Power-Law Citation Distributions are Not Scale-Free

  • Michael Golosovsky
Part of the SpringerBriefs in Complexity book series (BRIEFSCOMPLEXITY)


We analyze time evolution of statistical distributions of citations to scientific papers published in the same year. While these distributions seem to follow the power-law dependence, we find that they are nonstationary and the exponent of the power-law fit decreases with time and does not come to saturation. We attribute the nonstationarity of citation distributions to different longevity of the low-cited and highly-cited papers. By measuring citation trajectories of papers, we found that citation careers of the low-cited papers come to saturation after 10–15 years while those of the highly-cited papers continue to increase indefinitely. When the number of citations of a paper exceeds some citation threshold, it becomes a runaway. Thus, we show that although citation distribution can look as a power-law dependence, it is not scale-free and there is a hidden dynamic scale associated with the onset of runaways. We show that our model of citation dynamics based on copying/redirection/triadic closure accounts for these issues fairly well.


Power law distribution Scale-free distribution Citation lifetime 


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Copyright information

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Michael Golosovsky
    • 1
  1. 1.Racah Institute of PhysicsHebrew University of JerusalemJerusalemIsrael

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