Comparative Analysis of Co-authorship Networks Considering
Authors' Roles in Collaboration: Differences between the Theoreticaland Application Areas
Fuyuki Yoshikane*, Takayuki Nozawa* and Keita Tsuji***fuyuki@niad.ac.jp, nozawa@niad.ac.jp
Faculty of University Evaluation and Research, National Institution for Academic Degrees and University
Evaluation, 1-29-1 Gakuen-nishimachi, Kodaira, Tokyo 187-8587 (Japan)**keita@nii.ac.jp
National Institute for Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo 101-8430 (Japan)

Abstract
Many studies have analyzed "direct" partnerships in co-authorship networks. One the other
hand, the whole network structure, including "indirect" links between researchers, has notbeen sufficiently studied yet. This study aims at deriving knowledge about the communication
structures regarding production of papers by analyzing the researchers' activities fromdifferent viewpoints considering roles in co-authorship networks. In this study, we compare
the co-authorship networks between the theoretical and application areas in computer science.
By applying the modified HITS algorithm to the co-authorship networks, we analyze for eachresearcher in the co-authorship networks (1) the degree of importance as the leader and (2)that as the follower. We further examine the correlation between these two viewpoints. This
study has shown that the negative correlation between (1) and (2) is greater in the application
area. It suggests that, in computer science, the two roles (i.e., the leader and the follower) are
more clearly separated from each other in the application area than in the theoretical area.
Introduction
In academic research, it is exceedingly rare that a researcher produces outcomes with noconnection to the context of the research community. New findings are usually derived fromthe context of the research community, that is, from the accumulation of preceding researches
or cooperative relationships in the research domain. Therefore, when we analyze the activityof the researchers in some domain for the purpose of grasping the characteristics of thatdomain in producing knowledge, we must not only evaluate each researcher's activity
individually, but also take into consideration his/her position in the structure of some kind of
intellectual tie.
In recent years, certain factors, such as the specialization of researchers and the growth ofinterdisciplinary fields, have caused researchers to collaborate (Sacco & Milana, 1984;
Muñoz & Moore, 1985; Cason, 1992; Andersson & Persson, 1993; Bird, 1997; Bordons &Gómez, 2000). Now, collaborating with colleagues (i.e., synchronic networking), as well as
citing preceding researchers' outcomes (i.e., diachronic networking), is very important inresearch activities. There are a large number of studies which deal with collaboration(co-authorship) networks. Most of those chiefly analyzed "direct" partnerships incollaboration networks. For example, many studies examined how researchers' attributions,such as productivity, status and gender, influence their preferences in choosing collaboration
partners (e.g., Kretschmer, 1994; 1997; Bahr & Zemon, 2000; Yoshikane & Kageura, 2004).
One the other hand, some studies examined the whole structure of the collaboration network(e.g., Kretschmer, 2004). However, the whole network structure, including "indirect" links

