Power-law citation distributions are not scale-free

• Published in: Physical review. E 2017-09, Vol.96 (3-1), p.032306-032306, Article 032306
• Main Author: Golosovsky, Michael
• Format: Article
• Language: English
• ISSN: 2470-0045; 2470-0053
• DOI: 10.1103/PhysRevE.96.032306

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: The papers that exceed some citation threshold become runaways. 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 compare our measurements to our recently developed model of citation dynamics based on copying-redirection-triadic closure and find explanations to our empirical observations.