Statistics of citation networks

TL;DR

This paper analyzes the statistical properties of citation networks' out-degree distributions, revealing universal patterns and their relation to journal restrictions, modeled through a recursive search approach.

Contribution

It provides a detailed statistical analysis of citation out-degree distributions across journals and introduces a recursive search model to explain observed features.

Findings

Out-degree distribution peaks at intermediate values.

Universal distribution shape at high out-degrees across journals.

Average out-degree increases logarithmically over time.

Abstract

The out-degree distribution of citation networks is investigated. Statistical data of the number of papers cited within a paper (out-degree) for different journals in the period 1991-1999 is reported. The out-degree distribution is characterized by a maximum at intermediate out-degrees. At the left of the maximum there are strong fluctuations from journal to journal while is quite universal at the right, with two classes of journals. These two classes are associated with the existence or not of a restriction in the maximum number of pages per paper. The shape of the out-degree distribution does not change appreciable from period to period, but the average out-degree is observed to increase logarithmically with the number of published papers. These features are modeled using a recursive search model.