p-adic numbers encode complex networks

Abstract The Erdős-Rényi (ER) random graph G(n, p) analytically characterizes the behaviors in complex networks. However, attempts to fit real-world observations need more sophisticated structures (e.g., multilayer networks), rules (e.g., Achlioptas processes), and projections onto geometric, social...

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Autores principales: Hao Hua, Ludger Hovestadt
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Lenguaje:EN
Publicado: Nature Portfolio 2021
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Acceso en línea:https://doaj.org/article/117b3e84b4ed4297981a52e1598512ac
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spelling oai:doaj.org-article:117b3e84b4ed4297981a52e1598512ac2021-12-02T15:13:59Zp-adic numbers encode complex networks10.1038/s41598-020-79507-42045-2322https://doaj.org/article/117b3e84b4ed4297981a52e1598512ac2021-01-01T00:00:00Zhttps://doi.org/10.1038/s41598-020-79507-4https://doaj.org/toc/2045-2322Abstract The Erdős-Rényi (ER) random graph G(n, p) analytically characterizes the behaviors in complex networks. However, attempts to fit real-world observations need more sophisticated structures (e.g., multilayer networks), rules (e.g., Achlioptas processes), and projections onto geometric, social, or geographic spaces. The p-adic number system offers a natural representation of hierarchical organization of complex networks. The p-adic random graph interprets n as the cardinality of a set of p-adic numbers. Constructing a vast space of hierarchical structures is equivalent for combining number sequences. Although the giant component is vital in dynamic evolution of networks, the structure of multiple big components is also essential. Fitting the sizes of the few largest components to empirical data was rarely demonstrated. The p-adic ultrametric enables the ER model to simulate multiple big components from the observations of genetic interaction networks, social networks, and epidemics. Community structures lead to multimodal distributions of the big component sizes in networks, which have important implications in intervention of spreading processes.Hao HuaLudger HovestadtNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 11, Iss 1, Pp 1-11 (2021)
institution DOAJ
collection DOAJ
language EN
topic Medicine
R
Science
Q
spellingShingle Medicine
R
Science
Q
Hao Hua
Ludger Hovestadt
p-adic numbers encode complex networks
description Abstract The Erdős-Rényi (ER) random graph G(n, p) analytically characterizes the behaviors in complex networks. However, attempts to fit real-world observations need more sophisticated structures (e.g., multilayer networks), rules (e.g., Achlioptas processes), and projections onto geometric, social, or geographic spaces. The p-adic number system offers a natural representation of hierarchical organization of complex networks. The p-adic random graph interprets n as the cardinality of a set of p-adic numbers. Constructing a vast space of hierarchical structures is equivalent for combining number sequences. Although the giant component is vital in dynamic evolution of networks, the structure of multiple big components is also essential. Fitting the sizes of the few largest components to empirical data was rarely demonstrated. The p-adic ultrametric enables the ER model to simulate multiple big components from the observations of genetic interaction networks, social networks, and epidemics. Community structures lead to multimodal distributions of the big component sizes in networks, which have important implications in intervention of spreading processes.
format article
author Hao Hua
Ludger Hovestadt
author_facet Hao Hua
Ludger Hovestadt
author_sort Hao Hua
title p-adic numbers encode complex networks
title_short p-adic numbers encode complex networks
title_full p-adic numbers encode complex networks
title_fullStr p-adic numbers encode complex networks
title_full_unstemmed p-adic numbers encode complex networks
title_sort p-adic numbers encode complex networks
publisher Nature Portfolio
publishDate 2021
url https://doaj.org/article/117b3e84b4ed4297981a52e1598512ac
work_keys_str_mv AT haohua padicnumbersencodecomplexnetworks
AT ludgerhovestadt padicnumbersencodecomplexnetworks
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