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Journal of Probability and Statistics
Volume 2013, Article ID 707960, 12 pages
Research Article

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

Faculty of Informatics, University of Debrecen, P.O. Box 12, Debrecen 4010, Hungary

Received 8 April 2013; Accepted 1 August 2013

Academic Editor: Shein-chung Chow

Copyright © 2013 István Fazekas and Bettina Porvázsnyik. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 can be achieved. The proofs are based on martingale methods.