Folie 1

1
Methods of Social Network Analysis explained with
help of Collaboration Networks in COLLNET
Hildrun Kretschmer Department of Library
and Information Science, Humboldt-University of
Berlin, Germany E-mail kretschmer.h_at_onlinehome.d
e
2

• Abstract
• There is a rapid increase of network analysis in
  several scientific disciplines beginning some
  decades ago. The social network analysis (SNA) is
  developed especially in sociology and in social
  psychology in collaboration with mathematics,
  statistics and computer science.
• Social network analysis (SNA) can also be used
  successfully in the information sciences, as well
  as in studies of collaboration in science.
  Several methods of social network analysis will
  be explained with help of collaboration networks
  in COLLNET.

3
The growing importance of collaboration in
research and the still underdeveloped
state-of-the-art of research on collaboration
have encouraged scientists from more than 20
countries to establish in 2000 a global
interdisciplinary research network under the
title Collaboration in Science and in
Technology (COLLNET) with Berlin as its virtual
centre. The intention is to work together in
co-operation both on theoretical and applied
aspects. Since September 2000 seven COLLNET
conferences were organized in six countries. The
8th COLLNET Meeting will be held in March 2007 in
New Delhi, India.
4
Introduction The increase in scientific-technical
collaboration in the course of history has been
vividly documented through a number of analytical
studies. For example, it has been shown that
between 1650 and 1800 not more than 2.2 of
scientific papers were published in
co-authorship. By contrast, the second half of
the 20th century is characterized the world over
by teamwork and co-authorships in the natural
sciences and in medicine, i.e. about 60-70 of
the scientific papers were published during this
period in co-authorship. (DeB. Beaver Rosen
1978 1979a b).
5
(No Transcript)
6
With the importance of collaboration in research
and technology growing world-wide, it has become
necessary to examine the processes involved in
order to become aware of the implications for the
future organization of research as well as those
for science and technology policy. This has led
to an increase in the number of scientific
studies of this topic internationally. (Glanzel
2002, Borgman, C.L. Furner, J. 2002). The
outstanding works of Donald deB. Beaver (1978),
Derek John de Solla Price (1963) and others on
the topic of collaboration in science have, over
a number of years, encouraged a number of
scientists working in the field of quantitative
scientific research to concentrate their research
in this field.
7
This has led both to an increase in the number of
relevant publications concerning this topic in
international magazines, and to an increase in
the number of lectures in international
conferences (Basu 2001, Braun et. al. 2001, Davis
2001, Havemann 2001, Wagner-Döbler 2001, Kundra
Tomov 2001).
8
By all accounts, this field of research is
required to be a comprehensive and diversified
area ranging from small-group research in social
psychology/sociology to large network analyses
conducted into international co-authorship or
citation networks, including the concomitant
observation of informal communication via
interviews or interrogative surveys on
bibliometrical analyses. A common bibliometric
method for measuring the cooperation is the
analysis of co-authorship networks. A suitable
webometric method has to be developed in the
future.
9
There are various references to the positive
effect of "multi-authored papers" in the
co-authorship network for example several
studies show that international cooperation is
linked with a higher citation impact' (Glänzel
2002). The investigation of these processes can
be made by analyses at the micro level
(individuals), at the meso level (institutions)
or at the macro level (countries) (Glänzel
2002). In the field of science studies one most
frequently comes across investigations on
international cooperation in science, followed by
cooperation relationships between institutions.
10
The last few years have seen an ascendancy in how
to treat these international issues. However,
this trend has still failed to provide a concept
on a fundamental and interrelated theory
regarding the theme entitled Collaboration in
science and in technology. The different
approaches taken so far have revealed the
shortcomings of integration. On account of the
diversity of these issues it is possible to
obtain promising results only against the
backdrop of an interdisciplinary approach and
from an intercultural viewpoint. Both aspects
are of basic importance in COLLNET.
11
In summary The rise in collaboration in science
and technology experienced world-wide at national
and international level, has assumed such an
overriding importance that there is now an urgent
need perceptible to study such processes with a
view to acquiring fundamental knowledge for
organizing future research and its application to
science and technology policies.
12
Foundation of COLLNET Therefore in the year 2000
the time had come in the meantime to create a
global interdisciplinary research network COLLNET
on the topic "Collaboration in Science and in
Technology" with 64 members from 20 countries of
all continents. The members intended to work in
cooperation on both theoretical and applied
aspects on the topic "Collaboration in Science
and in Technology". The focus of this group is
to examine the phenomena of collaboration in
science, its effect on productivity, innovation
and quality, and the benefits and outcomes
accruing to individuals, institutions and nations
of collaborative work and co-authorship in
science.
13
Web site
www.collnet.de Journal Journal of Information
Management and Scientometrics (Incorporating the
COLLNET Journal) COLLNET Meetings (2000-2006) -
First COLLNET Meeting, September 2000, Berlin,
Germany - Second COLLNET Meeting, February 2001,
New Delhi, India - Third COLLNET Meeting, July
2001, Sydney, Australia - Fourth COLLNET Meeting,
August 2003, Beijing, China - Fifth COLLNET
