CoChat
Sign Up
Cited by 196scientometrics and bibliometrics researchWeb visibility and informetricsPsychology Research and Bibliometrics

Power laws in citation distributions: evidence from Scopus

Open access
Brzezinski, Michal·2015·Scientometrics
DOI 10.1007/s11192-014-1524-zPMC PMC4365275
Open this paper in CoChat — free account

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 claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.1007/s11192-014-1524-z

Cites

36 of 36 references verified0 citation errors · 0 not checkable

Statistics

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

  • Scopus is one of the most highly regarded academic databases globally, indexing approximately 70% more sources than the Web of Science.

    “Apart from this, Scopus is one of the most highly regarded academic databases globally, indexing approximately 70% more sources than the Web of Science (Brzezinski 2015).”

    From Blockchain technology in the smart city: A bibliometric review (2022) · cites this paper as Brzezinski 2015

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

Cites

Flagged first, then by citations

Cited by

Sorted by citations

Related

Authors
Brzezinski, M.
Venue
Scientometrics
Publisher
Springer Science and Business Media LLC
Published
2015-01-22
Volume
103
Issue
1
Pages
213-228
ISSN
  • 0138-9130 (ISSN-L)
  • 1588-2861
DOI
10.1007/s11192-014-1524-z
PMC
PMC4365275
OpenAlex
W2170265466
Cited by
196
References
36
Citations by year
2026: 8 · 2025: 24 · 2024: 21 · 2023: 15 · 2022: 14 · 2021: 17 · 2020: 40 · 2019: 10 · 2018: 13 · 2017: 14 · 2016: 14 · 2015: 6
FWCI
14.27
Type
journal article
Language
en
Open access
Licence
Locations
  • Scientometrics (publishedVersion, cc-by)
  • Europe PMC (PubMed Central) (publishedVersion, cc-by)
  • PubMed Central (publishedVersion, cc-by)
  • PubMed (publishedVersion)
  • RePEc: Research Papers in Economics (submittedVersion, cc-by)
Topics
  • Social Sciences › Decision Sciences › Statistics, Probability and Uncertainty › scientometrics and bibliometrics research
  • Physical Sciences › Computer Science › Information Systems › Web visibility and informetrics
  • Social Sciences › Psychology › Experimental and Cognitive Psychology › Psychology Research and Bibliometrics
Keywords
citation distribution, power law, highly cited papers, lognormal distribution, likelihood ratio test, model comparison, Scopus, scientific impact

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review