between researchers who are not each other's partners but have common partners, has notbeen sufficiently studied yet. By analyzing the researchers' activities from different
viewpoints considering roles in collaboration networks, this study aims at deriving knowledge
about the communication structures of research communities.
The idea that the researchers' activities should be understood in the context of the researchcommunity is also regarded as important in research evaluation. For instance, the National
Institution for Academic Degrees and University Evaluation, Japan (NIAD-UE) adopts
research collaboration and cooperation as an important viewpoint in evaluating research
activities (NIAD-UE, 2003). Research activities must be evaluated from various viewpoints,
including the roles in collaboration networks, and different viewpoints may yield different
results in research evaluation. In this study, we examine the correlation between measurescorresponding to some viewpoints in research evaluation, and show that those measures are
not necessarily positively correlated.
For this purpose, this study analyzes co-authorship networks of two different domains.
Cooperative relationships in research activities are not observed only in authorship credits ofcoauthored papers. Some of them are observed in acknowledgments of papers and not in
co-authorship credits. However, we assume that co-authorship credits cover all collaboratorsthat "substantially and technically" contribute to their coauthored papers while
acknowledgments are addressed only to subsidiary supporters1. So this study measures theactivity of research collaboration by analyzing co-authorship networks observed in publishedpapers.
There is another problem concerning co-authorship, that is, honorific authorship, by which
co-authorship credits are sometimes regarded to be irresponsible (Cason, 1992). Althoughmany studies have pointed out the problem of honorary coauthors that have no substantial
contribution to the work, ethical guidelines regarding authorship issues have been laid down
in recent years in each domain (e.g., ICMJE, 1997). Those guidelines state that authorshipcredits should be determined by substantial and technical contributions to the work. Somequestionnaire surveys illustrate that the majority of researchers reached a consensus following
those guidelines (Hoen, Walvoort & Overbeke, 1998; Bartle, Fink & Hayes, 2000). Taking
into account this situation, we reasonably assume that co-authorship credits represent thesubstantial and technical contributions.
The target domains whose networks are compared in this study are two subdomains incomputer science. There are two reasons why we chose computer science. One is that
researchers in this domain perform research collaboration very actively. Hence, the analysis of
their collaboration networks is deemed to be very important. The other reason is that, as not
only the theoretical research area but also the interdisciplinary application area is flourishingin this domain, it is expected that we will obtain useful knowledge about the correlation
between the collaboration tendency and research style from the differences between thetheoretical and application areas.
This paper is organized as follows. First we explain the source data used in the analysis, andthen, after narrating our viewpoints and methodology, we display the results of ourexperiments comparing the co-authorship networks of the two subdomains in computer1

For instance, Cronin, Shaw & Barre (2003) analyzed the acknowledgments of papers in psychology andphilosophy, and showed that the acknowledgments are used for signifying subsidiary support rather thansubstantial and technical collaboration.

science. Lastly, based on these results, we sum up the characteristics of each subdomain.
Data
The data used for observing co-authorship networks were extracted from SCI (Science
Citation Index) CD-ROM version, provided by Thomson ISI. From the database, we extracted
the records of papers published between 1999 and 2003. SCI is one of the mostcomprehensive bibliographic databases in natural sciences, though the journals contained in it
are, for the most part, English-language ones. Besides, SCI selects only core journals thatsatisfy the qualitative criteria2. We therefore chose SCI as the source data in this study. SCI
covers not only original papers but also various types of documents such as reviews, letters,
and so on. As mentioned in the previous section, our interest is in the network structures ofsubstantial and technical collaboration. Thus, as the target of observation, we extracted only
original papers3, which are considered to most directly reflect the structures of substantial andtechnical collaboration.
This study adopted the category classification of "List of source publications: arranged bysubject category" in SCI. According to it, we selected the core journals to be analyzed for eachof the two target domains, "the theoretical area in computer science" and "the application area
in computer science". Henceforth for succinctness, we call them "the theoretical area" and"the application area", respectively. From the database, we extracted the bibliographic data of
the papers of the journals included in the two categories, "computer science, theory &methods" and "computer science, interdisciplinary applications", as the data of the theoreticaland application areas. 21 journals (e.g., Journal of Algorithms) were extracted for thetheoretical area, and 22 journals (e.g., Computer Applications in the Biosciences) wereextracted for the application area. In this study, on the basis of the category of the journal
where the researcher's papers appear, the researcher is connected to the domain. That is to say,all authors whose papers appear in the journals classified to "computer science, theory &methods (or interdisciplinary applications)" in SCI are regarded to belong to the theoreticalarea (or the application area).

Table 1. The basic quantities of the data for the two domains.

