Fitting the linear preferential attachment model

Phyllis Wan, Tiandong Wang, Richard A. Davis, Sidney I. Resnick

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


Preferential attachment is an appealing mechanism for modeling power-law behavior of the degree distributions in directed social networks. In this paper, we consider methods for fitting a 5-parameter linear preferential model to network data under two data scenarios. In the case where full history of the network formation is given, we derive the maximum likelihood estimator of the parameters and show that it is strongly consistent and asymptotically normal. In the case where only a single-time snapshot of the network is available, we propose an estimation method which combines method of moments with an approximation to the likelihood. The resulting estimator is also strongly consistent and performs quite well compared to the MLE estimator. We illustrate both estimation procedures through simulated data and explore the usage of this model in a real data example.

Original languageEnglish (US)
Pages (from-to)3738-3780
Number of pages43
JournalElectronic Journal of Statistics
Issue number2
StatePublished - 2017


  • Estimation
  • Multivariate heavy tail statistics
  • Power laws
  • Preferential attachment

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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