POWER LAW RELATIONS IN SCIENCE BIBLIOGRAPHY—A SELF‐CONSISTENT INTERPRETATION
Abstract
Abstract Several power law relations are found to occur in bibliographic studies of scientific journals, articles, and citations. These can be interpreted in a self‐consistent manner in terms of growth parameters of articles, journals, and citations. Similar models have been proposed earlier in physical, biological, and behavioural sciences.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
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?
Empirical studies have shown that distributions of article citations are very skewed, even within single disciplines.
“The use of relative indicators is widespread, but empirical studies [19, 20, 21] have shown that distributions of article citations are very skewed, even within single disciplines.”
From Universality of citation distributions: Toward an objective measure of scientific impact (2008) · cites this paper as [20]
Cites
Human behavior and the principle of least effort
Zipf, G. K. (1949) · Max Planck Digital Library · Cited by 6,598 · see citing works
Price, D. J. D. S. (1963) · Columbia University Press eBooks · doi:10.7312/pric91844 · Cited by 4,340 · see citing works
Price, D. J. D. S. (1965) · Science · doi:10.1126/science.149.3683.510 · Cited by 3,121 · see citing works
(1961) · Information and Control · doi:10.1016/s0019-9958(61)80064-8 · Cited by 2,904 · see citing works
On the Origin of the Cosmic Radiation
Fermi, E. (1949) · Physical Review · doi:10.1103/physrev.75.1169 · Cited by 2,350 · see citing works
The frequency distribution of scientific productivity
Lotka, A. J. (1926) · Journal of the Washington Academy of Sciences · Cited by 1,999 · see citing works
nauk, R. A. (1965) · Medical Entomology and Zoology · Cited by 959 · see citing works
The Psycho-Biology of Language
Tinker, M. A., & Zipf, G. K. (1936) · The American Journal of Psychology · doi:10.2307/1415586 · Cited by 735 · see citing works
Joos, M. (1936) · Language · doi:10.2307/408930 · Cited by 731 · see citing works
Neural Events and the Psychophysical Law
Stevens, S. S. (1970) · Science · doi:10.1126/science.170.3962.1043 · Cited by 551 · see citing works
Bradford's Law and the Bibliography of Science
BROOKES, B. C. (1969) · Nature · doi:10.1038/224953a0 · Cited by 465 · see citing works
New factors in the evaluation of scientific literature through citation indexing
Garfield, E., & Sher, I. H. (1963) · American Documentation · doi:10.1002/asi.5090140304 · Cited by 429 · see citing works
Citation Indexing for Studying Science
GARFIELD, E. (1970) · Nature · doi:10.1038/227669a0 · Cited by 391 · see citing works
Fairthorne, R. A. (1969) · Journal of Documentation · doi:10.1108/eb026481 · Cited by 237 · see citing works
Age and area; a study in geographical distribution and origin of species,
Willis, J. C. (1922) · doi:10.5962/bhl.title.70451 · Cited by 237 · see citing works
Electrocardiographic Notching in Rats Deficient in Essential Fatty Acids
Caster, W. O., & Ahn, P. (1963) · Science · doi:10.1126/science.139.3560.1213-a · Cited by 185 · see citing works
Goffman, W., & Warren, K. S. (1969) · Nature · doi:10.1038/2211205a0 · Cited by 89 · see citing works
Bradford's Law of Bibliography of Science: an Interpretation
Naranan, S. (1970) · Nature · doi:10.1038/227631a0 · Cited by 88 · see citing works
Self-citationBradford's Law and Library Acquisitions
Goffman, W., & MORRIS, T. G. (1970) · Nature · doi:10.1038/226922a0 · Cited by 71 · see citing works
Brookes, B. C. (1970) · Nature · doi:10.1038/2271377b0 · Cited by 3 · see citing works
Holography-State of the Art Review 1969
Ennos, A. E. (1969) · Optica Acta International Journal of Optics · doi:10.1080/715120891 · Cited by 2 · see citing works
Flagged first, then by citations
Cited by
Sorted by citations
Universality of citation distributions: Toward an objective measure of scientific impact
Radicchi, F., Fortunato, S., & Castellano, C. (2008) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0806977105 · Cited by 828 · see citing works
Morris, S. A., & Martens, B. V. D. V. (2008) · Annual Review of Information Science and Technology · doi:10.1002/aris.2008.1440420113 · Cited by 286 · see citing works
