Illustrating a typical non power law by a downwards curved “log
(rank) – log (frequency)” distribution of science journal ranking by
average journal impact factors, JIF (left figure), and the corresponding
distribution of journal ranks, JRK (right figure), as separately assigned
within 107 disciplines. Incidentally, the journal rank distribution
coincides with that of a uniform sequence of random numbers. Similar
relationships hold also true for various subsets such as scientific fields
and disciplines (see figures in ADDENDUM
at the end of the
article).
Based on ISI annual data sets of
SCI-JCR (1974-1999)
Motto:“There is something still worse,
however, than being either criticized or dismantled by careless readers:
it is being ignored. Since the status of a claim depends on later
users' insertions, what if there are no later users whatsoever?
This is the point that people who never come close to the fabrication of
science have the greatest difficulty in grasping. They imagine that all
scientific articles are equal and arrayed in lines like soldiers, to be
carefully inspected one by one. However, most papers are never read at
all. No matter what a paper did to the former literature, if no one else
does anything with it, then it is as if it never existed at all. You
may have written a paper that settles a fierce controversy once and for
all, but if readers ignore it, it cannot be turned into a fact; it simply
cannot. …You may protest against this injustice; you may treasure
the certitude of being right in your inner heart; but it will never go
further than your inner heart; you will never go further in certitude
without the help of others.” (Bruno Latour, Science in Action, p. 40
(1987))
Humbly dedicated to cited
scientists
FOREWORD
Bibliometric indicators currently used to examine and
evaluate the published knowledge production are primarily based on impact
factors of journals covered by Science Citation Index database and
published annually since 1975 in the Journal Citation Reports [Garfield
(Editor)]. This concept has been introduced by Garfield [Garfield, 1972, 1979]
as a measure of the average citation frequency for a specific citable item
(article, review, letter, discovery account, note, and abstract) in a specific
journal during a specific year or period. Commonly, the impact factor of a
journal is defined as the ratio between citations and recent (previous two
years) citable items published or, in other words, as the average number of
citations in a given year of articles published in that journal in the
preceding two years. Thus, for instance, the impact factor for 1990 of
Physical Review Letters (PRL) has been calculated as the cumulated
number of 22,007 citations received in 1990 for articles published in the
considered journal in 1988 (11,497 citations) and 1989 (10,510 citations),
divided by the cumulated number of 2901 citable articles published in that
journal during the same two-year period, i.e. in 1988 (1430 articles) and 1989
(1471 articles). The impact factor of PRL in the year 1990 results
accordingly from the ratio 22,007 citations / 2901 papers = 7.586 citations
per paper and has the meaning of number of citations received by the "average
PRL article" during the considered two-year period. Obviously, the
definition can be extended over longer time spans. For more detailed recent
information about impact factors and their applications and extensions, see
also [Garfield, ISI Essays, 1994; PRESTìGIXTM,
2000, 2001]. Thus, for instance, while the impact factor is based on 4
independent variables (citations in the considered year to articles published
in the preceding two years, and their respective number of articles), the
prestige factor uses a more comprehensive algorithm (PRESTìGIXTM)
containing 6 independent variables (citations in the considered year to
articles published in that year and in the preceding two years, and their
respective number of articles). In other words, the prestige factor uses more
recent data, namely from 1998-2000 for the year 2000, and from 1999-2001 for
the year 2001.
Developed originally from the need to compare the journal
influence or performance, the impact factor provides nowadays the main
quantitative tool for ranking, evaluating, categorizing, and comparing
journals. Thus, it provides librarians a tool for the management of journal
collections and publishers a quantitative evidence in evaluating the position
of their journals. But data can as well be ranked to reveal interesting facts
about individual or collective performance and trends, such as highly cited
papers and authors (hot papers, hot authors), most active laboratories,
institutions or research fronts, up to countries and world science mapping and
policy [Aguillo, Braun, Garfield, Katz]. Accordingly, many institutions
worldwide are devoted to information science and technology based on citation
analysis and variously known as scientometrics, bibliometrics,
informetrics, cybermetrics, and webometrics – visit more sites
at USEFUL LINKS in the References. In Romania a specialized department
has recently been created under the Romanian Ministry of Education and
Research, namely CENAPOSS, an acronym for the National Center for Science
Policy and Scientometry, set up at the end of 1999.
