Power laws in citation distributions: evidence from Scopus

Abstract

Modeling distributions of citations to scientific papers is crucial for understanding how science develops. However, there is a considerable empirical controversy on which statistical model fits the citation distributions best. This paper is concerned with rigorous empirical detection of power-law behaviour in the distribution of citations received by the most highly cited scientific papers. We have used a large, novel data set on citations to scientific papers published between 1998 and 2002 drawn from Scopus. The power-law model is compared with a number of alternative models using a likelihood ratio test. We have found that the power-law hypothesis is rejected for around half of the Scopus fields of science. For these fields of science, the Yule, power-law with exponential cut-off and log-normal distributions seem to fit the data better than the pure power-law model. On the other hand, when the power-law hypothesis is not rejected, it is usually empirically indistinguishable from most of the alternative models. The pure power-law model seems to be the best model only for the most highly cited papers in “Physics and Astronomy”. Overall, our results seem to support theories implying that the most highly cited scientific papers follow the Yule, power-law with exponential cut-off or log-normal distribution. Our findings suggest also that power laws in citation distributions, when present, account only for a very small fraction of the published papers (less than 1 % for most of science fields) and that the power-law scaling parameter (exponent) is substantially higher (from around 3.2 to around 4.7) than found in the older literature.

Posted, visited, exported: Altmetrics in the social tagging system BibSonomy

“…Compared to fits of other possible candidate distributions, we find that both power-law fits are better than fits to exponential distributions, but also that other heavy-tailed distributions (among them the log-normal distribution) provide better fits. In that respect, the distribution of citations in our corpus is consistent with Brzezinski (2015), who similarly observed that other functions fit the empirical citation distributions of various disciplines better than power laws, and with Thelwall & Wilson (2015), who observed for 45 medical sub-fields that log-normal distributions are better fits to citation counts than power laws. Thelwall & Wilson (2015) further showed that for these disciplines a hooked power law is an even better fit than the log-normal distribution.…”

“…Since the threshold x min is very high -x min = 808 means that the part of the distribution that is fitted contains only publications with at least 808 citations -, we also consider the second (local) optimum: α = 2.34 for x min = 303. The exponents α of both fits are lower than reported by both Brzezinski (2015) and Albarrán & Ruiz-Castillo (2011). This is evidence that our corpus, which is collected from a web system, is indeed different to corpora that are collected from traditional article catalogs like Web of Science or Scopus.…”

“…The effect depends on the characteristics of the individual datasets that are merged (e.g., mean number of citations, correlations). Thelwall (2015); Thelwall & Wilson (2014) and Brzezinski (2015) confirmed that publication corpora of various disciplines indeed possess different statistical properties. The dataset in BibSonomy is heterogeneous as there is no mechanism in BibSonomy to explicitly assign a publication to a discipline.…”

“…To determine the optimal fit, we used the methodology by Clauset et al (2009), that was also used in previous studies of citation distributions (Albarrán & Ruiz-Castillo, 2011;Brzezinski, 2015). The optimal fit has parameters α = 2.59 and x min = 808.…”

The impact of structural genomics: the first quindecennial

“…Similarly as for other sets of scientific publications studied in the literature [56] it is characterized by a “heavy tail” of a small number of highly cited papers and the majority of papers with very few citations. Such distributions were suggested to follow a power law distribution, N ( x ) ~ x - α , with α ~ 3 [56], especially in the region of the most highly cited papers [57,58]. The theoretical model that appears to fit well to the dataset of the PSI publications has a dual character [59], with a direct mechanism describing the papers with few citations, and an indirect mechanism (citing a paper based on citations already existing) describing the highly cited papers.…”