Bibliometrics is the application of mathematics and statistics to books and communication media. It includes scientometrics, infometrics, and webometrics. Some key concepts in bibliometrics include Lotka's law, Bradford's law, and Zipf's law, which describe patterns in author productivity and journal usage. Bibliometric indicators like impact factor are used to analyze research contributions and citations. Co-citation analysis examines which articles are cited together to determine related topics. In summary, bibliometrics applies quantitative analysis to provide insight into properties of information objects and scholarly research trends.

1. BIBLIOMETRICS
S.M. Zabed Ahmed
University of Dhaka

2. What is bibliometrics?
Alan Pritchard coined the term bibliometrics as
“the application of mathematics and statistical
methods to books and other media of
communication.”
Journal of Documentation (1969) 25(4):348-349

3. Other metrics
Also used to study broader than books, articles
…
 Scientometrics
 covering science in general, not just publications
 Infometrics
 all information objects
 Webometrics or cybermetrics
 using bibliometric techniques to study the relationship or
properties of different sites on the web

4. Examples of laws and methods
 Lotka’s law
 Bradford’s law
 Zipf’s law
 Price square root law
 80/20 rules
 Impact factor
 Citation structures
 Co-citation structures

5. Lotka’s law
Lotka stated that “. . . the number (of authors)
making n contributions is about 1/n² of those
making one; and the proportion of all
contributors, that make a single contribution, is
about 60 percent” (Lotka, 1926). This means
that out of all the authors in a given subject,
about 60% produce only one article, 15% (1/2²
times .60) produce two articles, 7% (1/3² times
.60) produce three articles, and so on.

6. Lotka’s law: xn•y = C
The total number of authors y in a given subject,
each producing x publications, is inversely
proportional to some exponential function n of x.
 Where:
x = number of publications
y = no. of authors credited with x
publications
n = constant (equals 2 for scientific
subjects)
C = constant
 inverse square law of scientific productivity

7. Example

8. Example (contd.)

9. Bradford’s law
“If scientific journals are arranged in order of
decreasing productivity of articles on a given
subject, they may be divided into a nucleus
of periodicals more particularly devoted to
the subject and several groups or zones
containing the same number of articles as the
nucleus, when the numbers of periodicals in
the nucleus and succeeding zones will be as
1 : n : n2 …”

10. Bradford formulated his law after studying a
bibliography of geophysics, covering 326
journals in the field. He discovered that
9 journals contained 429 articles,
59 contained 499 articles,
and 258 contained 404 articles.
So it took 9 journals to contribute one-third of
the articles, 5 times 9, or 45, to produce the
next third, and 5 times 5 times 9, or 225, to
produce the last third.

11. Bradford's Law of scattering –
an idealized example
No. of
source journals
1
2
1
2
2
4
10
7
5
5
No. of articles
per source
60
35
30
25
9
8
6
5
4
3
Total no. of
articles
60
70
30
50
18
32
60
35
20
15
9
27
130
130
130
3

12. Bradford's Law of Scattering – zones
3 sources
130 articles
9 sources
130 articles
27 sources
130 articles
nucleus

13. Zipf’s law: r • f = c
Zipf stated that the rank of the word multiplied by
the frequency of the word equals a constant
(Potter 1988).
r =rank (in terms of frequency)
f =frequency (no. of times the given word is used
in the text)
c=constant for the given text
 Works well for high frequency words, not so
well for low ranked words.

14. Zipf illustrated his law with an analysis of
James Joyce's Ulysses. “He showed that
the 10th most frequent word occurred
2,653 times, the 100th most frequent
word occurred 265 times, the 200th word
occurred 133 times, and so on.

15. Price square root law
Price (1963) observed that half of the
published research output in any subject
field is contributed by a most productive
subset of authors approximately equal to
the square root of the total number of
authors publishing in that field.

16. 80/20 Rule
80/20 rule states that 80% of the total
research contributions in any subject are
accounted for approximately 20% of the
most productive authors (Burrell,1985;
PAO, 1986).

17. Collaborative authorship
Collaboration is determined by the following
formula (Subramanyam, 1983):
C = Nm/(Nm + Ns)
where,
C = degree of collaboration in a subject;
Nm = number of multiple-authored papers
published during a period of time;
Ns = number of single-authored research papers
published during the same period.

18. Impact factor (IF)
In a given year, the impact factor of a journal
is the average number of citations to those
papers that were published during the two
preceding years.

19. Example:
The 2003 impact factor of a journal would be calculated
as follows:
 A = the number of times articles published in 2001 and 2002
were cited by indexed journals during 2003
 B = the total number of "citable items" published in 2001 and
2002. ("Citable items" are usually articles, reviews,
proceedings, or notes; not editorials or Letters-to-the-Editor.)
 2003 impact factor = A/B
 (Note that 2003 impact factors are actually published
in 2004; it cannot be calculated until all of the 2003
publications had been received by the indexing
agency.)

20. cited
article
Citation matrix
cited
article
cited
article
article
citing
article
citing
article
citing
article
citing
article
citing
article
citing
article
citing
article

21. cited
article
Science Citation Index
cited
article
cited
article
article
citing
article
citing
article
citing
article
citing
article
citing
article
citing
article
citing
article
Association-of-ideas index

22. Co-citation analysis
Articles that cite the same article are likely to both
be of interest to the reader of the cited article
article
citing
article
citing
article
These two
articles are
likely to be
related

23. Conclusion
 Bibliometrics and related scientometrics,
infometrics, webmetrics provide insight
into a number of properties of
information objects
 some general, predictive “laws” formulated
 structures have been exposed, graphed
 myriad data collected and analyzed
 An interesting area of research!