Random hyperbolic graphs in 𝑑+1 dimensions
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1.
California Institute of Technology
Abstract
We consider random hyperbolic graphs in hyperbolic spaces of any dimension 𝑑 + 1 ≥ 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 → ∞. 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.
Copyright and License
© 2024 American Physical Society.
Acknowledgement
We thank F. Papadopoulos, M. Á. Serrano, M. Boguñá, P. van der Hoorn, and T. van der Zwan for useful discussions and suggestions. This work was supported by ARO Grant No. W911NF-17-1-0491 and NSF Grants No. IIS-1741355 and No. CCF-2311160. G.B. was supported by the NExTWORKx project, a collaboration between TU Delft and KPN on future telecommunication networks. M.K. acknowledges the Dutch Research Council (NWO) grant OCENW.M20.244.
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Additional details
- ISSN
- 2470-0053
- United States Army Research Office
- W911NF-17-1-0491
- National Science Foundation
- IIS-1741355
- National Science Foundation
- CCF-2311160
- Delft University of Technology
- Dutch Research Council
- OCENW.M20.244