Power-law citation distributions are not scale-free

TL;DR

This paper demonstrates that citation distributions, while resembling power-laws, are nonstationary and driven by different dynamics for low- and highly-cited papers, revealing a hidden scale and the presence of runaway papers.

Contribution

It uncovers the nonstationary nature of citation distributions and introduces a dynamic scale related to runaway citation trajectories, supported by a new model of citation dynamics.

Findings

Citation distributions are nonstationary and their exponents decrease over time.

Low-cited papers saturate their citation careers after 10-15 years.

Highly-cited papers continue to accumulate citations indefinitely.

Abstract

We analyze time evolution of statistical distributions of citations to scientific papers published in one year. While these distributions can be fitted by a 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, 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.