On the Heterogeneous Distributions in Paper Citations

TL;DR

This study analyzes 21 years of scientific citation data from over 42 million papers, revealing that normalized citation distributions follow a power-law with an exponential cutoff, highlighting the long-term influence of journal reputation.

Contribution

It provides a large-scale, systematic analysis of citation distributions across disciplines, introducing a method to normalize citations by removing journal reputation effects.

Findings

Raw citation counts follow a log-normal distribution, except in the first year.

Normalized citations follow a power-law distribution with an exponential cutoff.

Journal reputation significantly influences long-term citation patterns.

Abstract

Academic papers have been the protagonists in disseminating expertise. Naturally, paper citation pattern analysis is an efficient and essential way of investigating the knowledge structure of science and technology. For decades, it has been observed that citation of scientific literature follows a heterogeneous and heavy-tailed distribution, and many of them suggest a power-law distribution, log-normal distribution, and related distributions. However, many studies are limited to small-scale approaches; therefore, it is hard to generalize. To overcome this problem, we investigate 21 years of citation evolution through a systematic analysis of the entire citation history of 42,423,644 scientific literatures published from 1996 to 2016 and contained in SCOPUS. We tested six candidate distributions for the scientific literature in three distinct levels of Scimago Journal & Country Rank (SJR) classification scheme. First, we observe that the raw number of annual citation acquisitions tends to follow the log-normal distribution for all disciplines, except for the first year of the publication. We also find significant disparity between the yearly acquired citation number among the journals, which suggests that it is essential to remove the citation surplus inherited from the prestige of the journals. Our simple method for separating the citation preference of an individual article from the inherited citation of the journals reveals an unexpected regularity in the normalized annual acquisitions of citations across the entire field of science. Specifically, the normalized annual citation acquisitions have power-law probability distributions with an exponential cut-off of the exponents around 2.3, regardless of its publication and citation year. Our results imply that journal reputation has a substantial long-term impact on the citation.