Meeting, March 2004, Roorkee, India - Sixth
COLLNET Meeting, July 2005, Stockholm, Sweden -
Seventh COLLNET Meeting, May 2006, Nancy, France
Papers in Co-authorship between COLLNET
Members 223 co-authored papers (lifetime,
starting before official foundation of COLLNET)
14
(No Transcript)
15
The establishment of COLLNET has been reported in
a special issue of the international journal
Scientometrics. In this report, the work of both
the first and second meetings were outlined
(Kretschmer, H., L. Liang and R. Kundra, 2001).
The history and subsequent development of COLLNET
is described in the following sections. The
areas of expertise represented by member
scientists in COLLNET are varied mathematics,
physics, chemistry, biology, medicine, history of
science, social sciences and psychology. The team
includes many senior scientists such as directors
and/or deputy directors of large establishments,
organizers and/or deputy organizers of world
conferences in the field of scientometrics and
informetrics as well as winners of the Derek John
de Solla Price Medal.
16
Among these are board members of the
International Society for Scientometrics and
Informetrics (ISSI), members of the German
Society for Psychology and advisors to the
international journal, Scientometrics. Current
principal investigators, mainly from the field of
quantitative scientific research (scientometrics
and informetrics), engage in teamwork on the
nature, characteristics, growth and policy
relevance of collaboration and co-author
networks. It is proposed to include in future
more experts from other fields of scientific
research and particularly from the social
sciences, such as psychology and sociology.
17
COLLNET has been an important catalyst for
research on collaboration and has provided
opportunities for members to meet face to face at
various international conferences such as at ISSI
conferences (held every two years since 1987).
However, neither of these international
conferences is focussed solely on issues relating
to collaboration or collaborative networks, thus
establishment of COLLNET in 2000 has opened an
important forum in which ideas and work on these
issues is exchanged. Closer personal contact
between members inevitably leads to formal and
informal agreements on collaborative projects on
these crucial issues in research production.
18
Growth of Collaboration/Communication Structures
in COLLNET Since 2000 Two studies are
presented - Development of informal and formal
contacts between COLLNET members -
Development of the co-authorship network
19
Development of Informal and Formal Contacts
Between COLLNET Members The questionnaire
distributed to all of the COLLNET members asked
for the following details - Names of those
COLLNET members with whom informal (loose)
contacts exist in some form (either as e-mail or
exchange of reprints). - Names of those with
whom formal (intensive) contacts exist in the
form of discussions on common projects with
definitive titles or in the form of co-authorship
of joint papers. The development of
collaborative growth within the framework of
COLLNET has been illustrated in Figures 2, 3 and
4.
20
Fig. 2 shows the number of informal (loose)
contacts among the COLLNET-members at the time of
the Second COLLNET Meeting in February 2001.
All the COLLNET members are compiled
country-wise. 16 countries participated in
COLLNET in the month of February. The line
joining the front corner of Fig.2 (1/1) to the
opposite rear corner (16/16) represents the main
diagonal in which the contacts among COLLNET
members of the same country have been plotted. As
seen from Fig. 2, February 2001 witnessed the
maximum number of informal (loose) contacts among
COLLNET members within Germany (1/1) and between
Germany and India (1/2). Informal contacts
between other countries can also be observed.
21
Fig. 3 shows the number of the formal (intensive)
contacts (joint projects or papers with
definitive titles) as on the date of
establishment of COLLNET, viz. 1st January 2000.
22
Fig. 4 shows the increase in these formal
contacts over the one and a half years preceding
the 3rd COLLNET Meeting.
23
Fig. 2 Fig. 3 Fig. 4 It can be seen from
the main diagonal in Fig. 3 that at the time when
COLLNET was established, almost all the formal
(intensive) contacts existed only among members
belonging to the same country of origin.
However, Fig. 4 shows that during the subsequent
period, the intensive contacts had expanded
across the different countries. Fig. 4 resembles
Fig. 2 in the graphical structural representation
of informal (loose) contact.
24
Social Network Analysis (SNA) of COLLNET Sample
Set The bibliographies data of the 64 COLLNET
members were examined, under them - 26 female
and 38 male scientists - 30 members from the
European Union (EU) and 34 from non-European
Union countries (N)
25
From the 34 members from the non-European Union
countries (N) we have - 3 from Australia -
7 from America (4 of them from North America) -
19 from Asia - 4 from Eastern Europe - 1 from
South Africa The last COLLNET data are from
June 2003.
26
Data Assuming that the reflection of
collaboration is not limited to articles in SCI-
or other data bases, a request was made to all
the 64 COLLNET members for their complete
bibliographies, independently of the type of the
publications and independently from the date of
appearance of these publications.
27
From these bibliographies all publications were
selected that appeared in co-authorship
between at least two COLLNET members. Thus, it
concerns 223 bibliographic multi-authored
publications. From this, the respective number
of common publications between two members was
determined as the basis for the analysis of the
co-authorship network (SNA). The co-authorship
network developed according to this method covers
the entire lifetime collaboration between the
COLLNET members.
28
Developmental and structural formation processes
in the bibliographic networks are studied. For
information and brief overview the classification
of the 223 bibliographic multi-authored
publications according to their type is
shown CATEGORIES NUMBER 1. Articles in
Scientometrics 55 2. Articles in
