Power-Law Citation Distributions are Not Scale-Free
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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.
KeywordsPower law distribution Scale-free distribution Citation lifetime
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