Rank-Based Attachment Leads to Power Law Graphs

@article{Janssen2010RankBasedAL,
  title={Rank-Based Attachment Leads to Power Law Graphs},
  author={Jeannette C. M. Janssen and Paweł Prałat},
  journal={SIAM J. Discret. Math.},
  year={2010},
  volume={24},
  pages={420-440}
}
We investigate the degree distribution resulting from graph generation models based on rank-based attachment. In rank-based attachment, all vertices are ranked according to a ranking scheme. The link probability of a given vertex is proportional to its rank raised to the power $-\alpha$, for some $\alpha\in(0,1)$. Through a rigorous analysis, we show that rank-based attachment models lead to graphs with a power law degree distribution with exponent $1+1/\alpha$ whenever vertices are ranked… 

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