bellanca 2009 measuring interdisciplinary research- analysis of co-authorship for research staff at...

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Research article

Measuring interdisciplinary research: analysisof co-authorship for research staff at theUniversity of York

Leana Bellanca*

Department of Biology, University of York, Heslington, York, North Yorkshire YO10 5YW, UK.

* Corresponding author: Email: [email protected]

Supervisors: Dr Daniel Franks and Dr Leo Caves, York Centre for Complex Systems Analysis, Department of Biology, PO Box 373, University of York, Heslington, York,North Yorkshire YO10 5YW, UK.

Collaboration allows researchers to combine the strength of different disciplines to undertake research that neither could do individually.

Scientific collaboration can be examined by analysing patterns of co-authorship of papers in publication databases (e.g. Web of Science)

using methods from Social Network Analysis. In this project, I describe three networks consisting of researchers in the Biology and

Chemistry Departments at the University of York to investigate degree, degree distribution, key brokers and preference of researchers

for collaborating within or outside their own research field. Clustering (or transitivity) was used to describe whether collaboration is more

likely if two researchers have a collaborator in common. To introduce a control and realize the significance of the results produced, a

network consisting of 98 researchers from the Chemistry and Biology departments was produced and compared with a distribution

of 1000 ER random graphs for degree, transitivity and betweenness. We find that researchers in the Department of Biology (50 research-

ers) have fewer collaborations with their departmental colleagues than those in the Department of Chemistry (45 researchers): the

average number of links each researcher had with others in the Biology collaboration network was 2.6, the corresponding values for

Chemistry were 4.8 links per researcher. We also find that researchers within the Chemistry department were more likely than their col-

leagues in Biology to collaborate with another researcher if they had a collaborator in common. One aim of the study was to characterize

the extent of interdisciplinary research within the Department of Biology. Staff in the Biology department were categorized into distinct

research foci, indicating the discipline of the researcher. There were many links from the Bioinformatics and Mathematics, and Biophysics

and Biochemistry foci, to other foci, implying that staff within these foci were interdisciplinary in their research—indicative of their role in

providing techniques or tools that are applicable across discipline boundaries. This sort of analysis provides quantitative evidence to

understand the social patterns of scientific collaboration and may be a useful tool in the development of strategies to promote inter-

disciplinary research within research institutions.

Key words: collaboration, social network analysis, degree, random graphs, scientific research.

IntroductionScientific researchers aim to investigate, interpret and revise

knowledge of the world. A group of scientists who work

together may form a social network.1 Collaboration may

be utilized to produce a funding proposal, co-author a scien-

tific paper or share ideas through informal discussion.

Collaboration is often used to undertake interdisciplinary

research. Interdisciplinary research aims to combine the

strengths of several disciplines to create a new discipline

allowing researchers to undertake research that neither

could do independently. Funding bodies sometimes consider

grant proposals from groups of researchers whose research

incorporates an interdisciplinary approach to solve large

complex problems. Interdisciplinary research bridges gaps

in terminology, approach and methodology, generating

new approaches to thinking.2

Interdisciplinary Research

Collaboration allow scientists to pool resources to leverage

the cost of expensive scientific equipment and trained

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# 2009 The Author(s). This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License

(http://creativecommons.org/licenses/by-nc/2.0/uk/) which permits unrestricted non-commercial use, distribution, and reproduction in any

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specialists. The knowledge-based3 view suggests that finan-

cial resourcing affects how scientific collaborations form.

An organization is likely to develop resources such as exper-

tise and purchase of expensive equipment if the expertise is

used regularly. In comparison, if expertise is expensive to

develop internally, collaboration with another organization

may be beneficial. However, co-ordination costs involved

in multi-centre collaborations between scientists may

present a barrier to interdisciplinary research. For example,

travel costs to attend meetings with overseas collaborators.

Frequent communication between collaborators is often

associated with greater trust, increased output (i.e. scientific

publications) and greater value for money.3 Sharing

resources such as a common website or database between

collaborators may spread the cost of data handling and com-

munication for each investigator and potentially result in

improved, systematic methods and standardized measure-

ments. Collaboration must occur within a work and

reward structure largely focused on individual achievement

and reputation. The number of publications may be a

factor when considering a researcher for promotion.4

Network Theory

A pair of researchers has a relationship if they have collabo-

rated to publish a scientific paper together.5 A graph can be

produced to describe collaborations between many pairs of

researchers using network theory and bibliometrics.

Bibliometrics is the analysis of scientific publication

records. Each researcher in a graph is a node connected by

an edge or link. Each edge can be weighted to indicate the

number of times a researcher pair has collaborated together.

A node can be characterized by their degree (k) and attri-

bute6 with hubs being nodes of high degree. The degree is

the number of links the node has to other nodes, whereas

the attribute is the intrinsic characteristic of the node such

as a researcher’s research interest. The degree distribution

is the number of nodes with a particular degree. A node

can be also be characterized by its betweenness.