Theoretical area
Application area

NJ
21
22

NP
9663
11584

TA
22485
32341

DA
14525
21801

Aav
2.33
2.79

Pav
1.55
1.48

Table 1 shows the basic quantities of data in each of the theoretical and application areas.
There is not much of a difference between them in the number of journals NJ, the number of
papers NP, the average number of authors per paper Aav (= TA/NP), and the average numberof papers per author Pav (= TA/DA). With regard to the number of authors, the application area
is about one and half times larger than the theoretical area, both in the total number of author
tokens TA and in the number of different authors DA. As far as judging from the data, we can2

On the basis of peer review and citation analysis, the quality of researches is evaluated. Not only the quality of
researches but also the international and geographic diversity among authors of papers included in the journal istaken into consideration (Testa, 2004).
3
We extracted records whose "document type" fields are "article". SCI includes "meeting-abstract", "letter","review", "software-review", "biographical-item", "editorial-material", etc., besides "article".

state that, in computer science, the application area consists of more researchers than thetheoretical area.
Methodology
Viewpoints
This study analyzes the researchers' activity of producing papers from two viewpoints, (1) the
degree of importance as the first author and (2) that as the coauthor, excluding the first author,
in co-authorship networks. We differentiate between these two viewpoints, on the basis of theassumption that the first author designs the whole research as the leader and plays the specialrole, which is different from other coauthors' roles. In some domains, such criteria are
specified in guidelines, and we also see this in the results of awareness surveys (e.g.,
Bridgwater, Bornstein & Walkenbach, 1981). Thus, we can regard this assumption to bereasonable, at least to some extent. This study analyzes the two viewpoints, (1) and (2), on thebasis of the idea that both the roles, as a leader in producing papers and as a follower
collaborating with the leader, are important in the network of research collaboration, and thatthese two roles are essentially different.

Figure 1: An example of a co-authorship network

We assume the following model, for setting the operational definitions and measures of theabove two viewpoints.
zzAssuming directed graphs where the ties (links) are oriented from coauthors to the firstauthor for each paper (see Figure 1).
Assuming weighted graphs where the strength of co-authorship relations is taken into
account.

Many indices have been proposed for measuring the strength of co-authorship relations (e.g.,
Narin, Stevens & Whitlow, 1991; Arunachalam, Srinivasan & Raman, 1994). This study uses
the coauthoring frequency itself as the weight of ties in graphs simply, on the basis of theassumption that the strength of co-authorship relations between a pair of researchers grows inproportion to the number of times they have published co-authored papers. By applying the
HITS algorithm, which will be introduced in the next section, to the above-mentioned
weighted directed graphs, we calculate the degree of importance for each node (researcher) in
consideration of the global structures of networks.

The modified HITS algorithm
In this study, we calculate the degree of importance of each researcher in the network of
research collaboration, giving attention to the number of collaborating partners, therelationship strength with each partner, and moreover the degree of importance of each partner.
The degree of importance as the leader Cl(ni) and that as the follower Cf(ni) are obtained foreach researcher ni by the following formulas, respectively.

g

Cl (ni ) = ∑ ajiCf (nj )

(1)

j =1
g

Cf (ni ) = ∑ aijCl (nj )

(2)

j =1

where g represents the number of nodes in the network, that is, the number of researchers in
the domain. aij represents the value in cell (i, j) of the adjacency matrix A of the co-authorshipnetwork, and is equal to the relationship strength of the tie oriented from nj to ni, that is, thenumber of coauthored papers where ni is the first author and nj is his coauthor. (The value of
diagonal cells aii is 0.)
Here, we assume the mutual dependency that "a researcher who assists important leaders
plays an important role as the follower, and a researcher who organizes important followers
plays an important role as the leader". In the formulas (1) and (2), by repeating recursive
substitution, the global structure of the co-authorship network is reflected in the degree ofimportance of each researcher. This recursive substitution results in solving the eigenvector
problem of the adjacency matrix A.
The common idea that ties with more important nodes contribute to the degree of importancemore than those with less important ones is shared among the centrality measure of Bonacich(1987), the PageRank algorithm (Brin & Page, 1998), and the HITS (Hyperlink-Induced
Topic Search) algorithm (Kleinberg, 1998)4. Among the three, the HITS algorithm is mostsimilar to the measures used in this study, in that both of these assume two different rolesconsidering the direction of relationships. In this study, in addition to the direction ofrelationships, the strength (weight) of relationships is reflected in the calculation of themeasures. The co-authorship networks to be analyzed in this study have so many nodes(researchers) that it is hardly able to solve the eigenvector equations of their adjacency
matrices. Thus, we calculate Cl(ni) and Cf(ni) by recursively repeating substitution andnormalization of vectors in the same manner as the HITS algorithm5.
Results
For each of the application and theoretical areas in computer science, the degree ofimportance as the leader Cl(ni) and the degree of importance as the follower Cf(ni) arecalculated for each researcher. The correlation between these two types of importancemeasures is shown in Table 2. In this study, we used the Spearman's rank correlation
coefficient rs, because both of the two measures do not follow the normal distribution and
45

