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

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  • István Fazekas
  • Bettina Porvázsnyik

Abstract

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.

Suggested Citation

  • István Fazekas & Bettina Porvázsnyik, 2013. "Scale-Free Property for Degrees and Weights in a Preferential Attachment Random Graph Model," Journal of Probability and Statistics, Hindawi, vol. 2013, pages 1-12, September.
    • Handle: RePEc:hin:jnljps:707960
    DOI: 10.1155/2013/707960
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