Scale-Free Property for Degrees and Weights in a Preferential Attachment Random Graph Model
A random graph evolution mechanism is defined. The evolution studied is a combination of the preferential attachment model and the interaction of four vertices. The asymptotic behaviour of the graph is described. It is proved that the graph exhibits a power law degree distribution; in other words, i...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Probability and Statistics |
| Online Access: | http://dx.doi.org/10.1155/2013/707960 |
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| _version_ | 1832546195063439360 |
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| author | István Fazekas Bettina Porvázsnyik |
| author_facet | István Fazekas Bettina Porvázsnyik |
| author_sort | István Fazekas |
| collection | DOAJ |
| description | A random graph evolution mechanism is defined. The evolution studied is a combination of the preferential attachment model and the interaction of four vertices. The asymptotic behaviour of the graph is described. It is proved that the graph exhibits
a power law degree distribution; in other words, it is scale-free. It turns out that any exponent in (2,∞) can be achieved. The proofs are based on martingale methods. |
| format | Article |
| id | doaj-art-57a64abb6c7c481d89ad2095dbcaea2e |
| institution | Kabale University |
| issn | 1687-952X 1687-9538 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Probability and Statistics |
| spelling | doaj-art-57a64abb6c7c481d89ad2095dbcaea2e2025-02-03T07:23:35ZengWileyJournal of Probability and Statistics1687-952X1687-95382013-01-01201310.1155/2013/707960707960Scale-Free Property for Degrees and Weights in a Preferential Attachment Random Graph ModelIstván Fazekas0Bettina Porvázsnyik1Faculty of Informatics, University of Debrecen, P.O. Box 12, Debrecen 4010, HungaryFaculty of Informatics, University of Debrecen, P.O. Box 12, Debrecen 4010, HungaryA random graph evolution mechanism is defined. The evolution studied is a combination of the preferential attachment model and the interaction of four vertices. The asymptotic behaviour of the graph is described. It is proved that the graph exhibits a power law degree distribution; in other words, it is scale-free. It turns out that any exponent in (2,∞) can be achieved. The proofs are based on martingale methods.http://dx.doi.org/10.1155/2013/707960 |
| spellingShingle | István Fazekas Bettina Porvázsnyik Scale-Free Property for Degrees and Weights in a Preferential Attachment Random Graph Model Journal of Probability and Statistics |
| title | Scale-Free Property for Degrees and Weights in a Preferential Attachment Random Graph Model |
| title_full | Scale-Free Property for Degrees and Weights in a Preferential Attachment Random Graph Model |
| title_fullStr | Scale-Free Property for Degrees and Weights in a Preferential Attachment Random Graph Model |
| title_full_unstemmed | Scale-Free Property for Degrees and Weights in a Preferential Attachment Random Graph Model |
| title_short | Scale-Free Property for Degrees and Weights in a Preferential Attachment Random Graph Model |
| title_sort | scale free property for degrees and weights in a preferential attachment random graph model |
| url | http://dx.doi.org/10.1155/2013/707960 |
| work_keys_str_mv | AT istvanfazekas scalefreepropertyfordegreesandweightsinapreferentialattachmentrandomgraphmodel AT bettinaporvazsnyik scalefreepropertyfordegreesandweightsinapreferentialattachmentrandomgraphmodel |