JASIS 13 3. Papers in monographs 68 4.
Papers from conference proceedings 77 5.
Books 10 Total Sum 223
29
Methods (SNA) Otte and Rousseau (2002)
recently showed that social network analysis
(SNA) can be used successfully in the information
sciences, as well as in studies of collaboration
in science. The authors showed interesting
results by the way of an example of the
co-authorship network of those scientists who
work in the area of social network analysis.
Otte and Rousseau refer in their paper to the
variety of the application possibilities of SNA,
as well as to the applicability of SNA to the
analysis of social networks in the Internet
(webometrics, cybermetrics).
30
Introduction to SNA (copied partly from the
paper by Otte and Rousseau, 2002) Network
studies are a topic that has gained increasing
importance in recent years. The fact that the
Internet is one large network is not foreign to
this. Social network theory directly influences
the way researchers nowadays think and formulate
ideas on the Web and other network structures
such as those shown in enterprise interactions.
Even within the field of sociology or social
psychology network studies are becoming
increasingly important. In their article Otte
and Rousseau are going to study social network
analysis and show how this topic may be linked to
the information sciences. It goes without saying
that also Internet studies are to be mentioned,
as the WWW represents a social network of a scale
unprecedented in history.
31
Interest in networks, and in particular in social
network analysis, has only recently bloomed in
sociology and in social psychology. There are,
however, many related disciplines where networks
play an important role. Examples are computer
science and artificial intelligence (neural
networks), recent theories concerning the Web and
free market economy, geography and transport
networks. In informetrics researchers study
citation networks, co-citation networks,
collaboration structures and other forms of
social interaction networks.
32
What is social network analysis? (copied partly
from the paper by Otte and Rousseau,
2002) Social network analysis (SNA), sometimes
also referred to as structural analysis, is not
a formal theory, but rather a broad strategy of
methods for investigating social structures.
The traditional individualistic social theory
and data analysis considers individual actors
making choices without taking the behaviour of
others into consideration. This traditional
individualistic approach ignores the social
context of the actor. One could say that
properties of actors are the prime concern here.
In SNA, however, the relations between actors
become the first priority, and individual
properties are only secondary.
33
Social network analysis conceptualises social
structure as a network with ties connecting
members and focuses on the characteristics of
ties rather than on the characteristics of the
individual members. One distinguishes two main
forms of SNA the ego-network analysis, and the
global network analysis. In ego studies the
network of one person is analysed. An example in
the information sciences is Whites description
of the research network centred on Eugene
Garfield. In global network analyses one tries to
find all relations between the participants in
the network. Growth in the number of published
articles in the field of SNA The Fig. below
clearly shows the fast growth of the field in
recent years. More specifically, the real growth
began around 1981, and there is no sign of
decline.
34
Growth of social network analysis by Otte and
Rousseau
35
Some notions from graph theory (copied partly
from papers by Otte and Rousseau,
2002) Directed and undirected graphs A
directed graph G, in short digraph, consists of
a set of nodes, denoted as N(G), and a set of
links (also called arcs or edges), denoted as
L(G). In this text the words network and
graph are synonymous. In sociological research
nodes are often referred to as actors. A link
e, is an ordered pair (X,Y) representing a
connection from node X to node Y. Node X is
called the initial node of link e, X init(e),
and node Y is called the final node of the link
Y fin(e). If the direction of a link is not
important, or equivalently, if existence of a
link between nodes X and Y necessarily implies
the existence of a link from Y to X we say that
this network is an undirected graph.
36
A path from node X to node Y is a sequence of
distinct links (X, u1), (u1,u2), , (uk,Y).
A B C D The length of this path is the
number of links. The length of the path from A
to D can be 1 or 2 or 3. In this article we only
use undirected graphs. Consequently, the
following definitions are only formulated for
that case. A co-authorship network is an
example of an undirected graph if author A
co-authored an article with author B,
automatically author B co-authored an article
with A. An undirected graph can be represented by
a symmetric matrix M (mXY), where mXY is equal
to 1 if there is an edge between nodes X and Y,
and mXY is zero if there is no direct link
between nodes X and Y.
37
A B C D
Symmetric matrix M (mXY) A B C D A 1 B 1
C 1 D 1
A B C D
Asymmetric matrix M (mXY) A B C D A 1 B 1
C D
38
Components A component of a graph is a subset
with the characteristic that there is a path
between any node and any other one of this
subset. If the whole graph forms one component it
is said to be totally connected. A B C D
E F There are 2 components above. Next we
define some indicators describing the structure
(cohesion) of networks and the role played by
particular nodes. Many more are described in the
literature, but we will restrict ourselves to
these elementary ones.
39
Cliques A clique in a graph is a subgraph in
which any node is directly connected to any other
node of the subgraph Example A B C D
40
Indicators The density of a co-authorship
network (D) is an indicator for the level of
connectedness of this network D Number L of
edges divided by the maximum number Lmax of edges
in the network. It is a relative measure with
values between 0 and 1. LmaxV (V-1)/2 with
Vnumber of nodes D 2L / V(V-1)
D 22 / 430.33
A B C D
41

