Citations to articles citing Benford's law: a Benford analysis

TL;DR

This paper investigates whether the citations to articles citing Benford's law follow the law's predicted distribution, revealing a remarkable agreement and highlighting the law's influence across scientific literature.

Contribution

It introduces a novel analysis of citation data to assess the prevalence of Benford's law in scientific referencing patterns.

Findings

Citations to Benford's law articles follow the law's distribution

The data shows strong agreement with Benford's law predictions

Highlights the law's widespread influence in scientific literature

Abstract

The occurrence of first significant digits of numbers in large data is often governed by a logarithmically decreasing distribution called Benford's law (BL), reported first by S. Newcomb (SN) and many decades later independently by F. Benford (FB). Due to its counter-intuitiveness the law was ignored for decades as a mere curious observation. However, an indication of its remarkable resurgence is the huge swell in the number of citations received by the papers of SN/FB. The law has come a long way, from obscurity to now being a regular subject of books, peer reviewed papers, patents, blogs and news. Here, we use Google Scholar (GS) to collect the data on the number of citations received by the articles citing the original paper of SN/FB and then investigate whether the leading digits of this citations data are distributed according to the law they discovered. We find that the citations data of literature on BL is in remarkable agreement with the predictions of the law.