Are citations of scientific papers a case of nonextensivity?

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 4, 131 (1998)]. To fit the data, a stretched exponential (N(x) ∝ exp −(x/x 0 ) β ) 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) ∝ 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) ∝ 1/[1 + (q − 1) λ x] q q−1 for the available values of x. This is consistent with the connection recently established by Denisov [Phys. Lett. A 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.

Citation networks in high energy physics

“…[36] found the distribution of citations of scientists to be a stretched exponential, whereas it was argued in [37] that the citation distribution of papers was described by an asymptotic power law. The same data was attempted fitted to a curve ∼ (k i +const) −α in a later paper [40]. As demonstrated above, our data is of a much higher quality than the ISI and PRD data sets discussed in these two papers, but it seems to be the case that even with access to the highly homogeneous SPIRES data base, the cutoff mechanism still leaves room for speculation as to the topology of the citation distribution.…”

q-exponential distribution in urban agglomeration

“…In this way, the Zipf-Mandelbrot distribution is a natural generalization of an inverse power law. This distribution has been applied in many contexts; in particular, it was recently employed in the discussion of scientific citations [5] and football goal distribution [9]. Another important aspect of the Zipf-Mandelbrot's distribution is that it arises naturally in the context of a generalized statistical mechanics proposed some years ago [22][23][24][25].…”

Power-law distributions for the citation index of scientific publications and scientists

“…First, we consider the citations of publications. In both the earlier works on the citation of scientific publications [32,33], the number of publications versus citations is plotted and zeros are simply ignored. In a statistical distribution, we obtain the publication density, in other words, the number of publications in the interval of unit citation, instead of the number of publications.…”

“…Using the technique of the Zipf plots, Redner [32] has recently shown that the distribution of citations of the most cited scientific papers is described by a power law, N(x) ∼ x −α , with α 3.0. Tsallis and Albuquerque [33] claim that the newly proposed "Tsallis statistics" can as well account for the distribution of citations of scientific papers.…”