• In addition, we shall also focus on some selected
  indicators of centrality describing the structure
  of networks and the role played by particular
  nodes (In analogy to Otte and Rousseau 2002,
  Wassermann Faust 1994), Centrality measures
• Degree Centrality
• Closeness
• Betweenness
• Degree Centrality of a node A is equal to the
  number of nodes (or edges) that are adjacent to
  A
• DCAEA

A B C D
DCA3
42
The Degree Centrality of a node A is equal to the
number of his/her collaborators or co-authors. An
actor (node) with a high degree centrality is
active in collaboration. He/she has collaborated
with many scientists. The Degree Centrality in
a V-node network can be standardised by dividing
by V-1 DCAsDCA/(V-1) Example above
DCAs3/31 Mean Degree Centrality (MDC) of the
network is the ratio of the sum of the Degree
Centralities of all the nodes in the network to
the total number of nodes MDC2L/V Example
above MDC23/41.5
43
Closeness Centrality of a node is equal to the
total distance (in the graph) of this node from
all other nodes. CA SYdAY where dAY is the
number of ties in a shortest path from node A to
node Y. A B C D
The length of the path from A to D can be 1 or 2
or 3. dAD1 dAC1 dAB1 CA3
44
Closeness is an inverse measure of centrality in
that a larger value indicates a more central
actor. For this reason the standardised
closenenss is defined as CAs (V-1)/ CA making
it again a direct measure of centrality. CAs
(4-1)/ 31 The Closeness Centrality can be
calculated only in connected graphs or in
connected subgraphs because the shortest path
between two nodes of disconnected graphs is
infinite (8), for example the shortest path
between B and E . A B C D E F
45
Betweenness Centrality BCA is the number of
shortest paths (distance dxy) that pass through
A. Otte and Rousseau mention actors (nodes)
with a high betweenness play the role of
connecting different groups or are middlemen.
Wasserman and Faust (1994, p. 188) mention
Interactions between two nonadjacent actors
might depend on the other actors in the set of
actors who lie on the paths between the two.
These other actors potentially might have
some control over the interactions between the
two nonadjacent actors. A particular other
actor in the middle, the one between the others,
has some control over paths in the network.
46
BCASX,Y GXAY/ GXY GXAY is the number of
shortest paths from node X to node Y passing
through node A. GXY is the number of shortest
paths from node X to node Y (X,Y?A).
A B C D
shortest path from node B to node C dBC1 B to
C GBC1 (not passing through node A), GBAC0
GBAC/ GBC0 B to D dBD2 GBD2 GBAD1
GBAD/
GBD1/20.5 C to D dCD1 GCD1 GCAD0
GCAD/
GCD0 BCA0.5
47
It can be shown that for an V-node network the
maximum value for BCA is (V²-3V2)/2. Hence the
standardised betweenness centrality is BCAs
2 BCA/(V²-3V2) In the example above BCAs
20.5/(42-342)1/60.17
48
Example
BCUSX,Y GXUY/ GXY BCU (a)6 BCU (b)4 BCU
(c)4 BCUs (a)1 BCUs (b)0.67 BCUs
(c)0.67
49
The general formula CNETWORK(SX (Cmax-CX))/max
value possible can be applied for determining
degree, closeness or betweenness centrality for
the whole network. These measures are relative
measures with values between 0 and 1. Example
Group Degree Centralization S vi1 (DCmax -
DCX) GDC ------------------------
(V-1)(V-2) The DCX in the numerator are the V
Degree Centralities of the nodes and DCmax is the
largest observed value. This index reaches its
maximum value of 1 when one actor (node) has
collaborated with all other V-1 actor, and the
other actors interact only with this one, central
actor. This is exactly the case in a star graph.
The index attains its minimum value of 0 when all
degrees are equal
50
A B E C D
S vi1 (DCmax - DCX) GDC -------------------
------- (V-1)(V-2) DCmax DCE4 DCX
DCA DCB DCC DCD1 DCmax DCX4-13 GDC34/
(5-1)(5-2)1
51
Example An SNA co-authorship network (partly
copied from the paper by Otte and Rousseau,
2002) In this section Otte and Rousseau
perform a network analysis of authors in the
field of social network analysis. We will point
out the central players and the underlying
collaborative relationships between authors.
Co-authorship, a (strong) form of
collaboration, is not the only way to describe
relations between scientific authors. Citation
network, for instance, could reveal other
relations, but these are not studied in this
article.
52
In the 1601 articles dealing with SNA there were
133 authors occurring three times or more.
Forming an undirected co-authorship graph (of
these 133 authors) led to a big connected
component of 57 authors, 2 components of 4
authors, 2 components of 3 authors, 7 small
components consisting of two authors and 48
singletons. We will further concentrate on the
central cluster of 57 authors. Most important
scientists in the field belong to this cluster.
Network analysis was performed using UCInet
while the map was drawn with Pajek (Package for
Large Network Analysis). The Fig. below shows
the network of network analysts (central cluster
of 57 authors).
53
The network of network analysts by Otte and
Rousseau
54
Legend 1. D.D. Brewer 16. T.J. Fararo 30. M.S.
Mizruchi 44. M. Spreen 2. E.J. Bienenstock 17. J.
Galaskiewicz 31. D.L. Morgan 45. J. Szmatka 3.
S.D. Berkowitz 18. J.S. Hurlbert 32. C.
McCarthy 46. S.R. Thye 4. M. Gulia 19. C.
