Study of Lotka’s Law and Authorship Pattern in the
Conference Proceedings of COLLNET: an International Conference Covering
Exclusively Bibliometric Study
Maya Verma^{1},*, Pratima
Rajiv^{2}
^{1}School of Studies in Library and Information Science, Pt.
Ravishankar Shukla University, Raipur, C. G. (India)
^{2}Govt. Kavyopadhyay Hiralal College,
Abhanpur, Raipur, C. G. (India)
*Corresponding Author:
verma_maya64@rediffmail.com
[Received: 03 March 2020; Accepted: 18 September
2020; Published Online: 12 February 2021]
Abstract: This paper examines the authorship
pattern of 419 papers contributed to COLLNET Conference proceedings during the
period 20112015. The ranked authors list is prepared to identify the most
prolific authors who contribute significantly to the areas of bibliometric
study. Authorship Pattern is studied to understand collaboration behavior and
it is found that maximum papers are written by multiple authors. The degree of
collaboration is significantly high, which is 0.7852. Lotka’s law was tested
using KolmogorovSmirnov goodness of fit test and it is found that Lotka’s law
is not found fit in the observed distribution of COLLNET Conference Proceedings.
Keywords: Lotka’s Law; Authorship Pattern; Conference Proceedings; Bibliometrics.
Introduction:
Bibliometrics is a type
of research method used by researchers in different subject disciplines.
“Bibliometric techniques are used for a variety of purposes like the
determination of various scientific indicators, the evaluation of scientific
output, the selection of journals for libraries and even for forecasting of
potential Nobel laureates. Bibliometric analysis has become a wellestablished
part of information research. The most obvious use of Bibliometric data is to
improve bibliographic control, as it is not possible to provide efficient
secondary services without knowing the size and characteristics of literature.
Bibliometrics has grown out of the realization that literature is growing and
changing at a rate in which no librarian or information worker equipped with
traditional bibliographic methods and skills could keep abreast. (Zafrunnisha
10).
The two important elements of bibliometric studies are:
I.
Authors Productivity
II.
Citation Analysis
Author’s Productivity:
The author’s productivity study is conducted to identify the noble
laureates of any subject area. Bibliometric tools are used for this purpose.
Lotka’s law of scientific productivity which is a bibliometric law is applied
to the data of the author’s productivity. This helps to identify how many
authors are productive in research publications. This also helps to identify
the key contributors from organizations, states or countries in which data can
be useful in policy formulations, grants distributions, etc.
Citation Analysis:
Citation analysis is mainly conducted to measure the contribution of a
specific work of research to the growth of any discipline of study. It is used
to identify the good papers, standard authors, or journals in a specific field.
Bibliometric laws like Bradford’s law can be applied to the ranked journals to
validate the study.
Literature Review:
Maz Machado, Alexander et
al.(2017)
presents a bibliometric study on the fit of Lotka’s law on Information
Science & Library Science journals indexed in Social Science Citation Index
of Journal Citation Report from the period 1956 to 2014. The parameters of the Lotka's
law model, C and α, were found using the linear least squares method and the
KolmogorovSmirnov test was applied to estimate the kindness of adjustment of
the results to the Lotka’s distribution. It was found that the pattern of
publication of the LIS category articles fits to Lotka’s law.
Suresh Kumar, P.K. (2017) examines authorship pattern of 556 papers published in Journal of Documentation during 2003 to 2015. In addition to the papers, a sample of 1550 references from a population of 15,529 unique references given at the end of the papers was selected using simple random sample method. It was found that almost half of the publications were written by single authors. Lotka’s Law was tested on the resulting 2106 publications using KolmogorovSmrinov goodnessoffit. The KS test and the author productivity graph revealed that Lotka’s law was applicable to the set LIS publications.
Objective of the study:
1. To
study the authorship pattern in the proceedings.
2. To
examine the validity of Lotka’s law.
Hypothesis:
1. The
authorship distribution in the conference proceedings under the studied period
fits to the Lotka’s law.
2. The
single authored papers are lesser then multi authored papers.
Methodology:
The proceedings are
collected from different authors who have contributed their papers in the
conferences during the period of study. The period of study is from
20112015(five years).In the current study all the authors are given equal
credits. Ranking of authors is done using MS Excel. For validating Lotka’s law,
the KolmogorovSmirnov goodnessoffit test is used to compare the function
describing the observed and theoretical distribution of publication at 0.10
level of significance.
Authors Productivity:
Counting authors
productivity is an important aspect of bibliometric study. Various aspects of
contributing authors are considered for analysis like figure out the top
contributing authors in a particular area. The studies like top contributing
authors (authors in any position and only the first author) are also calculated
separately. Authorship pattern is also studied.
Top Contributing
authors:
The objective of
bibliometric study is vast where various calculations are done to reach to a
concrete result. One of the objectives of this study is to identify the most
prolific author’s from the data under study. This identification is hoped to be
useful for the professionals who looks for expert in a specific subject field,
as an expert can only contribute a significant number of articles in an area.
The authors are given equal
credits in spite of their position in writing the paper. The table is prepared
based on the number of papers they have contributed to the conference
proceedings during the period of study.
Table: 1
Name of Ranked Authors (COLLNET) (Author in any position)
Rank