Betweenness measures the number of times a researcher is

an intermediary in the path between two researchers.7 A

node with high betweenness may identify a researcher as a

broker, able to initiate or hinder communication flow

through a network.8 Path length is the number of edges

between two researchers.9 Links can be directed or undir-

ected. For example, in a directed network, node X is

parent to node Y. In an undirected graph, links are undir-

ected implying that each node/collaborator is perceived as

equal contributor to the relationship.10

Network Models

The Erdos–Renyi (ER) graph describes a random network

that follows a Poisson distribution.3, 10 That is, most nodes

have an equal number of edges relative to the network’s

average degree. Random graphs have a small mean shortest

path length and a small clustering coefficient. Clustering

coefficient (or transitivity) measures the probability of a

researcher pair collaborating if they have a collaborator in

common. Shortest mean path length means each researcher

can reach every other by a small number of links.11 An

advantage of having a small mean shortest path length is

that communication can flow through a network quickly.

A small world network more accurately reflects a scientific

collaboration network than a random graph.1 Small world

networks have a small mean shortest path length and a clus-

tering coefficient significantly higher than an ER random

graph.9 Thus, in a network graph nodes tend to group

together.

Interdisciplinary Research at the University of York

A recent report by the University of York, Information

Needs for a World Class University identifies information

needs for promotion of interdisciplinary research.12

This report maintains that research at the University of

York is moving towards interdisciplinary collaboration.

Collaboration becomes necessary as the university competes

in the global higher education market. The University of

York identified their current information services as a

barrier to internal and external collaboration. Simpler

access to data and communication between researchers is

needed to facilitate interdisciplinary research. An academic

social networking site, currently being developed by the

TRANSIT initiative13 at the University of York will allow

a researcher to undertake projects and input data into a data-

base without multiple points of entry.

Research Aims

In this project, I describe the scientific collaboration net-

works in the Biology and Chemistry departments at the

University of York. I define scientific collaboration as two

researchers having co-authored a scientific publication

together from 2001 to 2007.8 Three networks were con-

sidered to investigate degree, degree distribution, key

brokers and preference of researchers for collaborating

within or outside their own research field. Clustering (or

transitivity) was used to investigate whether collaboration

is more likely if two researchers have a collaborator in

common and if clustering had any effect on the structure

of the social network of scientists. A network consisting of

98 researchers from the Chemistry and Biology departments

was produced to test the hypothesis that collaboration does

not differ from a random distribution of 1000 ER random

graphs for measures of degree, transitivity and betweenness.

Materials and MethodsPublication data for researchers employed at the University

of York were extracted from records contained in Web of

Science,14 from the Biology Research Support office and

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Chemistry department. UCINET,15 a social network analysis

tool, was used to statistically analyse relational data.

Bibexcel16 was used to filter publication data to produce a

.coc file that detailed the number of times a pair of research-

ers had collaborated together. A .coc file was modified

slightly in Microsoft Excel17 to produce a UCINET input

file, .dl. Network analyses considered three networks

separately:

(1) Biology collaboration network;

(2) Chemistry collaboration network;

(3) Biology and Chemistry collaboration network.

Compiling Researcher Lists

A list of 85 Biology, 62 Chemistry department researchers

and a combined list of 147 Biology and Chemistry research-

ers at the University of York was compiled from 2001 to

2007.18, 19 Researchers who did not collaborate with their

departmental colleagues were not included in the network

graphs for the three networks subsequently produced. Fifty

out of 85 researchers collaborated with others in the

Biology department, 45 out of 62 collaborated with others

in the Chemistry department and 98 out of the 147 research-

ers collaborated with others in the Chemistry and Biology

departments. The period 2001–2007 was used because it

was when the last RAE at the University of York was con-

ducted. The three researcher lists for the three networks

included surname, initial of first and sometimes second

name. Researcher lists included independent research

fellows, lecturers and professors and excluded PhD students,

visiting fellows and teaching fellows. For this article,

researchers were designated a number from 1 to 147 for

anonymity.

Biology and Chemistry Publication Data

ISI Web of Science scientific publication database was used14

to mine journal publication records for researchers in the

Biology department. The following exemplifies parameters

used in the search page:

Location: Univ* York

Years: 2001–2007.

Publication data mined from Web of Science for Biology

researchers was found to be inaccurate. Difficulty was

experienced in identifying researchers from the Biology

department at the University of York. On many occasions,

there were a number of researchers with the same initials

and surname employed at the University of York.

Therefore, Biology researcher publication data from the

Biology Research Support Office was used because publi-

cation records had been verified by individual authors,

whereas data from Web of Science had not. Duplicate publi-

cation records were removed from the Biology Research

Support Office data by Endnote20 and data exported to

Bibexcel. Data from the Biology Research Support Office

included publications from journal publications, books, con-

ference proceedings, newspapers, patent, personal communi-

cation, report and generic (all types of publication). It was

thought that including all types of publication may have

affected the number of collaborations between researchers

in the three networks and the frequency at which they

occur (shown by the weight of an edge in a network graph).