Haythornthwaite 33. M. Oliver 47. M.A.J.Van
Duijn 5. P. Bonacich 20. V.A. Haines 34. S.
Potter 48. G.G. Van de Bunt 6. H.R. Bernard 21.
N.P. Hummon 35. B. Potts 49. B. Wellman 7. V.
Batagelj 22. I. Jansson 36. T. Patton 50. C.
Webster 8. K. Carley 23. E.C. Johnsen 37. D.
Ruan 51. S. Wasserman 9. K.E. Campbell 24. D.
Krackhardt 38. J. Skvoretz 52. D. Willer 10. P.
Doreian 25. P.D. Killworth 39. J.W. Salaff 53.
E.P.H. Zeggelink 11. J.S. Erger 26. M.J.
Lovaglia 40. T.A.B. Snijders 54. K.L.
Woodard 12. L.C. Freeman 27. B.A. Lee 41. J.J.
Suitor 55. S.L. Wong 13. K. Faust 28. P.V.
Marsden 42. F.N. Stokman 56. N.S. Wortley 14.
A. Ferligoj 29. B. Markovsky 43. G.A.
Shelley 57. S. Robinson 15. N.E. Friedkin
55
The density for the central network of network
analysts is 0.05. So this network is clearly not
dense at all, but very loose. The author with
the highest degree centrality is Barry Wellman
(University of Toronto), who has a degree
centrality of 9. The degree-centrality of the
whole network is 11, indicating that many
authors are not connected. Another way of
studying centrality is using the closeness
indicator. This indicator is more general than
the previous one, because it takes the structural
position of actors in the whole network into
account. A high closeness for an actor means that
he or she is related to all others through a
small number of paths. The most central author
in this sense is Patrick Doreian (University of
Pittsburgh). The closeness of the whole network
is 14.
56
Betweenness is based on the number of shortest
paths passing through an actor. Actors with a
high betweenness play the role of connecting
different groups, are middlemen and so on.
Again Patrick Doreian has the highest
betweenness. The betweenness of the whole network
is 47. UCInet found 16 cliques, this means 16
subgraphs consisting of three or more nodes. The
largest one consists of 6 authors Bernard,
Johnsen, Killworth, McCarty, Shelley and
Robinson. The second largest one consists of the
five authors Erger, Lovaglia, Markovsky,
Skvoretz and Willer. Bibliometric analysis The
most prolific authors in SNA (highest number of
papers) show also a central role in the SNA
network.
57
Results Collaboration Networks in COLLNET
(partly copied from the paper by Kretschmer, H.
Aguillo, I.) In analogy to the study of the
network of the network analysts by Otte and
Rousseau this paper examined the COLLNET
collaboration network. Additionally, the
development of the bibliographic COLLNET
co-authorship network is examined over a specific
time period. Thus, the social network analysis
(SNA) is applied to structure formation processes
in bibliographic networks. The results of the
Web network (Reflection of the bibliographic
network in the Web) are presented in a separate
paper as well as Gender studies in the
network. First let us have a view at the
collaboration network obtained from the
bibliographies in 2003 including all of the life
time papers.
58
(No Transcript)
59
1. Isidro Aguillo 2. Petra Ahrweiler 3. R.
Ambuja 4. Elise Bassecoulard 5. Aparna Basu
6. Donald deB. Beaver 7. Sujit Bhattacharya 8.
Maria Bordons 9. Martina Brandt 10. Mari Davis
11. Leo C.J. Egghe 12. Isabel Gomez 13.
Ulla Grosse 14. Brij Mohan Gupta 15. Frank
Hartmann 16. Frank Havemann 17. William W.
Hood 18. Margriet Jansz 19. Karisiddappa
20. Sylvan Katz 21. Ved Prakash Kharbanda
22. Hildrun Kretschmer 23. Ramesh Kundra 24.
Loet Leydesdorff 25. Liming Liang 26. Sofía
Liberman 27. Zeyuan Liu 28. Valentina
Markusova 29. Martin Meyer 30. Yoshiko
Okubo 31. Farideh Osareh 32. Koti S. Raghavan
33. Ravichandra Rao 34. Ronald Rousseau 35.
Jane Russell 36. Shivappa Sangam 37. Andrea
Scharnhorst 38. Annedore Schulze 39. Dimiter
Tomov 40. Rainer Voss 41. Caroline Wagner 42.
Roland Wagner-Döbler 43. Yan Wang 44. Vera
Wenzel 45. Concepcion S. Wilson 46. Paul
Wouters 47. Yishan Wu 48. Michel Zitt 49.-64.
are singletons up to June 2003. These 16
singletons are not included in the figure.
60
Bibliographic Co-authorship Network The methods
of social network analysis (SNA) are related to
Wassermann Faust (1994) and to Otte Rousseau
(2002). - There are 64 "nodes" ( 64 COLLNET
members) in the network above (network from
2003) - 48 of these COLLNET members ( 75) have
published in co-authorship at least once with at
least one of the other COLLNET members. That
means, at least 1"edge" is adjacent to each of
these 48 "nodes". - Differently expressed
Between two COLLNET members A and B, there
exists an edge if both have published at least
one publication in co-authorship. The members A
and B are called "pair of collaborators
(A,B). - There are LB63 edges between the nodes
or in other words 63 different pairs of
collaborators respectively.
61
- A path from node X to node Y is a sequence of
distinct edges between pairs of
collaborators (X, A1), (A1, A2), , (Aj,
Y) - The length of the path is equal to the
number of distinct edges. The shortest path
from X to Y is called distance dXY. -
The co-authorship structure of COLLNET is a
"disconnected graph", i.e., there is not a
''path'' between each pair of nodes X and Y.
However the COLLNET members can be divided into
several "connected subsets". A path also exists
between all pairs of nodes in a
"connected subset". The "connected subsets" are
denoted as "components'' or ''cluster".
62