Lotka's law: A testing procedure
Pao, M. L. (1985) · Information Processing & Management · doi:10.1016/0306-4573(85)90055-x · Cited by 291 · see citing works
For Your Citations Only? Hot Topics in Bibliometric Analysis
van Raan, A. F. J. (2005) · Measurement Interdisciplinary Research and Perspectives · doi:10.1207/s15366359mea0301_7 · Cited by 295 · see citing works
Citations to scientific articles: Its distribution and dependence on the article features
Vieira, E. S., & Gomes, J. A. N. F. (2009) · Journal of Informetrics · doi:10.1016/j.joi.2009.06.002 · Cited by 181 · see citing works
A bibliometric study of psychological research on tourism
Barrios, M., Borrego, A., Vilaginés, A., Ollé, C., & Somoza‐Fernández, M. (2008) · Scientometrics · doi:10.1007/s11192-007-1952-0 · Cited by 164 · see citing works
The skewness of science in 219 sub-fields and a number of aggregates
Albarrán, P., Crespo, J. A., Ortuño-Ortı́n, I., & Ruiz‐Castillo, J. (2011) · Scientometrics · doi:10.1007/s11192-011-0407-9 · Cited by 151 · see citing works
On Growth, Ageing, and Fractal Differentiation of Science
van Raan, A. F. J. (2000) · Scientometrics · doi:10.1023/a:1005647328460 · Cited by 126 · see citing works
Baum, J. A. C. (2011) · Organization · doi:10.1177/1350508411403531 · Cited by 136 · see citing works
Potter, W. G. (1981) · Illinois Digital Environment for Access to Learning and Scholarship (University of Illinois at Urbana-Champaign) · Cited by 87 · see citing works
van Raan, A. F. J. (2005) · Journal of the American Society for Information Science and Technology · doi:10.1002/asi.20284 · Cited by 86 · see citing works
Stationary scientometric distributions
Haitun, S. D. (1982) · Scientometrics · doi:10.1007/bf02018448 · Cited by 74 · see citing works
Simkin, M. V., & Roychowdhury, V. (2006) · CERN Document Server (European Organization for Nuclear Research) · Cited by 76 · see citing works
Stationary scientometric distributions
Haitun, S. D. (1982) · Scientometrics · doi:10.1007/bf02098003 · Cited by 61 · see citing works
van Raan, A. F. J. (2008) · Journal of the American Society for Information Science and Technology · doi:10.1002/asi.20765 · Cited by 57 · see citing works
Crossmaps: Visualization of overlapping relationships in collections of journal papers
Morris, S. A., & Yen, G. G. (2004) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0307604100 · Cited by 56 · see citing works
The use of patent titles for identifying the topics of invention and forecasting trends
Courtial, J., Callon, M., & Sigogneau, A. (1993) · Scientometrics · doi:10.1007/bf02016216 · Cited by 53 · see citing works
Models for power law relations in linguistics and information science
Naranan, S., & Balasubrahmanyan, V. K. (1998) · Journal of Quantitative Linguistics · doi:10.1080/09296179808590110 · Cited by 49 · see citing works
Self-citationVlachý, J. (1978) · Scientometrics · doi:10.1007/bf02016844 · Cited by 49 · see citing works
van Raan, A. F. J. (2001) · Scientometrics · doi:10.1023/a:1010501820393 · Cited by 48 · see citing works
Morris, S. A., & Goldstein, M. L. (2007) · Journal of the American Society for Information Science and Technology · doi:10.1002/asi.20661 · Cited by 42 · see citing works
Quantitative linguistics and complex system studies*
Balasubrahmanyan, V. K., & Naranan, S. (1996) · Journal of Quantitative Linguistics · doi:10.1080/09296179608599629 · Cited by 41 · see citing works
Self-citationTwo-step competition process leads to quasi power-law income distributions
van Raan, A. F. J. (2001) · Physica A Statistical Mechanics and its Applications · doi:10.1016/s0378-4371(01)00254-0 · Cited by 37 · see citing works
Numerical Methods of Bibliographic Analysis
Brookes, B. C. (1973) · Illinois Digital Environment for Access to Learning and Scholarship (University of Illinois at Urbana-Champaign) · Cited by 37 · see citing works
Simkin, M. V., & Roychowdhury, V. (2010) · Physics Reports · doi:10.1016/j.physrep.2010.12.004 · Cited by 36 · see citing works
Bradford ranking conventions and their application to a growing literature
Heine, M. H. (1998) · Journal of Documentation · doi:10.1108/eum0000000007173 · Cited by 28 · see citing works