Name of
Author

Number
of Papers

Percentage
of papers

Cum.
Number of Papers

1^{st}

Haiyan Hou

9

2.15

9

2^{nd}

R K Verma

8

1.91

17

2^{nd}

Sudhir Kumar

8

1.91

25

3^{rd}

Grant Lewison

7

1.67

32

3^{rd}

Hildrun Kretschmer

7

1.67

39

4^{th}

Amir Reza Asnafi

6

1.43

45

4^{th}

Arif Riahi

6

1.43

51

4^{th}

Farshid Danesh

6

1.43

57

4^{th}

Maryam Pakdaman Naeini

6

1.43

63

5^{th}

Chen Yue

5

1.19

68

5^{th}

Divya Srivastava

5

1.19

73

5^{th}

Elham Ahmadi

5

1.19

78

5^{th}

JeanCharles Lamirel

5

1.19

83

5^{th}

A.N Libkind

5

1.19

88

5^{th}

Masaki Nishizawa

5

1.19

93

5^{th}

Mohammad Hossein Biglu

5

1.19

98

5^{th}

N K Wadhwa

5

1.19

103

5^{th}

S L Sangam

5

1.19

108

5^{th}

Theo Kretschmer

5

1.19

113

The above table gives
the name of the most prolific authors of COLLNET conference. Dr. Haiyan Hou, Professor, Dalian
University of Technology, is the author who has contributed
maximum articles to COLLNET Conference proceedings with nine papers in a span of
five year. Second rank is held by two authors, Dr R K Verma, Scientist, NISCAIR
and Professor Dr Sudhir Kumar contributed eight papers each and held second
rank in the list. Third rank is held by two authors, Grant Lewison, Senior Research
Fellow, Kings College, and Hildrun Kretschmer, visiting professor with seven
papers each. Here it can be said that these people are experts in the field of
Biliometric study.
Ranking of authors:
A ranked list is
prepared based on the number of papers they have contributed during the period
of study.
Table 2:
Ranking of Authors (COLLNET) (Author in any position)
Rank

Number
of Authors in the Corresponding Rank

Number
of Papers for Corresponding Rank

Percentage
of Author (N=685)

Cum.
Number of Papers

1^{st}

1

9

0.15

9

2^{nd}

2

8

0.29

17

3^{rd}

2

7

0.29

24

4^{th}

4

6

0.58

30

5^{th}

10

5

1.46

35

6^{th}

18

4

2.63

39

7^{th}

42

3

6.13

42

8^{th}

102

2

14.89

44

9^{th}

504

1

73.58

45

Total

685


100


In
the above table, it can be seen that among 685 authors 0.15% author have
contributed maximum papers which is nine, 0.29% author have contributed eight
papers, 0.29% have contributed seven papers each, 0.58% authors have
contributed six papers each, 1.46% have contributed five papers, 2.63% of
authors have contributed four papers. 6.13% authors have contributed three
articles and 14.89% authors have contributed two articles each. 73.58% authors
have a single paper contribution in this specific conference proceeding in the
span of five years.
Authorship
Pattern:
Authorship
pattern is studied to understand the collaboration behavior of the authors as
it has a great impact on research. The authorship pattern is shifting from solo
work to collaborative works now a day. In this study too it is tried to
understand that whether there is any change in the trend or not.
Table
3:
Authorship Pattern
Authorship
Pattern

Number
of Papers (COLLNET)

Percentage
(COLLNET)

Single

90

21.5

Two

170

40.6

Three

90

21.5

Four

48

11.5

Five

12

2.86

Six

5

1.19

Seven

0

0

Eight

2

0.48

Nine

1

0.24

Ten

0

0

Eleven

1

0.24

Grand
Total

419

100

From the above table it can be seen that
two authored papers are higher with 40.6% of the total papers, where as single
authored papers. The percentage of single authored papers and three authored
papers are almost same. It is not commonly seen that more then four authors
write research or it can be said that it is not a common practice. But here it
can be seen that 11.5% papers are written by four authors in collaboration. So
here the hypothesis is proved that ‘The single authored papers are lesser then
multi authored papers.
Degree of Collaboration:
The degree of
collaboration is defined as the ratio of the number of collaborative research
papers to the total number of research papers in the discipline during a
certain period of time. The formula suggested by Subramanyam is used in this
study. It is expressed as where;
C
= N (m)/ (N (m) + N (s))
C
is the degree of collaboration in a discipline.
Nm
is the number of multiauthored research papers in the discipline published
during a year.
Ns is the number of
single authored research papers in the discipline published during a year.
Table: 4 Degree of Collaboration
Authors

