On conditional configuration graphs with random distribution of vertex degrees
We consider a configuration graph with N vertices. The degrees of the vertices are drawn independently from a discrete power-law distribution with positive parameter τ . They are equal to the number of each vertex’s numbered semiedges. The graph is constructed by joining all of the semiedges pairwis...
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| Format: | Article |
| Language: | English |
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Karelian Research Centre of the Russian Academy of Sciences
2016-09-01
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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/313 |
| _version_ | 1818532985868124160 |
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| author | Yury Pavlov |
| author_facet | Yury Pavlov |
| author_sort | Yury Pavlov |
| collection | DOAJ |
| description | We consider a configuration graph with N vertices. The degrees of the vertices are drawn independently from a discrete power-law distribution with positive parameter τ . They are equal to the number of each vertex’s numbered semiedges. The graph is constructed by joining all of the semiedges pairwise equiprobably to form edges. Research in the last years showed that configuration power-law random graphs with τ ∈ (1, 2) are deemed to be a good implementation of Internet topology. Such graphs could be used also for modeling forest fires as well as banking system defaults. But in these cases usually τ > 2. Parameter τ may depend on N and even be random. In the paper we consider configuration random graphs under the condition that the sum of vertex degrees is equal to n. Random graph dynamics as N → ∞ is assumed to take place in a random environment, where τ is a random variable following uniform distribution on the interval [a, b], 0 < a < b < ∞. We obtained the limit distributions of the maximum vertex degree and the number of vertices with a given degree as N, n → ∞. |
| first_indexed | 2024-12-11T17:52:42Z |
| format | Article |
| id | doaj.art-810eb47e6f6f42af95dd5a57f660bb42 |
| institution | Directory Open Access Journal |
| issn | 1997-3217 2312-4504 |
| language | English |
| last_indexed | 2024-12-11T17:52:42Z |
| publishDate | 2016-09-01 |
| 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-810eb47e6f6f42af95dd5a57f660bb422022-12-22T00:56:09ZengKarelian Research Centre of the Russian Academy of SciencesTransactions of the Karelian Research Centre of the Russian Academy of Sciences1997-32172312-45042016-09-0108627210.17076/mat313276On conditional configuration graphs with random distribution of vertex degreesYury PavlovWe consider a configuration graph with N vertices. The degrees of the vertices are drawn independently from a discrete power-law distribution with positive parameter τ . They are equal to the number of each vertex’s numbered semiedges. The graph is constructed by joining all of the semiedges pairwise equiprobably to form edges. Research in the last years showed that configuration power-law random graphs with τ ∈ (1, 2) are deemed to be a good implementation of Internet topology. Such graphs could be used also for modeling forest fires as well as banking system defaults. But in these cases usually τ > 2. Parameter τ may depend on N and even be random. In the paper we consider configuration random graphs under the condition that the sum of vertex degrees is equal to n. Random graph dynamics as N → ∞ is assumed to take place in a random environment, where τ is a random variable following uniform distribution on the interval [a, b], 0 < a < b < ∞. We obtained the limit distributions of the maximum vertex degree and the number of vertices with a given degree as N, n → ∞.http://journals.krc.karelia.ru/index.php/mathem/article/view/313configuration random graphrandom environmentvertex degreelimit theorems |
| spellingShingle | Yury Pavlov On conditional configuration graphs with random distribution of vertex degrees Transactions of the Karelian Research Centre of the Russian Academy of Sciences configuration random graph random environment vertex degree limit theorems |
| title | On conditional configuration graphs with random distribution of vertex degrees |
| title_full | On conditional configuration graphs with random distribution of vertex degrees |
| title_fullStr | On conditional configuration graphs with random distribution of vertex degrees |
| title_full_unstemmed | On conditional configuration graphs with random distribution of vertex degrees |
| title_short | On conditional configuration graphs with random distribution of vertex degrees |
| title_sort | on conditional configuration graphs with random distribution of vertex degrees |
| topic | configuration random graph random environment vertex degree limit theorems |
| url | http://journals.krc.karelia.ru/index.php/mathem/article/view/313 |
| work_keys_str_mv | AT yurypavlov onconditionalconfigurationgraphswithrandomdistributionofvertexdegrees |