How Popular is Your Paper? An Empirical Study of the Citation Distribution

TL;DR

This study analyzes citation distributions for scientific papers, revealing a power-law behavior in citation counts that suggests a small number of papers receive most citations, following a specific decay pattern.

Contribution

It provides empirical evidence that citation distributions follow a power-law with a specific exponent, enhancing understanding of scientific impact patterns.

Findings

Citation distribution follows a power-law with exponent close to -1/2 in Zipf plots.

Number of papers with x citations decays as x^{-3}.

Power-law behavior observed across different datasets and time spans.

Abstract

Numerical data for the distribution of citations are examined for: (i) papers published in 1981 in journals which are catalogued by the Institute for Scientific Information (783,339 papers) and (ii) 20 years of publications in Physical Review D, vols. 11-50 (24,296 papers). A Zipf plot of the number of citations to a given paper versus its citation rank appears to be consistent with a power-law dependence for leading rank papers, with exponent close to -1/2. This, in turn, suggests that the number of papers with x citations, N(x), has a large-x power law decay N(x)~x^{-alpha}, with alpha approximately equal to 3.