Web of Science was not used to analyse the Chemistry col-

laboration network because of inaccuracies found in the data

for the Biology collaboration network. Chemistry publi-

cation data were received from the Chemistry department

unformatted with each publication containing researchers’

names, title, abstract, journal reference, etc. in a Microsoft

Word document. Unformatted data were parsed in Awk21

by Caves22 to produce a Bibexcel output file, .out containing

researcher name and publication number. All types of publi-

cation were included when the Chemistry collaboration

network was produced.

UCINET: Social Network Analysis Tool

UCINET produced a square adjacency matrix that detailed

the number of times a pair of researchers had collaborated

together.23 A .dl was used as an input format for UCINET

and is similar to a Bibexcel .coc file.

A .dl file consisted of a data set preceded by the header:

dl n ¼ 50 format ¼ edgelist1 alpha ¼ no

labels embedded data:

n was the number of nodes in the network and Edgelist 1

specified that the data were textual. Labels were embedded

because UCINET drew the labels for the rows and columns

of the adjacency matrix from the first two fields in each

data record. The .dl data set was imported into UCINET

and saved as a REAL data set. REAL data sets are flexible

because they contained values that ranged from 21E36 to

þ1E36. A .dl file can be visualized using the network

graph visualization package, Netdraw distributed with

UCINET.

Binary, Weighted and Symmetric Data

Symmetrical data represented each researcher as an equal

contributor to the collaboration. Data were made symmetric

in UCINET using the symmetrize function from the

Transform menu. Binary data are where a relationship

between a researcher pair is coded 1 and no relationship is

coded 0. Weighted data are where a number is assigned to

each edge to indicate the number of publications for a

researcher pair. Weighted data were used in some measures

of collaboration when the Chemistry and Biology networks

were analysed separately.

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Describing the Characteristics of Each Node: Assigning aResearch Specialism to Each Node

Research foci classification data for each researcher in the

Biology collaboration network were provided by the

Biology Research Support Office. Analysis of research foci

for the Chemistry collaboration network was not conducted

because chemistry research foci data were difficult to obtain.

Each researcher in the Biology collaboration was character-

ized by its research field using Netdraw.24 Transform .

node attribute editor allowed the user to insert a column to

describe each node.

Generating a Random Graph

A graph of 98 researchers from a potential 147 was produced

using steps detailed in the Biology and Chemistry Publication

Data, UCINET: Social Network Analysis Tool, and Binary,

Weighted and Symmetric Data sections. Researchers who

did not collaborate with their Biology and Chemistry col-

leagues were not included in the graph. These observed

data were compared with 1000 ER random graphs generated

using the random function from the ‘data’ menu in UCINET.

The following parameters were used to generate the ER

random graphs and were the same as the Chemistry and

Biology network data.

Density: 0.0406 (binary and undirected)

Number of nodes: 98

Number of graphs: 1000

Type of graph: Undirected

Data: Binary.

Binary data were used to produce the Chemistry and Biology

collaboration network to allow direct comparison with a fre-

quency distribution of 1000 ER graphs. A frequency distri-

bution was generated in Excel.

Results

Accuracy of Data

To illustrate inaccuracies found in the Biology collaboration

network, weighted network data mined from Web of Science

( journal publications only) are shown in Fig. 1, and

weighted data from the Biology Research Support Office

( journal publications only) (Fig. 2). Figure 1 has 45 research-

ers compared with 50 in Fig. 3, indicative of discrepancies

between the two data sets.

The Biology collaboration network consisting of 50

researchers is shown in Fig. 3 where edges are weighted

and all types of publication are used from data from the

Biology Research Support Office. The weight of the edges

is affected by the type of publication used. For example,

Figure 1. The Biology collaboration network using journal publication data from Web of Science, 2001 –2007. Data are weighted and undirected. There are45 nodes. The number of publications between a pair of researchers ranges from 0 to 26. A thick line indicates the researcher pair has collaboratedtogether many times, and a thin line means collaboration has occurred infrequently.


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researchers 97 and 110 collaborated 20 times in Fig. 3 com-

pared with 15 times in Fig. 2 where only journal publications

were used.

A random sample of six Biology researchers was taken

from the Web of Science data set and compared with the

data set from Biology Research Support Office shown in

Table 1. Table 1 implies a tendency to overestimate the

number of publications in the Web of Science data set—a

false positive.

Chemistry Collaboration Network

Publication data were used to produce a weighted chemistry

collaboration network (Fig. 4). Forty-five out of 62 research-

ers (72%) collaborated with other researchers in the

Chemistry department compared with 59% in the Biology

department when both data sets used all types of publi-

cations and weighted data. Figure 4 has one giant and one

small component. Within the giant component, two sub-

components are evident connected by researchers 6, 26 and

43. The strongest links are between researchers 37 and 10

and researchers 33 and 61 with 88 and 101 publications,

respectively. This suggests these researchers had an intense

relationship for a short period of time and produced many

papers or a consistent relationship over a long period of time.