"Perhaps the most important and recent use of impact is
in the process of academic evaluation. The impact factor can be used to
provide gross approximation of the prestige of journals in which individuals
have been published. This is best done in conjunction with other
considerations such as peer review... Again, the impact factor should be used
with informed peer review" [Garfield, 1994]. Methods and techniques are
currently designed for evaluation and comparison of research groups and
individual scientists, such as the so called ISI’s Expected Citation Rates
(ECR) System [Garfield, 1994] and ISSRU’s precursory Mean Expected
Citation Rates (MECR), Mean Observed Citation Rates (MOCR) and Relative
Citation Rates (RCR) [Braun, 1985-1988].
A simple scientometric evaluation of individual
and group contributions in fundamental science has recently been proposed and
a particularly relevant scientometric indicator has been introduced, namely
the cumulative impact factor [Popescu, 1994], defined by the sum
:
S [(journal impact factor, q) / (article
author number, a)]
or, shortly, S (q/a), extended over the
whole list of scientific publications of the assessed individual or group.
Obviously, the cumulative impact factor has the meaning of author’s total
number of citations per author in the first two years after publication, with
its unit cites/author at this paper age. This unit is equivalent to a
single-authored (a = 1) article, published in a journal with impact
factor unity (q = 1).The cumulative
scientometric indicator defined above has successfully been tested for
promotion thresholds in Romanian physics research institutes and faculties
[Romanian Ministry of National Education, Order No. 5103, Appendage 1-II,
dated on 05.07.1999] and for accreditation of research excellence centers in
Mathematics, Physics, and Chemistry [Romanian CNCSIS - National Council
of Scientific Research in Higher Education]. The necessary thresholds
resulted from the "Romanian experiment" for any candidate to a high academic
position or grade are, for instance, a minimal score of 6 to 8 points for
associate university professor, of 9 to 12 points for full university
professor, and of 14 points for Ph.D. supervisor. In other words, these
minimal promotion scores require the equivalent of 6-8, 9-12, and 14
single-authored papers respectively, published in unity-valued impact factor
journals. The conversion of these figures from the field of physics to any
other scientific field can easily be carried out by multiplying with the ratio
of the corresponding average impact factors (AVEJIF) given in the linked
SUMMARY Version
2001(or in SUMMARY_Version_2002,
inasmuch as the AVEGIF-values remain essentially the same). Thus, for
instance, for ENGINEERING SCIENCES, the minimal promotion scores given above
for PHYSICAL SCIENCES should be reduced by a factor of (AVEJIF)ENG
/ (AVEJIF)PHYS = 0.42/1.41 »0.3.
Clearly, a
high number of citations mean a major impact in the specific field or a high
utility. However, as pointed out above, it is critical to take into account,
among other aspects, that publication and citation rates, as well as the peak
impacts, vary widely from field to field, and among different disciplines, and
we need to know what the average citation rate is within a field and a
discipline to assess an individual. To illustrate this diversity, the current
average values of impact factors for 12 scientific fields and 107 scientific
disciplines are given in the SUMMARY_Version_2001
or, respectively, in the updated version SUMMARY_Version_2002
. A convenient alternative way to consider this requirement consists in the use
of the relative rank, r, of the journal within its discipline instead of
the impact factor, q. The grounds consist in the fact that, according to
the Lavalette ranking law [Lavalette, 1996; Popescu, 1997; see also
ADDENDUM
], there exists a simple functional dependence between r and
q, namely
q = c [Nn/(N-n+1)]-b =
c [(N+1)/r - N]-b
where the positive exponent
b (roughly 1/2) and the scaling factor c are two fitting parameters,
N is the total number of journals in the considered discipline, and
r = 1 - (n -
1)/N
defines the journal
(relative) rank, corresponding to its (descending absolute) ranking number
n. Thus, for instance, a value r = 0.75 means that 75 % of
journals of the considered discipline have a rank (and the corresponding impact
factor) lower or equal to that of the considered journal. Incidentally, the
journal rank distribution coincides with that of a uniform sequence of random
numbers TOP
(right). For many reasons, mainly in interdisciplinary comparisons and
evaluations, it appears therefore more appropriate to use a "normalized"
indicator such as the cumulative rank, defined by:
S [(journal rank, r) / (article author number,
a)]
or simply, S (r/a), with its natural unit
rank. This unit is equivalent to a single-authored (a = 1)
article, published in the discipline top journal (r = 1). The major
advantages of the "ranks scale" S (r/a) in comparison
with the "cites scale" S (q/a) consist in both
(i) a bibliometric equivalence of journals belonging to various
disciplines but having the same rank, and (ii) a much higher stability
as compared to the corresponding impact factor. Generally, the journal rank
r = 1 - (n -
1)/N ranges from unity (for top journals) to 1/N
(for bottom journals). It follows, thus, that the journal average rank of
scientific disciplines (or fields) is given by (1+1/N)/2 » 1/2, as far as N >> 1.
