Power laws in citation distributions: Evidence from Scopus (1402.3890v1)

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.

• The paper rejects the power-law hypothesis in about half the fields, with alternative models better describing citation distributions in areas like humanities and social sciences.
• The study shows that in fields where power laws are plausible, such as Physics, the evidence does not decisively favor power-law over other models.
• A higher scaling parameter (3.24 to 4.69) is observed where applicable, highlighting a pronounced skew towards fewer high-impact papers.

Overview of Power Laws in Citation Distributions: Evidence from Scopus

This paper presents a rigorous empirical examination of power-law behavior in citation distributions using a dataset extracted from Scopus. The paper aims to determine whether the power-law model accurately describes the distribution of citations for highly cited scientific papers. Building upon the foundational hypothesis proposed by Price, this investigation utilized a statistically robust framework for comparing the power-law model against several alternative distributions, including Yule, power-law with exponential cut-off, and log-normal models.

Key Findings

1. Rejection of Power Law Hypothesis: Approximately half of the science fields analyzed from the Scopus database do not adhere to a power-law distribution, with alternative models providing a better fit. Notably, the fields of humanities and social sciences, as well as certain formal and life sciences, exhibit deviations from the power-law distribution, suggesting a more complex underlying mechanism for citation distributions.
2. Fields Conforming to Power Laws: For those fields where the power-law hypothesis remains plausible, such as Physics and Astronomy, the empirical data does not provide definitive superiority over the alternatives. This indicates that while the power-law could be applicable, it is statistically indistinguishable from other models within those fields.
3. Scaling Parameter: The power-law scaling parameter, when applicable, is markedly higher than older literature, ranging from 3.24 to 4.69, supporting recent findings from Albarrán and Ruiz-Castillo's work. This suggests a more pronounced skew towards fewer high-impact papers.
4. Proportion of Power-law Distributed Papers: In cases where power laws are plausible, they account for less than 1% of the published articles, confirming that the occurrence of such distributions is relatively rare across the scientific domains analyzed.

Implications

The findings highlight the complexity and variability of citation distributions across different scientific fields. The rejection of power-law behavior in many fields indicates the necessity for utilizing alternative statistical models to understand citation dynamics more accurately. The identified lack of universality of the power-law model has multiple implications:

• Practical Implications: These insights can refine metrics used in academic evaluations and alter approaches to bibliometric analysis, adapting the models employed to the specific characteristics of each field.
• Theoretical Implications: The results challenge the widespread assumption of ubiquitous power-law behavior in citation distributions, suggesting future research should explore the mechanisms driving citation practices in different disciplines.

Future Research Directions

Future investigations could benefit from assessing the mechanisms that lead to deviations from power-law distributions. By understanding these processes, researchers could develop tailored models that account for citation dynamics more precisely. Additionally, the exploration of larger and more diverse datasets could provide a broader understanding of publication and citation patterns, potentially identifying new factors influencing the distribution shapes.

In conclusion, this paper provides a nuanced overview of citation distributions by leveraging a large Scopus dataset and applying rigorous statistical analyses. It suggests that the use of power-law models in scientometric analysis should be carefully considered and complemented with alternative approaches to elucidate citation behaviors across different scientific fields.