Researcher Degree

The degree is the number of ties a node has to other nodes.10

Researchers are likely to influence those they are directly

adjacent to.25 The patterns of ties in a network define an

researcher’s social role and position.6, 7. Nieminen’s

measure (equation 1)26 was used to express the number of

nodes adjacent to a point, Pk where Pi and Pk represent

two nodes:

CD Pkð Þ ¼Xn

i¼1

a Pi;Pkð Þ ð1Þ

where, a(Pi, Pk) ¼ 1 if and only if Pi and Pk are connected by

a line, otherwise 0.

The CD(Pk) is confounded by network size because it is an

absolute count of degree. To compare the relative centrality

of points for Chemistry and Biology network graphs, CD(Pk)

was normalized. Tables 2 and 3 show the degree and normal-

ized degree for Chemistry and Biology Collaboration

Figure 2. The Biology collaboration network using journal publication data from Biology Research Support Office, 2001 –2007. Data are weighted andundirected. There are 50 nodes. The number of publications between a pair of researchers ranges from 0 to 15. A thick line indicates the researcherpair has collaborated together many times, and a thin line means collaboration has occurred infrequently.


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networks, respectively, using weighted undirected data.

Table 4 shows that the average number of links each

researcher has with others in the Biology collaboration

network was 2.6, the corresponding values for Chemistry

were 4.8 links per researcher.

Table 2 shows that researchers 6 and 16 had a normalized

degree of 27.273 and 25.000, respectively, occupying central

positions in the Chemistry collaboration network. Seven

researchers had a normalized degree of 2.273, occupying a

peripheral position in the network.

Table 3 shows researchers 88 and 64 have the highest nor-

malized degree of 16.327 and 14.286, respectively,

suggesting that they occupy a central position in the

Biology collaboration network and are able to influence

Figure 3. The Biology collaboration network using publication data from Biology Research Support Office, 2001– 2007. All types of publication used. Dataare weighted and undirected. There are 50 nodes with five components; one large and four small. A thick line indicates the researcher pair has collaboratedtogether many times, and a thin line means collaboration has occurred infrequently.

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Table 1. Researcher degree, number of publication records and percentage difference between a random sample of six Biology researchers

Researcher Node degreeusing Web ofScience data

Node degreeusing ResearchSupport officedata

Number ofpublications usingWeb of Science dataset

Number of publicationusing ResearchSupport Office dataset

Difference in number ofpublication between ResearchSupport Office and Web ofScience data set

Percentagedifference (%)

110 3 2 68 58 10 10

88 7 8 47 31 16 41

67 6 5 21 15 6 33

64 7 6 38 11 27 110

82 7 7 57 40 17 35

94 5 5 34 26 8 26

Data mined from Web of Science are compared with those from the Biology Research Support Office. Weighted data and journal publications only were used forboth data sets.


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whether collaboration takes place. Conversely, 18 research-

ers have a normalized degree of 2.041. This suggests that

these researchers do not occupy a peripheral position in the

network and are unlikely to influence potential for

collaboration.

Normalized degree distribution measures the number of

researchers with a particular degree and describes structural

properties of the network. Figure 5 shows the degree distri-

bution of the Biology and Chemistry collaboration networks

using binary data.

Betweenness

A researcher is also central to a social network if they are an

intermediary node between the paths of others.26 A

researcher will pursue all pathways that are independent of

each other (maximum flow) to collaborate with another pro-

portionally to the length of the pathways.27 Flow between-

ness measures the number of times a researcher lies on all

paths between another researcher pair. Flow betweenness

can be expressed by equation 2:7

CF xið Þ ¼Xn

jkk

Xn

mk xið Þ ð2Þ

where, mjk is the maximum flow from nodes xj to xk and

mjk(xi) the maximum flow from xj to xk that passes

through node xi.

Figure 4. The Chemistry collaboration network using publication data fromthe Chemistry department, 2001–2007. All types of publication used. Dataused are weighted and undirected. Forty-five researchers from a possible62 collaborated with their chemistry colleagues. The weight of the edge isindicated by the thickness of the line, with a thick line indicating many col-laborations and a thin line a few collaborations together.

