Variational principle for scale-free network motifs

Abstract For scale-free networks with degrees following a power law with an exponent τ ∈ (2, 3), the structures of motifs (small subgraphs) are not yet well understood. We introduce a method designed to identify the dominant structure of any given motif as the solution of an optimization problem. Th...

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Autores principales:	Clara Stegehuis, Remco van der Hofstad, Johan S. H. van Leeuwaarden
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2019
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/6459f12b53234a38ac2b0e9e373737b0
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spelling	oai:doaj.org-article:6459f12b53234a38ac2b0e9e373737b02021-12-02T15:08:32ZVariational principle for scale-free network motifs10.1038/s41598-019-43050-82045-2322https://doaj.org/article/6459f12b53234a38ac2b0e9e373737b02019-05-01T00:00:00Zhttps://doi.org/10.1038/s41598-019-43050-8https://doaj.org/toc/2045-2322Abstract For scale-free networks with degrees following a power law with an exponent τ ∈ (2, 3), the structures of motifs (small subgraphs) are not yet well understood. We introduce a method designed to identify the dominant structure of any given motif as the solution of an optimization problem. The unique optimizer describes the degrees of the vertices that together span the most likely motif, resulting in explicit asymptotic formulas for the motif count and its fluctuations. We then classify all motifs into two categories: motifs with small and large fluctuations.Clara StegehuisRemco van der HofstadJohan S. H. van LeeuwaardenNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 9, Iss 1, Pp 1-10 (2019)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Clara Stegehuis Remco van der Hofstad Johan S. H. van Leeuwaarden Variational principle for scale-free network motifs
description	Abstract For scale-free networks with degrees following a power law with an exponent τ ∈ (2, 3), the structures of motifs (small subgraphs) are not yet well understood. We introduce a method designed to identify the dominant structure of any given motif as the solution of an optimization problem. The unique optimizer describes the degrees of the vertices that together span the most likely motif, resulting in explicit asymptotic formulas for the motif count and its fluctuations. We then classify all motifs into two categories: motifs with small and large fluctuations.
format	article
author	Clara Stegehuis Remco van der Hofstad Johan S. H. van Leeuwaarden
author_facet	Clara Stegehuis Remco van der Hofstad Johan S. H. van Leeuwaarden
author_sort	Clara Stegehuis
title	Variational principle for scale-free network motifs
title_short	Variational principle for scale-free network motifs
title_full	Variational principle for scale-free network motifs
title_fullStr	Variational principle for scale-free network motifs
title_full_unstemmed	Variational principle for scale-free network motifs
title_sort	variational principle for scale-free network motifs
publisher	Nature Portfolio
publishDate	2019
url	https://doaj.org/article/6459f12b53234a38ac2b0e9e373737b0
work_keys_str_mv	AT clarastegehuis variationalprincipleforscalefreenetworkmotifs AT remcovanderhofstad variationalprincipleforscalefreenetworkmotifs AT johanshvanleeuwaarden variationalprincipleforscalefreenetworkmotifs
_version_	1718388062722981888

Variational principle for scale-free network motifs

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