Navigability of Random Geometric Graphs in the Universe and Other Spacetimes

Abstract Random geometric graphs in hyperbolic spaces explain many common structural and dynamical properties of real networks, yet they fail to predict the correct values of the exponents of power-law degree distributions observed in real networks. In that respect, random geometric graphs in asympt...

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Autores principales:	William Cunningham, Konstantin Zuev, Dmitri Krioukov
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2017
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/3963ebe6d337412997fc2efc87db6d25
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spelling	oai:doaj.org-article:3963ebe6d337412997fc2efc87db6d252021-12-02T15:06:15ZNavigability of Random Geometric Graphs in the Universe and Other Spacetimes10.1038/s41598-017-08872-42045-2322https://doaj.org/article/3963ebe6d337412997fc2efc87db6d252017-08-01T00:00:00Zhttps://doi.org/10.1038/s41598-017-08872-4https://doaj.org/toc/2045-2322Abstract Random geometric graphs in hyperbolic spaces explain many common structural and dynamical properties of real networks, yet they fail to predict the correct values of the exponents of power-law degree distributions observed in real networks. In that respect, random geometric graphs in asymptotically de Sitter spacetimes, such as the Lorentzian spacetime of our accelerating universe, are more attractive as their predictions are more consistent with observations in real networks. Yet another important property of hyperbolic graphs is their navigability, and it remains unclear if de Sitter graphs are as navigable as hyperbolic ones. Here we study the navigability of random geometric graphs in three Lorentzian manifolds corresponding to universes filled only with dark energy (de Sitter spacetime), only with matter, and with a mixture of dark energy and matter. We find these graphs are navigable only in the manifolds with dark energy. This result implies that, in terms of navigability, random geometric graphs in asymptotically de Sitter spacetimes are as good as random hyperbolic graphs. It also establishes a connection between the presence of dark energy and navigability of the discretized causal structure of spacetime, which provides a basis for a different approach to the dark energy problem in cosmology.William CunninghamKonstantin ZuevDmitri KrioukovNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 7, Iss 1, Pp 1-10 (2017)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q William Cunningham Konstantin Zuev Dmitri Krioukov Navigability of Random Geometric Graphs in the Universe and Other Spacetimes
description	Abstract Random geometric graphs in hyperbolic spaces explain many common structural and dynamical properties of real networks, yet they fail to predict the correct values of the exponents of power-law degree distributions observed in real networks. In that respect, random geometric graphs in asymptotically de Sitter spacetimes, such as the Lorentzian spacetime of our accelerating universe, are more attractive as their predictions are more consistent with observations in real networks. Yet another important property of hyperbolic graphs is their navigability, and it remains unclear if de Sitter graphs are as navigable as hyperbolic ones. Here we study the navigability of random geometric graphs in three Lorentzian manifolds corresponding to universes filled only with dark energy (de Sitter spacetime), only with matter, and with a mixture of dark energy and matter. We find these graphs are navigable only in the manifolds with dark energy. This result implies that, in terms of navigability, random geometric graphs in asymptotically de Sitter spacetimes are as good as random hyperbolic graphs. It also establishes a connection between the presence of dark energy and navigability of the discretized causal structure of spacetime, which provides a basis for a different approach to the dark energy problem in cosmology.
format	article
author	William Cunningham Konstantin Zuev Dmitri Krioukov
author_facet	William Cunningham Konstantin Zuev Dmitri Krioukov
author_sort	William Cunningham
title	Navigability of Random Geometric Graphs in the Universe and Other Spacetimes
title_short	Navigability of Random Geometric Graphs in the Universe and Other Spacetimes
title_full	Navigability of Random Geometric Graphs in the Universe and Other Spacetimes
title_fullStr	Navigability of Random Geometric Graphs in the Universe and Other Spacetimes
title_full_unstemmed	Navigability of Random Geometric Graphs in the Universe and Other Spacetimes
title_sort	navigability of random geometric graphs in the universe and other spacetimes
publisher	Nature Portfolio
publishDate	2017
url	https://doaj.org/article/3963ebe6d337412997fc2efc87db6d25
work_keys_str_mv	AT williamcunningham navigabilityofrandomgeometricgraphsintheuniverseandotherspacetimes AT konstantinzuev navigabilityofrandomgeometricgraphsintheuniverseandotherspacetimes AT dmitrikrioukov navigabilityofrandomgeometricgraphsintheuniverseandotherspacetimes
_version_	1718388504264704000

Navigability of Random Geometric Graphs in the Universe and Other Spacetimes

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