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Table 2. Degree and normalized degree for 45 authors in the Chemistry collaboration network

Researcher Degree Normalized degree Researcher Degree Normalized degree

6 12.0 27.273 37 4.0 9.091

16 11.0 25.000 51 4.0 9.091

62 10.0 22.727 13 4.0 9.091

40 9.0 20.455 9 3.0 6.818

1 9.0 20.455 10 3.0 6.818

59 8.0 18.182 30 3.0 6.818

43 8.0 18.182 53 3.0 6.818

61 8.0 18.182 42 3.0 6.818

4 8.0 18.182 26 3.0 6.818

54 8.0 18.182 36 3.0 6.818

20 7.0 15.909 7 2.0 4.545

22 7.0 15.909 24 2.0 4.545

17 7.0 15.909 8 2.0 4.545

21 7.0 15.909 41 2.0 4.545

23 6.0 13.636 27 2.0 4.545

19 6.0 13.636 48 1.0 2.273

35 6.0 13.636 29 1.0 2.273

14 6.0 13.636 34 1.0 2.273

39 5.0 11.364 45 1.0 2.273

32 5.0 11.364 12 1.0 2.273

55 5.0 11.364 5 1.0 2.273

33 5.0 11.364 60 1.0 2.273

58 5.0 11.364


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Flow betweenness increases with network size and

density because it is an absolute count, preventing compari-

son between two network data sets. Alternatively, normal-

ized flow-betweenness can be used to compare

betweenness of Biology and Chemistry Collaboration net-

works shown in equation 3, 7 by dividing flow that

passes through xi by the total flow where xi does not

participate in communication.

C0F pið Þ ¼

Pn

jkk

PnmjkðxiÞ

Pn

jkk

Pnmjk

ð3Þ

Researchers in the Biology and Chemistry Collaboration

networks with high normalized flow betweenness can be

considered brokers. That is, researchers who have power

to initiate or prevent collaboration between another pair

of researchers.11 Tables 5 and 6 describe normalized

betweenness using UCINET’s Flow Betweenness algorithm

and weighted data for Chemistry and Biology collaboration

networks, respectively.

Researchers 88, 67 and 113 were the top three brokers

with normalized flow betweenness of 19.969, 12.822 and

11.476, respectively, in the Biology collaboration network

shown in Table 6. Researcher 67 influences communication

flow in the network but is not the most connected author.

Researcher 67 has a normalized degree of 10.204 compared

with a minimum of 2.041 and maximum 16.327. Eighteen of

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Table 3. Degree and normalized degree for 50 authors in the Biology collaboration network

Researcher Degree Normalized degree Researcher Degree Normalized degree

88 8.0 16.327 117 2.0 4.082

64 7.0 14.286 137 2.0 4.082

82 7.0 14.286 124 2.0 4.082

113 6.0 12.245 133 2.0 4.082

94 5.0 10.204 95 2.0 4.082

67 5.0 10.204 110 2.0 4.082

65 5.0 10.204 135 2.0 4.082

132 5.0 10.204 69 1.0 2.041

71 4.0 8.163 115 1.0 2.041

146 4.0 8.163 118 1.0 2.041

99 3.0 6.122 119 1.0 2.041

81 3.0 6.122 147 1.0 2.041

130 3.0 6.122 108 1.0 2.041

74 3.0 6.122 109 1.0 2.041

143 3.0 6.122 126 1.0 2.041

78 3.0 6.122 111 1.0 2.041

98 3.0 6.122 112 1.0 2.041

128 3.0 6.122 131 1.0 2.041

122 3.0 6.122 73 1.0 2.041

100 3.0 6.122 97 1.0 2.041

85 3.0 6.122 77 1.0 2.041

120 3.0 6.122 136 1.0 2.041

66 2.0 4.082 102 1.0 2.041

91 2.0 4.082 103 1.0 2.041

93 2.0 4.082 106 1.0 2.041

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Table 4. Degree and normalized degree summary statistic table forBiology and Chemistry authors

Degree Normalized degree

Summary statistics for Chemistry collaboration network

Average 4.844 11.010

Minimum 1.00 2.273

Maximum 12.00 27.273

Summary statistics for Biology collaboration network

Average 2.6 5.306

Minimum 1.0 2.041

Maximum 8.0 16.327


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the 50 researchers have a normalized flow betweenness of

zero indicating they are not intermediaries in the flow of

communication between two researchers.

Researchers 21, 6 and 26 are the top three brokers in the

Chemistry collaboration network with normalized flow

betweenness values of 19.095, 16.254 and 14.095, respect-

ively. Researcher 26 is one of the nodes that connect the

two sub-compartments of the giant component and has an

average normalized degree of 6.818 compared with a

minimum of 2.273 and maximum of 27.273. This implies

that researcher 26 can influence communication flow

without being a highly connected researcher. Researcher 26

is connected to two highly connected researchers, 16 and

6, who have a normalized degree of 25.000 and 27.273,

respectively. Seven of the 45 researchers in the Chemistry col-

laboration network have a normalized flow betweenness of

0.00. This implies that intermediaries in the Chemistry col-

laboration network have greater potential to hinder or

promote communication compared with the Biology collab-

oration network.

Research Foci

Is research focus a meaningful way to classify authors?

Analysis of the normalized degree of a researcher to research-

ers within the same or different research foci can describe

this. Classification of each node into one of the nine research

foci may reveal whether a researcher tends to collaborate

with people within their own research foci or different.

