The structure of a configuration graph with a normally distributed parameter of the power series distribution of vertex degrees

<p>We consider configuration graphs with N vertices. The degrees of the vertices are independent random variables identically distributed according to the power law, with a positive parameter τ . They are equal to the number of vertex semiedges that are numbered in an arbitrary order. The grap...

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Bibliographic Details
Main Author:	Yury Pavlov
Format:	Article
Language:	English
Published:	Karelian Research Centre of the Russian Academy of Sciences 2018-06-01
Series:	Transactions of the Karelian Research Centre of the Russian Academy of Sciences
Subjects:	random configuration graph vertex degree limit theorems
Online Access:	http://journals.krc.karelia.ru/index.php/mathem/article/view/768

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spelling	doaj-a2f958702d704ee1b9b71e7942b6bf0b2020-11-25T03:05:35ZengKarelian Research Centre of the Russian Academy of SciencesTransactions of the Karelian Research Centre of the Russian Academy of Sciences1997-32172312-45042018-06-01710.17076/mat768605The structure of a configuration graph with a normally distributed parameter of the power series distribution of vertex degreesYury Pavlov0Institute of Applied Mathematical Research, Karelian Research Centre, Russian Academy of Sciences<p>We consider configuration graphs with N vertices. The degrees of the vertices are independent random variables identically distributed according to the power law, with a positive parameter τ . They are equal to the number of vertex semiedges that are numbered in an arbitrary order. The graph is constructed by joining all of the semiedges pairwise equiprobably to form edges. We study the subset of such random graphs under the condition that the sum of vertex degrees is known and it is equal to n. Let τ be a random variable following a truncated normal distribution on an arbitrary fixed finite interval. We obtained the limit distributions of the maximum vertex degree and the number of vertices with a given degree for various zones of N and n tendency to infinity.</p>http://journals.krc.karelia.ru/index.php/mathem/article/view/768random configuration graphvertex degreelimit theorems
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Yury Pavlov
spellingShingle	Yury Pavlov The structure of a configuration graph with a normally distributed parameter of the power series distribution of vertex degrees Transactions of the Karelian Research Centre of the Russian Academy of Sciences random configuration graph vertex degree limit theorems
author_facet	Yury Pavlov
author_sort	Yury Pavlov
title	The structure of a configuration graph with a normally distributed parameter of the power series distribution of vertex degrees
title_short	The structure of a configuration graph with a normally distributed parameter of the power series distribution of vertex degrees
title_full	The structure of a configuration graph with a normally distributed parameter of the power series distribution of vertex degrees
title_fullStr	The structure of a configuration graph with a normally distributed parameter of the power series distribution of vertex degrees
title_full_unstemmed	The structure of a configuration graph with a normally distributed parameter of the power series distribution of vertex degrees
title_sort	structure of a configuration graph with a normally distributed parameter of the power series distribution of vertex degrees
publisher	Karelian Research Centre of the Russian Academy of Sciences
series	Transactions of the Karelian Research Centre of the Russian Academy of Sciences
issn	1997-3217 2312-4504
publishDate	2018-06-01
description	<p>We consider configuration graphs with N vertices. The degrees of the vertices are independent random variables identically distributed according to the power law, with a positive parameter τ . They are equal to the number of vertex semiedges that are numbered in an arbitrary order. The graph is constructed by joining all of the semiedges pairwise equiprobably to form edges. We study the subset of such random graphs under the condition that the sum of vertex degrees is known and it is equal to n. Let τ be a random variable following a truncated normal distribution on an arbitrary fixed finite interval. We obtained the limit distributions of the maximum vertex degree and the number of vertices with a given degree for various zones of N and n tendency to infinity.</p>
topic	random configuration graph vertex degree limit theorems
url	http://journals.krc.karelia.ru/index.php/mathem/article/view/768
work_keys_str_mv	AT yurypavlov thestructureofaconfigurationgraphwithanormallydistributedparameterofthepowerseriesdistributionofvertexdegrees AT yurypavlov structureofaconfigurationgraphwithanormallydistributedparameterofthepowerseriesdistributionofvertexdegrees
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The structure of a configuration graph with a normally distributed parameter of the power series distribution of vertex degrees

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