Are citations of scientific papers a case of nonextensivity ?

TL;DR

This paper demonstrates that a nonextensive statistical framework can effectively model the entire distribution of scientific paper citations, unifying the previously observed exponential and power-law behaviors.

Contribution

It introduces a nonextensive formalism to fit citation distributions, challenging the prior view that different mechanisms govern low and high citation counts.

Findings

A single nonextensive curve fits citation data well across all ranges.

The model connects to the Zipf-Mandelbrot law, unifying citation distribution behaviors.

Contrasts with previous partial fits using stretched exponential models.

Abstract

The distribution $N(x)$ of citations of scientific papers has recently been illustrated (on ISI and PRE data sets) and analyzed by Redner [Eur. Phys. J. B {\bf 4}, 131 (1998)]. To fit the data, a stretched exponential ($N(x) \propto \exp{-(x/x_0)^{\beta}}$) has been used with only partial success. The success is not complete because the data exhibit, for large citation count $x$, a power law (roughly $N(x) \propto x^{-3}$ for the ISI data), which, clearly, the stretched exponential does not reproduce. This fact is then attributed to a possibly different nature of rarely cited and largely cited papers. We show here that, within a nonextensive thermostatistical formalism, the same data can be quite satisfactorily fitted with a single curve (namely, $N(x) \propto 1/[1+(q-1) \lambda x]^{q/{q-1}}$ for the available values of $x$. This is consistent with the connection recently established by Denisov [Phys. Lett. A {\bf 235}, 447 (1997)] between this nonextensive formalism and the Zipf-Mandelbrot law. What the present analysis ultimately suggests is that, in contrast to Redner's conclusion, the phenomenon might essentially be one and the same along the entire range of the citation number $x$.