Nonparametric Estimation of the Preferential Attachment Function in Complex Networks: Evidence of Deviations from Log Linearity

  • Thong PhamEmail author
  • Paul Sheridan
  • Hidetoshi Shimodaira
Conference paper
Part of the Springer Proceedings in Complexity book series (SPCOM)


We introduce a statistically sound method called PAFit for the joint estimation of preferential attachment and node fitness in temporal complex networks. Together these mechanisms play a crucial role in shaping network topology by governing the way in which nodes acquire new edges over time. PAFit is an advance over previous methods in so far as it does not make any assumptions on the functional form of the preferential attachment function. We found that the application of PAFit to a publicly available Flickr social network dataset turned up clear evidence for a deviation of the preferential attachment function from the popularly assumed log-linear form. What is more, we were surprised to find that hubs are not always the nodes with the highest node fitnesses. PAFit is implemented in an R package of the same name.


Preferential attachment fitness Prowth models Complex networks MM algorithms Maximum likelihood estimation 



This work was supported by grants from Japan Society for the Promotion of Science KAKENHI (Grant numbers 26120523 and 24300106 to Hidetoshi Shimodaira).


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Thong Pham
    • 1
    Email author
  • Paul Sheridan
    • 2
  • Hidetoshi Shimodaira
    • 1
  1. 1.Osaka UniversityOsakaJapan
  2. 2.The University of TokyoTokyoJapan

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