This narrow distribution of average rank values, in contrast to that of
average impact factors, indicates the "normalization" of the rank scale
notwithstanding the variety of disciplines and fields displayed in the
attached SUMMARY_Version_2001
or SUMMARY_Version_2002
tables, and illustrated in the TOP
(right) figure by the normalized linear distribution of journal
ranks. Consequently, the rank scores and the promotion, appointment, and
accreditation thresholds, established in the cites scale, S (q/a), can be roughly converted into the rank scale,
S (r/a), by simply multiplying by the ratio
0.5/AVEJIF.
Obviously,
for the use of the rank scale it is of major importance the proper placement
of journals into various possible disciplines. In the present database
version, as a general rule, each journal has been "optimally assigned" to one
(and only one) discipline, namely to the 1999-ISI discipline in which that
journal has the optimal position, i.e. the highest rank number. Thus, for
instance, the journal Int. J. Mod. Phys. C has the rank r = 0.80
in the discipline Computer Sciences (Interdisciplinary) and the rank r
= 0.40 in the discipline Mathematical Physics. In a similar way, the journal
J. Magn. Magn. Mater. has the rank r = 0.82 in the discipline
Material Sciences and the rank r = 0.57 in the discipline Condensed
Matter Physics. In the previous database version (July 2000), both these
journals were located in the field PHYSICS, namely in the disciplines
Mathematical Physics and Condensed Matter Physics, respectively. In the
present version, however, by virtue of the aforementioned principle of maximal
positioning (ranking) within possible disciplines, the two journals of the
example given above have been assigned to the discipline Computer Applications
of the field COMPUTER SCIENCES, respectively to the discipline Materials of
the field MATERIALS SCIENCES. Thus, it happens that some interdisciplinary
journals rather get out of their "traditional" or "intuitive" discipline and
move into more related ones. The biggest number of disciplines into which ISI
arranged journals in 1999 is 6 (six) as, for instance, the journal
Chem-Biol. Interact., which appears in Chemistry (r = 0.83),
Toxicology (r = 0.82), Chemical Medicine (r = 0.77), Biology
(r = 0.74), Pharmacology and Pharmacy (r = 0.72), and
Biochemistry and Molecular Biology (r = 0.54). According to the rule
adopted here, the journal in this later case has been allotted to the
Chemistry discipline. Perhaps the most useful table needed for further
improvement of discipline definition and journal allocation consists in the
word frequency listing of scientific journal titles. The one corresponding to
the latest records, containing the vocabulary and the occurrence frequency of
(mostly abbreviated) 4196 distinct words used in the titles of 7832 science
journals, can be found in the TXT file: Science_Journal_Titles_Word_Frequency_Version_2002
(65KB).