This is shown in Fig. 6 using the Biology collaboration

network data. Figures 7 and 8 show normalized degree

within and between research foci, respectively. Figure 8

shows that Bioinformatics and Mathematics has a normal-

ized between foci degree of 0.17 compared with a within

normalized degree of 0.06. This implies that Bioinformatics

and Mathematics authors collaborate more with authors of

other foci than themselves. Figure 9 summarizes the

number of links between research foci on a network graph.

Normalized flow betweenness can be used to measure

whether a focus can promote or hinder communication

flow. If normalized flow betweenness using weighted data

is summed for all authors in a focus and divided by the

number of authors, the average normalized flow betweenness

can be calculated. Figure 10 shows the average normalized

flow betweenness between foci. The data suggest that the

two foci, Ecology and Evolution and Bioinformatics and

Mathematics, with normalized flow betweenness values of

5.48 and 5.40, respectively, are influential in promoting or

inhibiting potential for collaboration, indicating that they

may act as brokers in the network. Molecular

Microbiology and Molecular and Cellular Medicine have

Figure 5. Degree distribution for (A) the Biology Collaboration networkand (B) the Chemistry collaboration network. Most researchers in theBiology collaboration network (18 researchers) are connected to few indi-viduals and have a degree of 1 whereas eight researchers have a largedegree (5 –8) and are highly connected to others. The Chemistry collabor-ation network has six researchers with a degree of 1 and one researcherwith a degree of 12. Twenty-six researchers have a degree of 5– 12. To sum-marize, the Chemistry collaboration network has more researchers withhigher degree who occupy a central position in the network than theBiology collaboration network.

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Table 5. Normalized weighted flow betweenness for 45 researchersin the Chemistry collaboration network

Researcher Normalized weightedflow betweenness


1 2.326 32 8.693

4 0.415 33 1.792

5 0.00 34 0.000

6 16.254 35 2.794

7 4.228 36 0.299

8 0.344 37 0.520

9 1.207 39 4.573

10 0.117 40 0.788

12 0.000 41 0.037

13 4.264 42 0.057

14 0.846 43 9.391

16 1.235 48 0.000

17 0.335 51 10.258

19 2.992 53 0.207

20 1.973 54 4.612

21 19.095 55 5.025

22 5.618 58 1.347

23 8.051 59 4.003

24 0.106 60 0.000

26 14.095 61 2.813

27 0.306 62 4.607

29 0.000 121 0.000

30 1.618

All types of publications were used.


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little influence in promoting collaboration with normalized

flow betweenness values of 0 and 0.02, respectively. All

five authors belonging to the Molecular and Cellular

Medicine group are disconnected from the main component

of the graph, indicating that they either do not collaborate

with others or collaborate with researchers outside of the

Biology department.

Clustering

Is There Evidence of Clustering in the Biology and

Chemistry Collaboration Networks?

High transitivity or clustering means that there is a heigh-

tened probability of two people having collaborated if they

have one or more collaborators in common.11 Transitivity

can be measured by the clustering coefficient described by

equation 4.9

C ¼ 6� ðnumber of transitive triples on a graphÞðnumber of paths of length 2Þ ð4Þ

The Biology collaboration network shows little evidence of

clustering since only 0.09% of all types of triples are transi-

tive (Table 7). The Biology collaboration network consisted

of 102 transitive triples from a possible of 117 600 triples

of all kinds The Biology collaboration network has a

density of 0.05%, making collaboration between two

researchers who have a collaborator in common unlikely.

In comparison, the Chemistry collaboration network

shows 624 transitive triples from a possible 85 140 triples

of all kinds. The Chemistry collaboration network has a

higher percentage of transitive triples (0.72%) compared

with Biology (0.09%). The Chemistry collaboration

network has a density of 0.1%. Two authors in the

Chemistry collaboration network are more likely to publish

if they have collaborator in common than the Biology collab-

oration network.

Chemistry and Biology Collaboration Network ERRandom Graphs

Erdos and Renyi9 proposed the Gn,p random graph to

describe the random occurrence of a collection of nodes con-

nected by edges.11, 28 Each pair of nodes in a Gn,p graph is

connected together with independent probability p or not

connected with probability 1 2 p.

The observed network is a binary network consisting of

researchers from the Biology and Chemistry departments.29, 30

The density and number of nodes in the observed data and

1000 Gn,p graphs do not differ. If the average of a measure

such as transitivity, flow betweenness and degree in observed

data does not deviate from the average of 1000 random

graphs, when random graphs are plotted on a frequency distri-

bution, it is implied collaboration is a random process.29, 31, 32

Figure 11 displays a network graph of the observed data and

Fig. 12 is a frequency distribution that shows the average

flow betweenness for all nodes in each random graph for

1000 ER random graphs.

The average flow betweenness for 1000 ER random

graphs was 114.363 compared with 130.966 in the observed

network data. The observed average flow betweenness was

above the 95th (.127) percentile in the frequency distri-

bution of 1000 random graphs; therefore, average flow

betweenness occurs more often in observed data than at

random. Flow betweenness is not a random process that

occurs in the Biology and Chemistry scientific collaboration

network.