• - However between a pair of nodes from different
  components there exists no path.
• - The COLLNET co-authorship network consists of
  23 components
• 1 large central component of 32 members (57 by
  Otte and Rousseau)
• 1 component of 4 members (2 by O. R.)
• 2 components of 3 members (2 by O. R.)
• 3 components of 2 members (7 by O. R.)
• 16 singletons (48 by O. R.)
• The largest cluster covers 50 of the COLLNET
  members (43 in the network by Otte and
  Rousseau). In addition there are 22 small and
  very small (singletons) clusters (59 by O. R.).
  
• This structure of clusters, which contain a
  single very large cluster and also a large number
  of small clusters, is in agreement with the
  existing findings in the literature (Newman 2001,
  Genest Thibault 2001, Kretschmer 2003, Otte
  Rosseau 2002). It is possible this could denote a
  general rule in a special type of co-authorship
  network (?).

63
The studied bibliographic co-authorship network
in 2003 is a network with low density of DB0.031
(similar to the network of network analysts,
studied by Otte and Rousseau D0.05). However
because of intended development studies the
COLLNET results refer to the whole network but
the results by O. R. to the largest component
only. Therefore, maybe the density value by O.
R. is higher than the other. The indicators
density, mean degree centrality and betweenness
centrality are applied in analyses of the
bibliographic co-authorship network. The general
formula is applied for Betweenness.
Furthermore, the development of number of
edges, number of components, number of singletons
and the size of largest component (number of
nodes in the largest component) are studied
(Table 2).
64

