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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.00371 |
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| _version_ | 1866912937754492928 |
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| author | Doležal, Martin Kubiś, Wiesław |
| author_facet | Doležal, Martin Kubiś, Wiesław |
| contents | We define and study a natural category of graph limits. The objects are pairs $(π,μ)$, where $π$ (the distribution of vertices) is an abstract probability measure on some abstract measurable space $(X,\mathcal{A})$ and $μ$ (the distribution of edges) is an abstract finite measure on the square $(X,\mathcal{A})^2$. Morphisms are random maps between the underlying measurable spaces which preserve the distribution of vertices as well as the distribution of edges. We also define a convergence notion (inspired by s-convergence) for sequences of graph limits. We apply tools from category theory to prove the compactness of the space of all graph limits. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_00371 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Categorical approach to graph limits Doležal, Martin Kubiś, Wiesław Combinatorics Category Theory 05C80, 60B10, 05C35 We define and study a natural category of graph limits. The objects are pairs $(π,μ)$, where $π$ (the distribution of vertices) is an abstract probability measure on some abstract measurable space $(X,\mathcal{A})$ and $μ$ (the distribution of edges) is an abstract finite measure on the square $(X,\mathcal{A})^2$. Morphisms are random maps between the underlying measurable spaces which preserve the distribution of vertices as well as the distribution of edges. We also define a convergence notion (inspired by s-convergence) for sequences of graph limits. We apply tools from category theory to prove the compactness of the space of all graph limits. |
| title | Categorical approach to graph limits |
| topic | Combinatorics Category Theory 05C80, 60B10, 05C35 |
| url | https://arxiv.org/abs/2412.00371 |