Number
of Papers (COLLNET)

Single Author Papers (Ns)

90

Multi Author Papers (Nm)

329

Total (Nm + Ns)

419

Degree of Collaboration Nm/(Nm+Ns)

0.7852

Here it can be seen that the
degree of collaboration is very high.
Author’s productivity
and Application of Lotka’s law:
Alfred James Lotka in
his study emphasise that It stated that “... the number of authors making n
contributions is about 1/of those making
one; and the proportion of all contributors, that make a single contribution,
is about 60 percent”. . Lotka’s Law is often called “inverse square law”
indicating that there is an inverse relation between the number of publications
and the number of authors producing these publications. The generalized form of
Lotka’s Law can be expressed as “”, where y is the number of
authors with x articles, the exponent n and constant c are
parameters to be estimated from a given set of author productivity data.
This paper used the
least square method given by Pao. The n value
is calculated by this method using the following formula:
Here
N= Number of pairs of data
X=
Logarithm of articles(x) and Y=Logarithm of authors (y)
The value of constant C
is calculated using the following formula.
Results
of the Study:
The first step in the
testing of Lotka’s law is to determine the value of n.
Table: 5 Determination of exponent value of ‘n’
Number
of papers

Number
of Authors






X

Y

%
Authors

X=logx

Y=logy

XY

XX

1

663

82.7715

0.0000

2.8215

0.0000

0

2

92

11.4856

0.3010

1.9638

0.5912

0.090619

3

26

3.2459

0.4771

1.4150

0.6751

0.227645

4

11

1.3733

0.6021

1.0414

0.6270

0.362476

5

1

0.1248

0.6990

0.0000

0.0000

0.488559

6

2

0.2497

0.7782

0.3010

0.2342

0.605519

7

2

0.2497

0.8451

0.3010

0.2544

0.714191

8

1

0.1248

0.9031

0.0000

0.0000

0.815572

9

1

0.1248

0.9542

0.0000

0.0000

0.910579

10

1

0.1248

1.0000

0.0000

0.0000

1

11

1

0.1248

1.0414

0.0000

0.0000

1.084499


801

100

7.601156

7.843727

2.3819

6.299658

Table: 6 Computation of ‘c’
X

x^n

1/x^n

1

1

1

2

0.11219121

8.913354612

3

0.03120472

32.04642975

4

0.01258687

79.44789044

5

0.00622404

160.6672346

6

0.0035009

285.6411924

7

0.00215227

464.6252383

8

0.00141214

708.1472206

9

0.00097373

1026.97366

10

0.00069828

1432.084037

11

0.00051689

1934.650475

Summation=

1.17146105

6134.196732

c=1/Sum(1/x^n)


0.000163021

N.B. The fractional part is
ignored

Suitability
of Lotka’s law using KolmogorovSmirnov (KS) Test:
Table:
5.2.5.2.3 Observed & Expected Distribution of Authors (COLLNET)
Number of Papers

Number of
Authors

Observed

Expected


X

Y

% of Authors

Cum.% of Authors

% of Authors

Cum.% of Authors

Difference

1

663

0.8277

0.8277

0.00016302

0.00016302

0.827552

2

92

0.1149

0.9426

0.00145306

0.00161608

0.940956

3

26

0.0325

0.975

0.00522423

0.006840306

0.968191

4

11

0.0137

0.9888

0.01295164

0.019791943

0.968972

5

1

0.0012

0.99

0.02619206

0.045984001

0.944028

6

2

0.0025

0.9925

0.04656538

0.09254938

0.89996

7

2

0.0025

0.995

0.07574345

0.168292832

0.826713

8

1

0.0012

0.9963

0.11544253

0.283735367

0.712519

9

1

0.0012

0.9975

0.16741779

0.451153157

0.54635

10

1

0.0012

0.9988

0.2334591

0.684612255

0.314139

11

1

0.0012

1

0.31538775

1

0

Dmax=

0.968972

n=

2.90141868

c=

0.00016302

Critical value=

1.22/(n+1)^0.5=

0.61765










KolmogorovSmirnov
(KS) goodness of fit Statistics was found at 0.10 level of significance. It
was found that Dmax > Critical value. Thus, null hypothesis is rejected and
it is concluded that the Observed distribution is different from theoretical
distribution predicted by Lotka's law. The law does not fit in the observed
distribution of COLLNET.
Conclusion:
The paper examines the
authorship pattern, Degree of Collaboration and testing of Lotka’s law to the
present dataset. The data is taken from the conference Proceedings of COLLNET
Conference which is an international conference dedicated to Bibliometric, Scientometric
and Webometric study. The authorship pattern in the conference proceeding is
studied and it is found that more authors are preferring to write in
collaboration, than writing independently. Lotka’s law of author productivity
is considered as a classical law of bibliometrics. In this study it is found
that Lotka’s law is not applicable to the current data set.
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