• Development of COLLNET
• Four stages are considered in the development of
  COLLNET
• Until 1997 Collaboration of the future COLLNET
  members before 1998 (preliminary stage)
• Until 1999 Collaboration until 1999 (cumulative,
  including collaboration until 1997, i.e.
  preliminary stage and first step of COLLNET
  development)
• Until 2001 Collaboration until 2001
  (cumulative, including collaboration until 1997,
  i.e. preliminary stage, first and second steps
  of COLLNET development)
• Until 2003 Collaboration until 2003
  (cumulative, including collaboration until 1997,
  i.e. preliminary stage, first, second and third
  steps of COLLNET development)

65
Collaboration until 1997 Collaboration until
1999 Collaboration until 2001
Collaboration until 2003.
66
Table 2 Development of Bibliographic Networks
1997 1999 2001 2003
Number of edges or of pairs of collaborators 16 25 47 63
Number of components 48 44 30 23
Number of singletons 39 36 22 16
Size of largest component 7 11 23 32
Density .008 .012 .023 .031
Mean degree centrality of the network MDC .53 .78 1.47 1.97
Betweenness .008 .028 .101 .22
67
The values of the indicators describing the
structure of networks (density, mean degree
centrality and betweenness) increase from 1997 to
2003 with a particular rise from 1999 to 2001
(cf. Figure). The growth in the number of pairs
of collaborators (edges) is in correspondence
with the growth of density. The probability is
high that both the foundation of COLLNET and
first COLLNET meeting in 2000 maybe the reasons
for this increase.
68

• Structure Formation Process Measured by Entropies
• Whereas the size of the largest component grows,
  the number of components and the number of
  singletons diminish (cf. Table 2). This kind of
  structure formation processes in both the
  bibliographic and the Web networks can be
  measured by entropies H
• There is a series of numbers Kf(f1,2,z), Kf ?0
• z
• h f Kf / S Kf
• f1
• z
• H - S hf lg2hf
• f1
• Kf is the size of a component f. The number of
  components in the network is called z.

69
(No Transcript)
70

• The structure formation process is characterized
  by the growth of the number of edges (pairs of
  collaborators), the decreasing number of
  clusters, the growth of the large cluster and the
  decreasing number of singletons (Table 2).
• The entropy H is decreasing with increasing size
  of the components and with decreasing number of
  components.
• The maximum entropy H is reached in a network
  under the condition there are singletons only.
  The minimum entropy is reached under the
  condition where there is one large cluster only
  and there are not any other components.
• The structure formation processes in the
  bibliographic network is shown in the figure
  above.

71
Some Details of the Development of COLLNET
Networks First step of the development of
COLLNET (1998-1999) An important trigger to the
creation of COLLNET was the first Berlin Workshop
on Scientometrics and Informetrics/Collaboration
in Science, Berlin, August 1998. This workshop
was organized by the Association of Science
Studies (Gesellschaft fuer Wissenschaftsforschung
e.V., Berlin), and supported by the Free
University Berlin, and DFG.
72
Second step (2000-2001) Two years later in
September 2000, in conjunction with the Second
Berlin Workshop on Scientometrics and
Informetrics/Collaboration in Science and in
Technology, the first COLLNET meeting was held at
the Free University Berlin. From this time on,
COLLNET meetings have been regularly held
regularly the Second COLLNET Meeting at the
National Institute of Science, Technology and
Development Studies (NISTADS) in February 2001 in
New Delhi (India). Again, COLLNET used the
synergy of conjoint activity with the
International Workshop on Emerging Trends in
Science and in Technology Indicators Aspects of
Collaboration. A third COLLNET Meeting took
place in July 2001 in Sydney (Australia) in
conjunction with the 8th International Conference
on Scientometrics and Informetrics.
73
Third step (2002-2003) Future strategies were
discussed at the 4th COLLNET Meeting which took
place on Agust 29th, 2003, in Beijing in
conjucntion with the 9th ISSI Conference (ISSI -
International Society for Scientometrics and
Informetrics). At this time, further measures of
the effectiveness of collaborative engagements
among members and productivity in the field of
collaboration in science and in technology were
discussed. Thus, these 3 steps, along with the
additional inclusion of the preliminary stage,
will be incorporated to show the development of
the bibliographic COLLNET co-authorship network
in 4 stages
74

• Four stages derived from the 3 steps
• Until 1997 Collaboration of the future COLLNET
  members before 1998 (preliminary stage)
• Until 1999 Collaboration until 1999 (cumulative,
  including collaboration until 1997, i.e.
  preliminary stage and first step of COLLNET
  development)
• Until 2001 Collaboration until 2001
  (cumulative, including collaboration until 1997,
  i.e. preliminary stage, first and second steps
  of COLLNET development)
• Until 2003 Collaboration until 2003
  (cumulative, including collaboration until 1997,
  i.e. preliminary stage, first, second and third
  steps of COLLNET development)