The HITS and PageRank algorithms were devised for the scoring of results of web page searches.
Substitution and normalization are repeated 10 times.

these are not expected to be linearly associated with each other. In addition to the correlation
coefficient, Table 2 shows the average values of the degree (outdegree or indegree) per node
Dav in those co-authorship networks.
Table 2. The co-authorship network properties for the two domains.

Theoretical area
Application area

Dav
1.60
1.72

rs
-0.438-0.488The average value of the degree per node represents how many leaders or followers a
researcher is linked with on average. In the average value of the degree per node Dav, as wellas in the average number of authors per paper Aav shown in Table 1, the application area isslightly higher than the theoretical area. It suggests that researchers in the application area
have more cooperative relationships than do those in the theoretical area. A negative
correlation between the two importance measures, Cl(ni) and Cf(ni), is observed, both in thetheoretical and application areas. That is to say, there is a tendency that the roles as the leader
and as the follower are played by different researchers rather than that the same researcher
plays both of these two roles. As the negative correlation is greater in the application area, it issuggested that the two roles are separated from each other in the application area more clearly
than in the theoretical area. A possible reason for this is that, in application area, there are
more "peripheral" researchers whose main fields are the targets of application (chemistry,
medicine, geoscience and so on) rather than computer science itself. They might collaborate
only as followers.
Tables 3 and 4 show the characteristics of researchers ranked as the most important leaders
and the most important followers. Din and Dout represent the indegree and the outdegree of
each node (researcher). While P represents the number of published papers of each researcher,Psin, P1, P2-, and Plast represent the number of his single-authored papers, the number ofmultiple-authored papers where he is the first author, the number of multiple-authored papers
where he is not the first author but a coauthor, and the number of multiple-authored papers
where his name is listed last, respectively. There is no researcher that is listed in the top ten as
both the leader and the follower, except two researchers (a researcher in the theoretical area
who is ranked as the third most important leader and the second most important follower, anda researcher in the application area who is ranked as the tenth most important leader and theninth most important follower).
The modified HITS algorithm used in this study calculates scores on the basis of the positionin collaboration networks. By this algorithm, we aim to measure not researchers' productivity
but the degree of importance in collaboration networks. So, it assigns high scores toresearchers who occupy important positions with linkages to important researchers, whether
they themselves publish many papers or not6.

6

However, some extreme instances are observed in Table 3. That is, two researchers with only one paper are
ranked as the most important leaders. It might be necessary for more reasonable scoring scheme to refine themethod of weighting.

Table 3. The characteristics of researchers ranked as the most important leaders.

