Random hyperbolic graphs in $d+1$ dimensions
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2020
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| _version_ | 1866909214121656320 |
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| author | Budel, Gabriel Kitsak, Maksim Aldecoa, Rodrigo Zuev, Konstantin Krioukov, Dmitri |
| author_facet | Budel, Gabriel Kitsak, Maksim Aldecoa, Rodrigo Zuev, Konstantin Krioukov, Dmitri |
| contents | We consider random hyperbolic graphs in hyperbolic spaces of any dimension $d+1\geq 2$. We present a rescaling of model parameters that casts the random hyperbolic graph model of any dimension to a unified mathematical framework, leaving the degree distribution invariant with respect to the dimension. Unlike the degree distribution, clustering does depend on the dimension, decreasing to 0 at $d \rightarrow \infty$. We analyze all of the other limiting regimes of the model, and we release a software package that generates random hyperbolic graphs and their limits in hyperbolic spaces of any dimension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2010_12303 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Random hyperbolic graphs in $d+1$ dimensions Budel, Gabriel Kitsak, Maksim Aldecoa, Rodrigo Zuev, Konstantin Krioukov, Dmitri Physics and Society We consider random hyperbolic graphs in hyperbolic spaces of any dimension $d+1\geq 2$. We present a rescaling of model parameters that casts the random hyperbolic graph model of any dimension to a unified mathematical framework, leaving the degree distribution invariant with respect to the dimension. Unlike the degree distribution, clustering does depend on the dimension, decreasing to 0 at $d \rightarrow \infty$. We analyze all of the other limiting regimes of the model, and we release a software package that generates random hyperbolic graphs and their limits in hyperbolic spaces of any dimension. |
| title | Random hyperbolic graphs in $d+1$ dimensions |
| topic | Physics and Society |
| url | https://arxiv.org/abs/2010.12303 |