Tsallis $q$-exponential describes the distribution of scientific citations - A new characterization of the impact

TL;DR

This paper demonstrates that the distribution of scientific citations across multiple countries can be effectively modeled using the Tsallis q-exponential distribution, revealing a universal pattern and introducing a new impact ranking index based on an effective temperature.

Contribution

It introduces a novel application of the Tsallis q-exponential distribution to model citation distributions and proposes a new impact metric based on the effective temperature parameter.

Findings

Citation distributions fit well with the Tsallis q-exponential model.

A universal parameter q ≈ 4/3 describes all citation data.

The effective temperature T provides a new impact ranking index.

Abstract

In this work we have studied the research activity for countries of Europe, Latin America and Africa for all sciences between 1945 and November 2008. All the data are captured from the Web of Science database during this period. The analysis of the experimental data shows that, within a nonextensive thermostatistical formalism, the Tsallis \emph{q}-exponential distribution $N(c)$ satisfactorily describes Institute of Scientific Information citations. The data which are examined in the present survey can be fitted successfully as a first approach by applying a {\it single} curve (namely, $N(c) \propto 1/[1+(q-1) c/T]^{\frac{1}{q-1}}$ with $q\simeq 4/3$ for {\it all} the available citations $c$, $T$ being an "effective temperature". The present analysis ultimately suggests that the phenomenon might essentially be {\it one and the same} along the {\it entire} range of the citation number. Finally, this manuscript provides a new ranking index, via the "effective temperature" $T$, for the impact level of the research activity in these countries, taking into account the number of the publications and their citations.