A general formulation of bradford's distribution: The graph‐oriented approach
Asai, I. (1981) · Journal of the American Society for Information Science · doi:10.1002/asi.4630320206 · Cited by 28 · see citing works
Verification of bibliometric methods' applicability for thesaurus construction
Schneider, J. W. (2005) · ACM SIGIR Forum · doi:10.1145/1067268.1067293 · Cited by 25 · see citing works
Ronda‐Pupo, G. A., & Katz, J. S. (2017) · Scientometrics · doi:10.1007/s11192-017-2612-7 · Cited by 26 · see citing works
Reference-based publication networks with episodic memories
van Raan, A. F. J. (2005) · Scientometrics · doi:10.1007/s11192-005-0227-x · Cited by 26 · see citing works
MODELLING THE BRADFORD PHENOMENON
Burrell, Q. L. (1988) · Journal of Documentation · doi:10.1108/eb026816 · Cited by 25 · see citing works
Bibliometric models for journal productivity
Hubert, J. J. (1977) · Social Indicators Research · doi:10.1007/bf00353144 · Cited by 24 · see citing works
Lotka’s law and author productivity pattern of research in law discipline
Sahu, A., & Jena, P. (2021) · Collection and Curation · doi:10.1108/cc-04-2021-0012 · Cited by 23 · see citing works
Ronda-Pupo, G. A., & Pham, T. (2018) · Scientometrics · doi:10.1007/s11192-018-2761-3 · Cited by 23 · see citing works
Morris, S. A. (2005) · Journal of the American Society for Information Science and Technology · doi:10.1002/asi.20208 · Cited by 23 · see citing works
Chang, Y. (2016) · Information Processing & Management · doi:10.1016/j.ipm.2015.12.011 · Cited by 22 · see citing works
A relationship between two forms of Bradford's law
Hubert, J. J. (1978) · Journal of the American Society for Information Science · doi:10.1002/asi.4630290311 · Cited by 21 · see citing works
BIBLIOMETRIC ANALYSIS OF A NEW RESEARCH SUB‐FIELD
Magyar, G. (1974) · Journal of Documentation · doi:10.1108/eb026568 · Cited by 20 · see citing works
Prompt nuclear analysis: Growth and trends
Bujdosó, E., Lyon, W. S., & Noszlopi, I. (1982) · Journal of Radioanalytical and Nuclear Chemistry · doi:10.1007/bf02520372 · Cited by 18 · see citing works
Scaling behavior in the dynamics of citations to scientific journals
Picoli, S., Mendes, R. S., Malacarne, L. C., & Lenzi, E. K. (2006) · Europhysics Letters (EPL) · doi:10.1209/epl/i2006-10162-1 · Cited by 17 · see citing works
Sangwal, K. (2012) · Journal of Informetrics · doi:10.1016/j.joi.2012.09.002 · Cited by 14 · see citing works
Construction of bipartite and unipartite weighted networks from collections of journal papersPreprint
Morris, S. A., & Yen, G. G. (2005) · arXiv (Cornell University) · doi:10.48550/arxiv.physics/0503061 · Cited by 14 · see citing works
Bradford's law in relation to the evolution of a field. A case study of solar power research
Garg, K. C., Sharma, P., & Sharma, L. (1993) · Scientometrics · doi:10.1007/bf02016547 · Cited by 13 · see citing works
An empirical approach to compare the performance of heterogeneous academic fields
Ruocco, G., & Daraio, C. C. (2013) · Scientometrics · doi:10.1007/s11192-013-1038-0 · Cited by 12 · see citing works
COHERENT INFORMATIONAL ENERGY AND ENTROPY
Avramescu, A. (1980) · Journal of Documentation · doi:10.1108/eb026700 · Cited by 12 · see citing works
Gupta, S., Kanaujia, A., Lathabai, H. H., Singh, V. K., & Mayr, P. (2024) · International Journal of Intelligent Systems · doi:10.1155/2024/5511224 · Cited by 11 · see citing works
Growth of food science and technology literature: A comparison of CFTRI, India and the world
Seetharam, G., & Rao, I. K. R. (1999) · Scientometrics · doi:10.1007/bf02458478 · Cited by 10 · see citing works
Balasubrahmanyan, V. K., & Naranan, S. (2000) · Journal of Quantitative Linguistics · doi:10.1076/0929-6174(200008)07:02;1-z;ft153 · Cited by 10 · see citing works
Self-citation“Power law” version of Bradford's law: Statistical tests and methods of estimation
Naranan, S. (1989) · Scientometrics · doi:10.1007/bf02026411 · Cited by 10 · see citing works
Self-citationPlagiarism in Academic Writing in Higher Education Institutions: A Bibliometric Analysis
Ahmad, H., & Fauzi, M. A. (2024) · International Journal on Social and Education Sciences · doi:10.46328/ijonses.623 · Cited by 14 · see citing works
