Power-Law Citation Distributions are Not Scale-Free

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.

‘Paperdemic’ during the COVID-19 pandemic

“…The power-law exponents were estimated to be 2.4, and was substantially lower than those found in the earlier literatures (2.9∼5.3). Previous studies have found that the exponent of power-law fit decreased with time [9] , implying an even greater skewness to the right in the future for the scientific impact of COVID-19 articles. The power-law exponent of the citation distribution at the journal level was 2.0, smaller than those for the individual COVID-19 articles, meaning that a small number of journals contributed most of the citations ( Fig.…”

Estimation of heavy tails in optical non-linear processes

“…Heavy-tailed distributions, and power-law (or Pareto) distributions in particular have been reported from a very broad range of areas, including earthquake intensities [1][2][3], avalanche sizes [4], solar flares [5], degree distributions of various social and biological networks [6][7][8], incomes [9,10], insurance claims [11,12], number of citations of scientific publications [13][14][15], and many more. For financial institutions, the importance of heavy-tailed behavior comes from the fact that a simple Gaussian model severely underestimates the risks associated with different products or investment strategies, which in turn results in considerable losses.…”