Modeling a Century of Citation Distributions
  Changes in citation distributions over 100 years can reveal much about the evolution of the scientific communities or disciplines. The prevalence of uncited papers or of highly-cited papers, with respect to the bulk of publications, provides important clues as to the dynamics of scientific research. Using 25 million papers and 600 million references from the Web of Science over the 1900-2006 period, this paper proposes a simple model based on a random selection process to explain the "uncitedness" phenomenon and its decline in recent years. We show that the proportion of uncited papers is a function of 1) the number of articles published in a given year (the competing papers) and 2) the number of articles subsequently published (the citing papers) and the number of references they contain. Using uncitedness as a departure point, we demonstrate the utility of the stretched-exponential function and a form of the Tsallis function to fit complete citation distributions over the 20th century. As opposed to simple power-law fits, for instance, both these approaches are shown to be empirically well-grounded and robust enough to better understand citation dynamics at the aggregate level. Based on an expansion of these models, on our new understanding of uncitedness and on our large dataset, we are able provide clear quantitative evidence and provisional explanations for an important shift in citation practices around 1960, unmatched in the 20th century. We also propose a revision of the "citation classic" category as a set of articles which is clearly distinguishable from the rest of the field. 
Matthew L. Wallace, Vincent Larivi\`ere, Yves Gingras