W. Physics and Society In contrast to dyadic interactions, higher-order interactions may contain one another, with subgroups naturally embedded within larger groups. These containment patterns arise empirically in ecology, sociology, computer science and the science of science, and have been studied under the names nestedness, simpliciality, encapsulation, and inclusion. In this chapter, we review each of these measures and unify them through a mathematical object known as the encapsulation directed acyclic graph, formulating each measure as a function of its properties. We demonstrate that nested structure is prevalent in social systems across several domains, show that different measures capture complementary aspects of this structure, and find that the absence of nestedness can itself be a powerful indicator of the mesoscale organization of a system. |
| title | The nestedness of higher-order networks |
| topic | Physics and Society |
| url | https://arxiv.org/abs/2605.18420 |