In order to
meet the increasing needs of journal impact factors for a variety of
purposes, this work stands for a completed and updated continuation of
the previous versions (Popescu, version December 1999, with 2,935 journals;
version July 2000, with 5,762 journals). It represents at this time (of version
2001) a collection of 7,557 journals and their 93,618 annual impact factors from
SCI Journal Citation Reports of general and special interest to
scientists engaged in fundamental, life and engineering sciences, and covering
all available journal impact factors in the window 1974-1999 (excepting the not
edited 1976 year). Thus, the "ever-changing river of journals", has an average
lifetime of [93,618 (years) / 7,557 (journals)] » 12.4
years/journal, i.e. of about one half of the considered effective 25 years of
ISI quotation. The linked SUMMARY_Version_2001
(and, similarly, SUMMARY_Version_2002)
presents the data of the corresponding 12 scientific fields and 107 scientific
disciplines, with their brief definition, the journal number N, the discipline
(field) weighted average journal impact factor (AVEJIF), and the discipline or
field top journal title and its impact factor in 1999 (or in 2000,
respectively). As to the news in the version 2001, compared with previous
versions, these are mainly the domains of MEDICAL SCIENCES (1906 journals) and
AGROSCIENCES (487 journals), so that the present database displays the main
stream of all scientific journals. For convenience, the actual database
will be divided into separate Excel files and links to each of the 12 scientific
fields, as given in the following list. Also the currently updated database
version 2002 is added below, confirming, as expected, the stabilization of the
average impact factors:
Each sheet is self-explanatory, has a heading, a legend, and the same Excel
format, with the following columns, namely: identification number (ID),
DISCIPLINE, journal rank (JRK), abbreviated JOURNAL TITLE,
average journal impact factor (JIF) for the entire time span of ISI
quotation, the corresponding number of years of ISI quotation (YRS), and
the impact factor standard deviation (DEV). The rank JRK of
journals has been established FOR EACH DISCIPLINE SEPARATELY in terms of the
ranking by average journal impact factor JIF.These particularly
important columns JRK and JIF (yellow filled) stand by on the left and right
side, respectively, of the JOURNAL TITLE column. Journal ranking by average
scientometric indicators, such as by the average impact factors in the present
application, could serve for simple uses of extant data in any assessment of
research performance for hiring, promotion, tenure, appointment, accreditation,
and other academic rewards. The TOP FIGURE
summarizes both scientometric evaluation alternatives, i.e. by journal absolute
average impact factor and/or by journal rank within the corresponding
discipline. For link to the corresponding scientometric tables in TXT files
(easy to copy and paste) click on the following addresses:
Science_Journal_Ranking_Version_2001for
7557 journals (285 KB) Science_Journal_Ranking_Version_2002
for 7832 journals (305 KB) As expected, the annual data “shift” of the
considered consecutive years, as measured by the average standard deviation,
ranges within percents, namely of 5.1% for JRK and of 2.6% for JIF. Still lower
becomes this deviation at larger journal set scales (disciplines < fields
< science), such as that of weighted average journal impact factors (AVEJIF)
of disciplines (1.15%) > of fields (1.10%) > of the complete science
journal listing (0.86%), click on SUMMARY_Version_2001_versus_2002
(35 KB).
Generally, the (counted or estimated) citations in the
scientific literature appear to be the most objective measure of any hierarchy
by scientific output. Though far from perfect (see, for instance, a recent
"anti-scientometric" essay [Kutzelnigg, 1998], criticism [Amin and Mabe, 2000;
Adam, 2002], or the sophisticated scientometric algorithm
PRESTìGIXTM), the simple “poor man’s citation indicators”
proposed above enable to examine several key facets of individual and collective
knowledge production. Almost the same results one gets appealing to rather
expensive and time consuming direct citation counts. Actually, a “high
resolution scientometry” becomes nonsensical inasmuch as needs merely consist in
gross definitions of thresholds, classes, and trends.Wondering to which scientometric classes might really belong angry
anti-scientometric people, it would be, however, gratifying if some day
scientists will bear with pride objective cumulative ranks above traditional
scientific ranks and distinctions.
Acknowledgements.
The author gratefully appreciates the interest in this work of
Professor Tibor Braun, Professor Daniel Lavalette, and Professor Mircea Oncescu.
Special thanks are due to Dr. Victor Sofonea for documentation, Mr. Claudiu
Cezar Vasilescu, Dr. Savu-Sorin Ciobanu and Dr. Magdalena Nistor for
computer assistance, and Dr. Andrei Barborica, Dr. Eugen Aldea and Mr. Sorin
Vizireanu for database programs and homepages. The Alexander von
Humboldt-Foundationis gratefully acknowledged for generous
donations of computer facilities.
