Unifying Directed and Undirected Random Graph Models
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866913712763305984 |
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| author | van Santvoort, Mike van der Hoorn, Pim |
| author_facet | van Santvoort, Mike van der Hoorn, Pim |
| contents | In this paper we explore mathematical tools that can be used to relate directed and undirected random graph models to each other. We identify probability spaces on which a directed and an undirected graph model are equivalent, and investigate which graph events can subsequently be translated between equivalent models. We finally give coupling techniques that can be used to establish an approximate equivalence between directed and undirected random graph models. As an application of these tools, we give conditions under which two broad classes of random graph models are equivalent. In one of these classes the presence of edges/arcs is determined by independent Bernoulli random variables, while in the other class a fixed number of edges/arcs is placed in between vertices according to some probability measure. We finally use these equivalences to extend a previously established relationship between the directed versions of these model classes to their undirected counterparts. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_21083 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Unifying Directed and Undirected Random Graph Models van Santvoort, Mike van der Hoorn, Pim Probability 60B99, 05C80, 60F99 In this paper we explore mathematical tools that can be used to relate directed and undirected random graph models to each other. We identify probability spaces on which a directed and an undirected graph model are equivalent, and investigate which graph events can subsequently be translated between equivalent models. We finally give coupling techniques that can be used to establish an approximate equivalence between directed and undirected random graph models. As an application of these tools, we give conditions under which two broad classes of random graph models are equivalent. In one of these classes the presence of edges/arcs is determined by independent Bernoulli random variables, while in the other class a fixed number of edges/arcs is placed in between vertices according to some probability measure. We finally use these equivalences to extend a previously established relationship between the directed versions of these model classes to their undirected counterparts. |
| title | Unifying Directed and Undirected Random Graph Models |
| topic | Probability 60B99, 05C80, 60F99 |
| url | https://arxiv.org/abs/2502.21083 |