If our observed data for node degree approximate a

random graph, each node in the observed data will have a

degree similar to the network graph’s average. Few nodes

will have a degree higher or lower than the graphs’s

average. The average degree (3.939) for 1000 ER graphs

and observed data did not differ. This is because the

number of edges each node is connected to may vary in 1

Gn,p replication, but the average number of edges per

................................................................................................................

Table 6. Normalized weighted flow betweenness for 50 researchersin the Biology collaboration network



64 11.252 108 0.00

65 10.619 109 0.00

66 0.879 110 0.085

67 12.822 111 0.00

69 0.00 112 0.00

71 5.659 147 0.00

73 0.00 113 11.476

74 3.210 115 0.00

77 0.00 117 0.006

78 1.546 118 0.00

81 1.542 119 0.00

82 8.505 120 0.961

85 2.062 122 0.903

88 19.229 124 3.231

91 0.085 126 0.00

93 0.009 128 4.535

94 8.829 130 6.378

95 3.231 131 0.00

98 3.242 132 6.576

97 0.00 133 0.021

99 3.274 135 1.190

100 0.903 136 0.00

102 0.00 137 0.006

103 0.00 143 1.373

106 0.00 146 4.755

All types of publications were used


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node in each graph does not differ from the other 999 Gn,p

replications.32

Transitivity shows that two authors are likely to collabor-

ate if they have an acquaintance in common.9 The percentage

of transitive triples for the random and observed networks is

,0.01% and 0.09%, respectively. Thus, transitivity in the

observed data occurs more often than at random. It is

likely that the process of introducing colleagues to one

another is important in the community structure of the

Biology and Chemistry collaboration network.

DiscussionWith knowledge of the structure of the Biology and

Chemistry collaboration network, through co-publication

of scientific papers, what have we learnt about interdisciplin-

ary research and scientific collaboration? The results give

Figure 6. Classification of the Biology collaboration network by research foci. Relationships are undirected and binary. All types of publication were used.The key details each author by research focus.

Figure 7. Normalized number of links within each research foci in theBiology department at the University of York. Data are binary and undir-ected. The normalized degree within a foci ranges from 0 to 0.29 with amean of 0.14. The Ecology and Evolution has the highest normalizeddegree of 0.29. Bioinformatics has the lowest normalized degree withinfoci of 0.06. This implies that Ecology and Evolution is well connectedwithin their own foci and Bioinformatics is poorly connected. However,Ecology and Evolution ( population 9) has increased opportunity to collab-orate within their own foci than Bioinformatics ( population 2).

Figure 8. Normalized number of links between each research foci in theBiology department at the University of York. Data are binary and undir-ected. The normalized between foci degree ranges from 0.13 to 0.25.Biochemistry and Biophysics has the highest normalized between degreeof 0.25. Conversely, Molecular and Cellular Medicine has the lowestbetween normalized degree of 0.04. Molecular and Cellular Medicineauthors collaborate to a lesser extent with other foci.


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support to the idea that authors collaborate in a non-random

way, where measures of transitivity and betweenness in the

observed co-authorship network deviate from a frequency

distribution of 1000 ER random graphs. Authors make

informed decisions about who to collaborate with. Critique

of the assumptions underlying the measures used to analyse

the scientific collaboration network is needed to realize the

significance of the results. Is the structure of the Biology

and Chemistry networks, reported by this work, replicable

in other networks? Data mining methods used to analyse

publication data from the Biology and Chemistry depart-

ments and the problems of missing data may have skewed

results providing an inaccurate representation of the

Biology and Chemistry collaboration networks.

Data Mining and Sampling Bias

A tie between two authors occurs when they have published

a scientific paper together. A tie is a crude measure of

Figure 9. Number of times collaboration has occurred between authors ofdifferent foci. Data are undirected.

Figure 10. Average normalized flow betweenness values betweenresearch foci. Weighted undirected data are used. The Ecology andEvolution and Bioinformatics and Mathematics are brokers in the Biologycollaboration network. The normalized flow betweenness forBioinformatics and Mathematics and Ecology and Evolution are 5.397833and 5.479818, respectively. The normalized flow betweenness forMolecular Microbiology and Molecular and Cellular Medicine is 0.0 and0.014, respectively.

.................................................................................................................

