A case of limit behaviour of vertex degrees in conditional configuration graphs
<p>We consider configuration graphs with N vertices. The degrees of the vertices<br />are independent identically distributed random variables according to power-law<br />distribution with positive parameter . They are equal to the number of vertex’s<br />semiedges that are n...
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| Format: | Article |
| Language: | English |
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Karelian Research Centre of the Russian Academy of Sciences
2017-08-01
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| Series: | Transactions of the Karelian Research Centre of the Russian Academy of Sciences |
| Subjects: | |
| Online Access: | http://journals.krc.karelia.ru/index.php/mathem/article/view/613 |
| _version_ | 1819063945591259136 |
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| author | Yury Pavlov |
| author_facet | Yury Pavlov |
| author_sort | Yury Pavlov |
| collection | DOAJ |
| description | <p>We consider configuration graphs with N vertices. The degrees of the vertices<br />are independent identically distributed random variables according to power-law<br />distribution with positive parameter . They are equal to the number of vertex’s<br />semiedges that are numbered in an arbitrary order. The graph is constructed by<br />joining all of the semiedges pairwise equiprobably to form edges. Such models can<br />be used for describing different communication networks and Internet topology. We<br />study the subset of random graphs under the condition that the sum of vertex<br />degrees is known and it is equal to n. The properties of the graph depend on the<br />behaviour of the parameter . We assume that is a random variable following<br />uniform distribution on the interval [a; b]; 0 < a < b < 1. Let (N) and r be the<br />maximum vertex degree and the number of vertices with a given degree r. Limit<br />distributions of these random variables as N; n ! 1 in such a way that n=N ! 1<br />were known only if a 6 1. In the paper we proved limit theorems for (N) and r<br />in the case a > 1</p> |
| first_indexed | 2024-12-21T15:22:44Z |
| format | Article |
| id | doaj.art-14ff1f25ffe04aefbe7c9a376cb909a5 |
| institution | Directory Open Access Journal |
| issn | 1997-3217 2312-4504 |
| language | English |
| last_indexed | 2024-12-21T15:22:44Z |
| publishDate | 2017-08-01 |
| publisher | Karelian Research Centre of the Russian Academy of Sciences |
| record_format | Article |
| series | Transactions of the Karelian Research Centre of the Russian Academy of Sciences |
| spelling | doaj.art-14ff1f25ffe04aefbe7c9a376cb909a52022-12-21T18:58:59ZengKarelian Research Centre of the Russian Academy of SciencesTransactions of the Karelian Research Centre of the Russian Academy of Sciences1997-32172312-45042017-08-018667510.17076/mat613459A case of limit behaviour of vertex degrees in conditional configuration graphsYury Pavlov<p>We consider configuration graphs with N vertices. The degrees of the vertices<br />are independent identically distributed random variables according to power-law<br />distribution with positive parameter . They are equal to the number of vertex’s<br />semiedges that are numbered in an arbitrary order. The graph is constructed by<br />joining all of the semiedges pairwise equiprobably to form edges. Such models can<br />be used for describing different communication networks and Internet topology. We<br />study the subset of random graphs under the condition that the sum of vertex<br />degrees is known and it is equal to n. The properties of the graph depend on the<br />behaviour of the parameter . We assume that is a random variable following<br />uniform distribution on the interval [a; b]; 0 < a < b < 1. Let (N) and r be the<br />maximum vertex degree and the number of vertices with a given degree r. Limit<br />distributions of these random variables as N; n ! 1 in such a way that n=N ! 1<br />were known only if a 6 1. In the paper we proved limit theorems for (N) and r<br />in the case a > 1</p>http://journals.krc.karelia.ru/index.php/mathem/article/view/613configuration random graphvertex degreelimit theorems. |
| spellingShingle | Yury Pavlov A case of limit behaviour of vertex degrees in conditional configuration graphs Transactions of the Karelian Research Centre of the Russian Academy of Sciences configuration random graph vertex degree limit theorems. |
| title | A case of limit behaviour of vertex degrees in conditional configuration graphs |
| title_full | A case of limit behaviour of vertex degrees in conditional configuration graphs |
| title_fullStr | A case of limit behaviour of vertex degrees in conditional configuration graphs |
| title_full_unstemmed | A case of limit behaviour of vertex degrees in conditional configuration graphs |
| title_short | A case of limit behaviour of vertex degrees in conditional configuration graphs |
| title_sort | case of limit behaviour of vertex degrees in conditional configuration graphs |
| topic | configuration random graph vertex degree limit theorems. |
| url | http://journals.krc.karelia.ru/index.php/mathem/article/view/613 |
| work_keys_str_mv | AT yurypavlov acaseoflimitbehaviourofvertexdegreesinconditionalconfigurationgraphs AT yurypavlov caseoflimitbehaviourofvertexdegreesinconditionalconfigurationgraphs |