75
References Balaban, A. T. Klein, D. J. (2002).
Co-authorship, rational Erdös numbers, and
resistance distances in graphs, Scientometrics,
55, 59-70 Basu, A. R. Aggarwal (2001).
International collaboration in science in India
and its impact on international performance,
Scientometrics, 52, 379-394 Batagelj, V.,
Ferligoj, A., and Doreian, P. (1992). Direct and
indirect methods for structural equivalence,
Social Networks, 14, 63-90 Beaver, D. deB.
Rosen, R. (1978). Studies in Scientific
Collaboration. Part III. Professionalization and
the Natural History of Modern Scientific
Co-Authorship. Scientometrics, 3, 231-245
Borgman, C. L., Furner, J. (2002). Scholarly
communication and bibliometrics. In B. Cronin
(Ed.), Annual review of information science and
technology Vol. 36 (pp. 3-72). Medford, NJ
Information Today. Braun, T., Glänzel, W.
Schubert, A. (2001). Publication and cooperation
patterns of the authors of neuroscience journals.
Scientometrics, 51, 499-510
76
Davis, M. C.S. Wilson (2002), Elite researchers
in ophthalmology Aspects of publishing
strategies, collaboration and multi-disciplinarity
. Scientometrics, 52, 395-410 Glänzel, W.
(2002).Coauthorship patterns and trends in the
sciences (1980-1998) A bibliometric study with
implications for database indexing and search
strategies. Library Trends, 50, 461-473 Genest,
C. Thibault, C. (2001). Investigating the
concentration within a research community using
joint publications and co-authorship via
intermediaries. Scientometrics, 51, 429-440
Havemann, F. (2001) Collaboration behaviour of
Berlin life science researchers in the last two
decades of the twentieth century as reflected in
the Science Citation Index, Scientometrics, 52,
435-444 Herring, S. C. (2002). Computer-Mediated
Communication on the Internet. In Cronin, B.
(ed.), Annual Review of Information Science and
Technology 36, Medford, NJ Information Today
Inc., pp. 109-168. Ingwersen, P. (1998). The
calculation of Web Impact Factors. Journal of
Documentation, 54(2), 236-243.
77
Kling, R. McKim, G. (2000). Not Just a Matter
of Time Field Differences in the Shaping of
Electronic Media in Supporting Scientific
Communication. Journal of the American Society
for Information Science, 51(14),
1306-1320. Kretschmer, H., L. Liang R. Kundra
(2001) Foundation of a global interdisciplinary
research network (COLLNET) with Berlin as the
virtual center, Scientometrics, 52,
531-538 Kretschmer, H. M. Thelwall (2004)
From Librametry to Webometrics. Journal of
Information Management and Scientometrics. Vol.
1, No. 1, (2004), 1-7 Kretschmer.H. (2004).
Author productivity and Erdös distances in
co-authorship and in Web networks.
Scientometrics. Vol.60, No.3, 409-420
78
Kundra, R. D. Tomov (2001), Collaboration
patterns in Indian and Bulgarian epidemiology of
neoplasms in Medline for 1966-1999 Newman, M.
(2001). The structure of scientific collaboration
networks. Proc. Natl. Sci. USA, 98,
404-409 Otte, E. Rousseau, R. (2002). Social
network analysis a powerful strategy, also for
the information sciences. Journal of Information
Science, 28, 443-455 Price, D.J. de Solla.
(1963). Little Science, Big Science. New York
Columbia University Press. (dt.1974. Little
Science, Big Science. Von der Studierstube zur
Großforschung. Frankfurt am Main Suhrkamp
Verlag Schubert, A. (2002)The Web of
Scientometrics. A statistical overview of the
first 50 volumes of the journal. Scientometrics,
53, 3-20 Terveen, L.G and Hill, W.C. Evaluating
Emergent Collaboration on the Web, in Proceedings
of CSCW 1998 (Seattle WA, November 1998), ACM
Press, 355-362.
79
Thelwall, M. (2003). What is the link doing here?
Beginning a fine-grained process of identifying
reasons for academic hyperlink creation.
Information Research, 8, Vaughan, L. and Shaw,
D. (2003) Bibliographic and Web Citations What
Is the Difference? Journal of the American
Society for Information Science and Technology,
54(14), 1313-1322. Wagner-Dobler, R. (2001),
Continuity and discontinuity of collaboration
behaviour since 1800- from a bibliometric point
of view, Scientometrics, 52, 503-518 Wasserman,
S. Faust, K. (1994). Social network analysis.
Methods and applications. Cambridge Cambridge
University Press 1994 Wilkinson, D., Harries,
G., Thelwall, M. Price, L. (2003). Motivation
for academic web site interlinking evidence for
the web as a novel source of information on
informal scholarly communication. Journal of
Information Science, 29, 59-66
80
Thank You!