Title: 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.