Lotka’s Law and productivity patterns of authors in biomedical science in Nigeria on HIV/AIDS
Adigwe, I. (2016) · The Electronic Library · doi:10.1108/el-02-2014-0024 · Cited by 9 · see citing works
The citation-based impact of complex innovation systems scales with the size of the system
Ronda‐Pupo, G. A. (2017) · Scientometrics · doi:10.1007/s11192-017-2401-3 · Cited by 9 · see citing works
Zitt, M., Ramanana-Rahary, S., & Bassecoulard, E. (2003) · Scientometrics · doi:10.1023/a:1023675620752 · Cited by 7 · see citing works
On the naranan interpretation of Bradford's law
Hubert, J. J. (1976) · Journal of the American Society for Information Science · doi:10.1002/asi.4630270510 · Cited by 6 · see citing works
Braun, T., Erńó, B., & Lyon, W. S. (1982) · C R C Critical Reviews in Analytical Chemistry · doi:10.1080/10408348208542753 · Cited by 6 · see citing works
Authorship productivity in the knowledge management literature
Wallace, D. P. (2012) · Proceedings of the American Society for Information Science and Technology · doi:10.1002/meet.14504901017 · Cited by 5 · see citing works
Methodological and conceptual questions of bibliometric standards
Rao, I. K. R. (1996) · Scientometrics · doi:10.1007/bf02018484 · Cited by 5 · see citing works
Bipartite Yule Processes in Collections of Journal PapersPreprint
Morris, S. A. (2005) · arXiv (Cornell University) · doi:10.48550/arxiv.cond-mat/0501386 · Cited by 4 · see citing works
Oluić-Vuković, V. (1991) · Journal of Information Science · doi:10.1177/016555159101700504 · Cited by 3 · see citing works
Libraries, Economics, and Information: Recent Trends in Information Science Literature
Pratt, A. D. (1975) · College & Research Libraries · doi:10.5860/crl_36_01_33 · Cited by 3 · see citing works
Mathematical formulations of Bradford's law
Umino, B. (1987) · Library and Information Science · doi:10.46895/lis.24.11 · Cited by 2 · see citing works
A Lei de Lotka: modelo lagrangiano de poisson aplicado a produtividade de autores
Alvarado, R. U. (2008) · LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Científicas) · Cited by 1 · see citing works
Journal Productivity in Fishery Science - An Informetric Analysis
Girijakumari, S., & Pillai, C. R. (1997) · Eprints@CMFRI Open Access Institutional Repository (Central Marine Fisheries Research Institute)
Bibliometric Research: History [ELIS Classic]
Hertzel, D. H. (2009) · CRC Press eBooks · doi:10.1081/e-elis3-120009034
Hubert, J. J. (1981) · Illinois Digital Environment for Access to Learning and Scholarship (University of Illinois at Urbana-Champaign)
Ronda‐Pupo, G. A., & Pham, T. (2017) · arXiv (Cornell University)
A Framework to Assess the Citation Performance of Complex Innovation Systems
Ronda‐Pupo, G. A. (2021) · Frontiers in Research Metrics and Analytics · doi:10.3389/frma.2021.622006
(1991) · Emerald Group Publishing Limited eBooks · doi:10.1108/s1876-0562(1991)000091b012
(2016) · Wiley eBooks · doi:10.1002/9783527681969.biblio
(2005) · Emerald Group Publishing Limited eBooks · doi:10.1108/s1876-0562(2005)0000005011
Ahmad, H. (2023) · SSRN Electronic Journal · doi:10.2139/ssrn.4502880
Derivation of nonstationary Lotka-type distributions without divergence of moments
Onodera, N. (2025) · Quantitative Science Studies · doi:10.1162/qss.a.403
- Authors
- NARANAN, S.
- Affiliations
- Tata Institute of Fundamental Research (IN)
- Corresponding author
- NARANAN, S.
- Venue
- Journal of Documentation
- Publisher
- Emerald
- Published
- 1971-02
- Volume
- 27
- Issue
- 2
- Pages
- 83-97
- ISSN
- 0022-0418 (ISSN-L)
- OpenAlex
- W1981342820
- Cited by
- 72
- References
- 21
- Citations by year
- 2025: 1 · 2024: 2 · 2023: 1 · 2021: 2 · 2018: 1 · 2017: 3 · 2016: 3 · 2013: 1 · 2012: 2
- FWCI
- 3.55
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of Documentation (publishedVersion)
- 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
- power-law relationship, scientific journals, scientific articles, citation analysis, bibliometric analysis, growth parameters
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 ›
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