Isidro F. Aguillo (Editor), Cybermetrics, International Journal
of Scientometrics, Informetrics and Bibliometrics, published by Centro de
Información y Documentación Científica (CINDOC, http://www.cindoc.csic.es/) of
the Consejo Superior de Investigaciones Científicas (CSIC, http://www.csic.es/), Joaquín Costa 22,
28002 Madrid, Spain (isidro@cindoc.csic.es).
Cybermetrics is both an electronic-only journal and a virtual forum
open to worldwide researchers to publish, discuss and disseminate their
findings to a greater audience on the Internet.
T. Braun (Editor-in-Chief),Scientometrics, An International
Journal for all Quantitative Aspects of the Science of Science, Communication
in Science and Science Policy, published by Akadémiai Kiadó, P.O.Box 245,
H-1519 Budapest, Hungary (http://www.akkrt.hu), and Kluwer
Academic Publishers, P.O.Box 17, 3300 AA Dordrecht, The Netherlands (http://www.wkap.nl/). The journal
Scientometrics has been founded in 1979 within the Information Science
and Scientometrics Research Unit (ISSRU) of the Hungarian Academy of
Sciences and awarded the international Derek John de Solla Price medal
for outstanding achievements in scientometrics - so far to the following
scientists: Eugene Garfield (USA 1984); Michael J. Moravcsik (USA 1985); Tibor
Braun (Hungary 1986); Vasiliy V. Nalimov (USSR 1987) and Henry Small (USA
1987); Francis Narin (USA 1988); Bertram C. Brookes (UK 1989) and Jan Vlachý
(Czech Republic 1989); András Schubert (Hungary 1993); Robert K. Merton (USA
1995) and Anthony F.J. van Raan (The Netherlands 1995); Belver C. Griffith
(USA 1997); John Irvine (UK 1997) and Ben R. Martin (UK 1997); Wolfgang
Glänzel (Hungary 1999) and Henk F. Moed (The Netherlands 1999); Leo Egghe
(Belgium 2001) and Ronald Rousseau (Belgium 2001). The founder and director of
ISSRU is Professor Dr. Tibor Braun, Institute for Inorganic and
Analytical Chemistry, L. Eötvös University, P.O. Box 123, 1443 Budapest,
Hungary, E-mail: mailto:h1533bra@ella.hu
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Publication Productivity and Citation Impact (with W. Glänzel and A.
Schubert), World Scientific, Singapore, pp. 346-399 (1985); Relative
Indicators and Relational Charts for Comparative Assessment of Publication
Output and Citation Impact (with A. Schubert), Scientometrics, Vol. 9, Nos
5-6, 281-291 (1986); Against Absolute Methods: Relative Scientometric
Indicators and Relational Charts as Evaluation Tools (with A. Schubert and
W. Glänzel), Handbuch of Quantitative Studies of Science and Technology,
A.F.J. van Raan (editor), Elsevier, North-Holland, pp. 137-176 (1988)
E. Garfield (Editor),Science Citation Index, Journal Citation
Reports: a bibliometric analysis of science journals in the ISI database,
published by the Institute for Scientific Information (ISI, http://www.isinet.com/), 3501 Market Street,
Philadelphia, PA 19104, USA, a worldwide leading provider of information for
researchers. On September 15, 2000, Dr. Eugene Garfield, ISI’s founder
and chairman emeritus, celebrated his 75th birthday at the company’s
headquarters in Philadelphia (The Web of Knowledge, A Festschrift in Honor
of Eugene Garfield, visit http://www.infotoday.com/catalog/asist.htm).
Many of Garfield’s writings can be found at his Web site at http://www.garfield.library.upenn.edu/.
Some are pointed out below. On June 7, 2001, Dr. Henry Small has been
named the Chief Scientist of ISI. Starting with his milestone paper
Co-citation in the scientific literature: A new measure of the relationship
between two documents, J. Am. Soc. Inform. Sci., Vol. 24, 265-269 (1973),
Dr. Small is recognized for his outstanding contributions to co-citation
analyses, citation mapping, and visualization techniques. "It was exciting to
find that co-citation arrayed highly cited documents so cleanly into
specialties, and that, in turn, specialties could join to form a global map"
(1998 ASIS&T Award of Merit to Henry Small: On the Shoulders of
Giants, Bull. Am. Soc. Inform. Sci., Vol. 25, No 2, December/January 1999,
http://www.asis.org/Bulletin/Jan-99/small.html).