Table 7. Transitivity of the Biology and Chemistry collaborationnetworks

Transitivity Chemistrycollaborationnetwork

Biologycollaborationnetwork

Number of non-vacuous transitive

ordered triples

624 102

Number of triples of all kinds 85 140 117 600

Number of triples in which i! j and

j! k

1232 366

Number of triangles with at least two

legs

2448 894

Number of triangles with at least three

legs

624 102

Percentage of all ordered triples 0.72% 0.09%

Transitivity: % of ordered triples in which

i! j and j! k that are transitive

50.65% 27.87%

Transitivity: % of triangles with at least

two legs that have three legs

25.49% 11.41%

Data are undirected and weighted.

Figure 11. Network graph using data from Biology and Chemistry publi-cation records. Data are binary and undirected and all types of publicationdata were used. There are three components disconnected from the giantcomponent. The Chemistry and Biology collaboration network combinedhas 98 nodes and a density (matrix average) of 0.0406.


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collaboration since not all collaborators may be included in

the author list.33 Gift authorship is when an author is

included in a publication and has made no contribution to

research but has influenced the career of a main author.34

Conversely, an individual may not be included in the

author list but made significant contributions to research

efforts.

The use of co-publication to represent a tie has repercus-

sions when sampling ties in Biology and Chemistry collab-

oration networks. Bias is created when author lists are

incomplete. Authors employed for part of the 2001–2007

periods are less likely to collaborate with many of their col-

leagues than an author who has worked in the department

for the full 2001–2007 term. The effects of missing data

are unknown since we are unable to compare the observed

network data with a data set that includes all research

fellows, professors or lecturers. The Biology and

Chemistry networks have different numbers of links,

despite having similar population sizes. The Chemistry col-

laboration network had a density of 0.11% and had 45

nodes compared with a density of 0.05% in the Biology

collaboration network with 50 nodes. Therefore, caution

should be exercised when making comparisons

between the two networks. Constructing a scientific

collaboration network is a time-consuming process,

making it difficult to produce a number of replicates for

each network.31

The boundary specification problem35 refers to inclusion

parameters for authors in social networks. Authors who col-

laborated with others outside the Biology and Chemistry

departments at the University of York were not recorded in

the data sets. Thus, we cannot comment on the total

degree of an author only the degree in relation to other

authors in the Biology and Chemistry department.

Random Graphs

Comparison of measures for observed network data with a

random distribution of the measure allows us to introduce a

control. If we did not compare our data with a random

graph, we would not know whether observed data were a

random occurrence or not. One thousand replications of

the ER graph is adequate to investigate whether the

Biology and Chemistry collaboration network, detailed in

Fig. 12, does not differ from a random distribution.

However, we cannot statistically infer whether the Biology

and Chemistry collaboration network deviates or not

significantly from the random model because of the small

sample size.36 Thus, we have only carried out descriptive

analysis of the networks. Although rich in information,

generalizations about social relationships cannot be made.

A problem of comparing social network data with a

random graph is that random graphs poorly reflect social net-

works. The Biology and Chemistry collaboration networks

violate the independence assumption of Gn,p graphs

because collaboration networks demonstrate transitivity

where nodes are dependent on others: a property that ER

random graphs lack.28 However, given the tools available

to compare observed network data with a null model, the

ER random model was adequate. Similarly, care should be

taken when attempting to fit network data to a network

model such as small world due to small sample size.

ConclusionsWe conclude that scientific collaborators, quantified using

the Biology and Chemistry collaboration networks, seek

expertise from their colleagues in a non-random way to

fulfil a research goal. Highly connected authors have poten-

tial to influence whether collaboration occurs or not. Some

authors may not be well connected but influence collabor-

ation by acting as a communication point between two

highly connected authors. Publication records have provided

a documented source of information about professional

relationships among researchers. Future directions could

include investigating how scientific collaboration changes

over time in the Chemistry and Biology department. Will

the same authors be identified as brokers or highly connected

in 4 years time? Similarly, the change, if any, of foci member-

ship over time could be investigated and whether this affects

practice of interdisciplinary research.

AcknowledgementsThe author is grateful to Dr Daniel Franks and Dr Leo Caves

for providing feedback.

Figure 12. Frequency distribution of 1000 ER random graphs measuringflow betweenness. The graph peaks at the 112–114 interval with 241/

1000 having an average flow betweenness in this range. The 130–132and 97 –99 intervals had the lowest frequency of 2 and 3, respectively.The shape of the line deviates slightly from the Gn,p frequency distributionwith a sharp peak at 112–114 opposed to a rounded peak. This may bebecause too few data points were used.


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FundingFunding to undertake this research was provided by

Department of Biology, University of York.

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Author BiographyLeana Bellanca studied for a BSc (Hons) degree in Molecular Cell Biology at the University of York. She developed interests in

Systems Biology, including network theory and relational data analysis. Leana is also interested in Immunology and

Epidemiology. She is employed as a Medical Information Officer at Professional Information, Richmond, North

Yorkshire. This involves drug safety reporting and providing information about medicinal products to healthcare

professionals and patients. Leana intends to remain in this field of work.

Submitted on 30 September 2008; accepted on 18 December 2008; advance access publication 8 April 2009


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