Scale-Free Property for Degrees and Weights in a Preferential Attachment Random Graph Model

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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Main Authors: István Fazekas, Bettina Porvázsnyik
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:Journal of Probability and Statistics
Online Access:http://dx.doi.org/10.1155/2013/707960
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spelling doaj-57a64abb6c7c481d89ad2095dbcaea2e2020-11-24T23:37:51ZengHindawi LimitedJournal 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
collection DOAJ
language English
format Article
sources DOAJ
author István Fazekas
Bettina Porvázsnyik
spellingShingle István Fazekas
Bettina Porvázsnyik
Scale-Free Property for Degrees and Weights in a Preferential Attachment Random Graph Model
Journal of Probability and Statistics
author_facet István Fazekas
Bettina Porvázsnyik
author_sort István Fazekas
title 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_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_sort scale-free property for degrees and weights in a preferential attachment random graph model
publisher Hindawi Limited
series Journal of Probability and Statistics
issn 1687-952X
1687-9538
publishDate 2013-01-01
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.
url http://dx.doi.org/10.1155/2013/707960
work_keys_str_mv AT istvanfazekas scalefreepropertyfordegreesandweightsinapreferentialattachmentrandomgraphmodel
AT bettinaporvazsnyik scalefreepropertyfordegreesandweightsinapreferentialattachmentrandomgraphmodel
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