Rank
1
2
3
4
5
6
7
8
9
10

Din
41
6
18
1
5
3
21
8
2
2

Theoretical area
Dout P Psin P1 P21 20
1 18
1
2 12
1 8
3
1 13
0 9
4
0 3
1 2
0
5 7
0 2
5
0 2
0 2
0
0 9
0 9
0
1 10
0 9
1
1 2
0 1
1
2 3
0 1
2

Plast
1
1
0
0
1
0
0
0
0
1

Din
69
20
5
6
2
12
3
3
3
3

Application area
Dout P Psin P1 P20 2
0 2
0
2 14
0 12
2
2 16
1 9
6
2 18
0 8 10
0 1
0 1
0
8 33
0 23 10
2 10
0 4
6
0 2
0 2
0
0 1
0 1
0
1 3
0 1
2

Plast
0
1
0
0
0
9
0
0
0
0

A major difference between the theoretical and application areas is observed in thecharacteristics of followers (see Table 4). In the theoretical area, there are researchers who not
only often collaborate as the follower with a few specific leaders (i.e., Dout is not zero but verysmall, and P2- is large), but also publish coauthored papers as the leader actively (i.e., P1 islarge). The second most important follower mentioned above is a typical example of this type.
On the other hand, there is another type of important follower in the theoretical area. This
type of follower collaborates with various leaders (i.e., Dout is large) as the supervisor (i.e.,
Plast/P is large)7. The first, sixth and ninth most important followers in the theoretical area are
typical examples of this type.

Table 4. The characteristics of researchers ranked as the most important followers.

Rank
1
2
3
4
5
6
7
8
9
10

7

Din
2
18
0
1
1
0
0
0
0
1

Theoretical area
Dout P Psin P1 P29 18
0 1 17
1 13
0 9
4
6 8
0 0
8
4 8
0 1
7
3 9
3 1
5
7 10
0 0 10
1 8
0 0
8
3 4
0 0
4
5 7
0 0
7
3 9
4 1
4

Plast
16
0
0
2
2
6
2
0
6
1

Din
0
0
0
1
0
0
0
0
3
1

Application area
Dout P Psin P1 P23 4
0 0
4
2 3
0 0
3
2 3
0 0
3
2 4
0 1
3
2 3
0 0
3
2 3
0 0
3
2 3
0 0
3
2 3
0 0
3
1 3
0 1
2
1 3
0 1
2

Plast
2
0
1
0
0
0
1
1
0
0

In many cases, the name of the supervisor is listed last in coauthored papers. For example, in the case of
students' works, their faculty advisors are often listed last as the supervisor.

The latter type is assumed to play a role as a kind of coordinator who arranges researchgroups, bringing over proper specialists for research projects on the basis of his own
connections. It seems that, while leaders function as "hubs" in the networks of knowledge
communication, those coordinators function as "bridges" which intermediate between the"hubs" (e.g., the node (a) in Figure 2). In the application area, by contrast, this kind of
coordinator does not appear as an important follower in Table 4. The application area incomputer science is close to "Mode 2" (Gibbons et al., 1994) in which researches aretransdisciplinary and are carried out in the context of application arising from society rather
than within the discipline. Therefore, it may be assumed that persons who play the role as the"coordinator" in the application area often exist outside the domain and have no substantial
and technical cooperative relationship with "leaders", and that it is reflected in theco-authorship network in this domain.

b
c
a
d

Figure 2: A coordinator and leaders

Conclusions
This study has compared the co-authorship networks of the two subdomains in computerscience, that is, the theoretical and application areas, from two viewpoints giving attention to
the roles in collaboration networks. By applying the modified HITS algorithm to theco-authorship networks, we analyzed (1) the degree of importance as the leader and (2) that as
the follower, for each researcher in the co-authorship networks. Subsequently, the correlation
between these two viewpoints was examined.
It was shown that the negative correlation between (1) and (2) is greater in the application
area. This result suggests that, as for computer science, the two roles (i.e., the "leader" and the"follower") are separated from each other in the application area more clearly than in thetheoretical area. Moreover, we indicated the differences between the two subdomains
regarding the characteristics of researchers occupying the most important positions in theco-authorship networks. Strictly speaking, of course, the differences among the theoreticaland application areas shown in this study can be regarded just as the features in computerscience. In future studies, we will analyze co-authorship networks of other domains, andexamine whether these differences can be generalized.
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