Since 1992 ISI is a Thomson Scientific Company, and part of The
Thomson Corporation (visit http://www.thomson.com/), providing
high-quality essential Web-based information products for researchers,
information specialists, and administrators in diverse fields. For more
information about ISI, visit http://www.isinet.com/isi and
particularly the following recent and most popular web-publications and sites:
E. Garfield, Citation Analysis as a Tool in Journal
Evaluation, Science, 178, 471- 479 (1972); Citation Indexing,
Its Theory and Application in Science, Technology, and Humanities, John
Wiley & Sons, New-York (1979); The Impact Factor, Current Contents,
25, 3-7 (June 20, 1994); Using the Impact Factor, Current
Contents, 29, 3-5 (July 18, 1994); Expected Citation Rates,
Half-Life, and Impact Ratios, Current Contents (September 12, 1994);
Research Fronts, Current Contents, 41, 3-7 (October 10,
1994);Scientography: Mapping the Tracks of Science, Current
Contents (November 7, 1994); available also at http://www.isinet.com/
J. S. Katz, Questions of Collaboration (with D. M. Hicks),
Nature, 375, 99 (11 May 1995); Desktop Scientometrics,
Scientometrics, 8 (1) 141-153 (1997); What is Research Collaboration
(with B. R. Martin), Research Policy, 26, 1-18 (1997);
Indicators for Systems of Innovation:A Report on the IDEA
(Indicators and Data for European Analysis) Project (with D. M. Hicks),
IDEA Paper Series, 12, 1-66 (1998); The Self-Similar Science
System, Research Policy, 28, 501-517 (1999); Scale-Independent
Indicators and Research Evaluation, Science and Public Policy (6 March
2000); some available athttp://www.sussex.ac.uk/spru/jskatz;%20http:/www.sol.no/step/IDEA
W. Kutzelnigg, Nachr. Chem. Tech. Lab., 46, 826-831 (1998)
B. Latour, Science in Action, Milton Keynes: Open University
Press (1987)
D. Lavalette, Facteur d’impact: impartialité ou impuissance
?, Internal Report, INSERM U350, Institut Curie - Recherche, Bât. 112,
Centre Universitaire, 91405 Orsay, France (November 1996), http://www.curie.u-psud.fr/U350/
I.-Iovitz Popescu, A Simple Scientometric Assessment of
Individual Contributions in Fundamental Physics, Romanian Reports in
Physics, 46, 899-905 (December 1994); On the Lavalette Ranking
Law (with M. Ganciu, M. C. Penache, and D. Penache), Romanian Reports in
Physics, 49, 3-27 (January 1997); Journal Impact Factors of Interest
to Basic Sciences, Version December 1999, Horia Hulubei Publishing House,
Bucharest (December 1999); Journal Ranking and Average Impact Factors of
Basic and Allied Sciences, Version July 2000, 60 pages, Horia Hulubei
Publishing House, Bucharest (October 2000); Science Journal Ranking and
Average Impact Factors, Version October 2001, Horia Hulubei Publishing
House, Bucharest (pending 2002); for electronic versions 2000 and 2001 see web
sites at URL: http://www.geocities.com/iipopescu;
http://alpha2.infim.ro/~ltpd/iipopescu.html
Romanian Ministry of National Education, Order No. 5103, Appendage
1-II, dated on 05.07.1999
Romanian Ministry of Education and Research, CENAPOSS - an acronym
for the National Center for Science Policy and Scientometry, a departament of
CNCSIS - National Council of Scientific Research in Higher Education,
http://www.cncsis.ro/cenaposs/inform.html%20(1999)
C. Tsallis and M. P. de Albuquerque,Are citations of scientific
papers a case of nonextensivity ?, Eur. Phys. J. B, 13, 777-780
(2000); web site http://tsallis.cat.cbpf.br/biblio.htm
J. S. Katz and L. Katz,Power laws and athletic performance,
J. Sport Sciences, 17, 467-476 (1999)
S. Redner,How popular is your paper ? An empirical study of the
citation distribution, Eur. J. Phys. B, 4, 131-134 (1998)
J. Laherrère and D. Sornette,Stretched exponential
distributions in nature and economy: "fat tails" with characteristic
scales, Eur. J. Phys. B, 2, 525-539 (1998)
G. L. Barenblatt,Scaling, self-similarity, and intermediate
assumptions, Cambridge Univ. Press (1997)
B. B. Mandelbrot,Fractals and scaling in finance:
discontinuity, concentration, risk, Springer Verlag (1997)
M. Buchanan,One law to rule them all, New Scientist
(November 8, 1997)
G. K. Zipf, Human Behavior and the Principle of Least Effort: An
Introduction to Human Ecology, Cambridge, MA, Addison-Wesley (1949); 2nd
edition, New York, Hafner (1965); a comprehensive bibliography on Zipf's Law
has been gathered by W. Li from Rockefeller University at http://linkage.rockefeller.edu/wli/zipf/
The ranking law, established in 1996 by the French
biophysicist Daniel Lavalette (http://www.curie.u-psud.fr/U350/),
states that the impact factor q of a set of N scientific journals,
ordered by the descending ranking number n (a positive integer in the [1,
N] range), obeys the general relationship
q (n)= c [Nn/(N-n+1)]-b
with only two fitting parameters, namely the exponent b and the
scaling constant c = q(1). In other words, the expression proposed by
Lavalette represents a linear function in the double logarithmic log(q), log
[n/(N-n+1)] scale. Offering the promise for various applications and
theoretical investigations, this is barely more complex than the well known
rank-frequency Zipf’s law q = c n-b.
It is important to point out that the independent variable in the Zipf’s law is
the descending ranking number, n, whereas in the Lavalette’s law this is
the ratio n/(N-n+1) between the descending and the ascending ranking
numbers, thus explicitly enclosing the set size number N.
Fig.1.The normalized Lavalette ranking function q/c
= [Nn/(N-n+1)]-b in terms of
the descending ranking number n for typical values of the
parameters N and b.
.
Fig.2. Illustrating the Lavalette ranking law for three
random subsets (1000, 2000, and 4000 journals) excerpted from the present
collection (7557 journals) and ranked by average journal impact factors
(JIF). The journals with JIF = 0 have been excluded.
Fig.3. Illustrating the Lavalette
fitting for 4 random subsets of journals with title initial letter A, B,
C, or D, as excerpted from the present collection (7557 journals) and
ranked by average journal impact factors (JIF).
Fig.4. Ranking of 26 random subsets
of journals with title initial letter belonging to various letters
of the alphabet, as excerpted from the present collection (7557
journals) and ranked by average journal impact factors (JIF). The non
power law shaping is obvious and the fitting pleasure is left to the
reader (power law
means straight line on log-log plot).
Fig.5. Illustrating the Lavalette ranking law for the
present collection (7557 journals) and two disjoint subsets of the fields
of Medicine (1906 journals) and Physics (575 journals) respectively,
ranked by average journal impact factors (JIF). The journals with JIF = 0
have been excluded.
Fig.6. Ranking of 12 natural subsets
of journals belonging to various scientific fields, as excerpted from the
present collection (7557 journals) and ranked by average journal impact
factors (JIF). The non power law shaping is obvious and the fitting
pleasure is left to the reader (power law means straight line
on log-log plot).
Fig.7. Testing of Lavalette’s variable
Nn/(N-n+1) for the average impact factors (JIF) of 7557 journals,
as assigned within 12 scientific fields, shows a systematic departure from
a perfect Lavalette fitting, i.e. from a straight line on a log(JIF),
log [Nn/(N-n+1)] plot.
Fig.8. Illustrating the King’s effect in the
particular case of the Science &
Education field, as revealed by the first
three positions held by Nature (JIF = 15.68), Science (JIF = 14.31),
and P. Natl. Acad. Sci.
USA (JIF = 9.53), in contrast to the field average journal
impact factor amounting only to AVEJIF = 0.88. The matching to the
rest of the sequence can be substantially improved by simply eliminating
the anomalous members.
This is a page of the site:
Prof.
dr. Ioan-Iovitz POPESCU Member of the
Romanian Academy Vita & Opera:
Plasma, Lasers, Scientometrics
Links dedicated to my dearly beloved Denisa
(Daisy): 
