Nonuniversal power law scaling in the probability distribution of scientific citations

TL;DR

This paper presents a model explaining the distribution of scientific citations, highlighting how direct and indirect citation mechanisms contribute to a nonuniversal power-law distribution with a citation threshold for becoming a classic.

Contribution

The study introduces a dual-mechanism model for citation distribution, revealing nonuniversal power-law behavior and identifying citation thresholds for classic papers across different datasets.

Findings

Indirect citations produce a power-law tail in citation distribution.

The 'tipping point' for classic papers varies by dataset, around 21-39 citations.

Highly cited individuals have smaller power-law exponents than less cited ones.

Abstract

We develop a model for the distribution of scientific citations. The model involves a dual mechanism: in the direct mechanism, the author of a new paper finds an old paper A and cites it. In the indirect mechanism, the author of a new paper finds an old paper A only via the reference list of a newer intermediary paper B, which has previously cited A. By comparison to citation databases, we find that papers having few citations are cited mainly by the direct mechanism. Papers already having many citations ('classics') are cited mainly by the indirect mechanism. The indirect mechanism gives a power-law tail. The 'tipping point' at which a paper becomes a classic is about 21 citations for papers published in the Institute for Scientific Information (ISI) Web of Science database in 1981, 29 for Physical Review D papers published from 1975-1994, and 39 for all publications from a list of high h-index chemists assembled in 2007. The power-law exponent is not universal. Individuals who are highly cited have a systematically smaller exponent than individuals who are less cited.