Betweenness and diversity in journal citation networks as measures of interdisciplinarity—A tribute to Eugene Garfield
Betweenness and diversity in journal citation networks
as measures of interdisciplinarity-A tribute to Eugene
Loet Leydesdorff 0 1 2
Caroline S. Wagner 0 1 2
Lutz Bornmann 0 1 2
0 Division for Science and Innovation Studies, Administrative Headquarters of the Max Planck Society , Hofgartenstr. 8, 80539 Munich , Germany
1 John Glenn College of Public Affairs, The Ohio State University , Columbus, OH 43210 , USA
2 Amsterdam School of Communication Research (ASCoR), University of Amsterdam , PO Box 15793, 1001 NG Amsterdam , The Netherlands
Journals were central to Eugene Garfield's research interests. Among other things, journals are considered as units of analysis for bibliographic databases such as the Web of Science and Scopus. In addition to providing a basis for disciplinary classifications of journals, journal citation patterns span networks across boundaries to variable extents. Using betweenness centrality (BC) and diversity, we elaborate on the question of how to distinguish and rank journals in terms of interdisciplinarity. Interdisciplinarity, however, is difficult to operationalize in the absence of an operational definition of disciplines; the diversity of a unit of analysis is sample-dependent. BC can be considered as a measure of multi-disciplinarity. Diversity of co-citation in a citing document has been considered as an indicator of knowledge integration, but an author can also generate trans-disciplinary-that is, non-disciplined-variation by citing sources from other disciplines. Diversity in the bibliographic coupling among citing documents can analogously be considered as diffusion or differentiation of knowledge across disciplines. Because the citation networks in the cited direction reflect both structure and variation, diversity in this direction is perhaps the best available measure of interdisciplinarity at the journal level. Furthermore, diversity is based on a summation and can therefore be decomposed; differences among (sub)sets can be tested for statistical significance. In the appendix, a general-purpose routine for measuring diversity in networks is provided.
Betweenness Diversity Granularity
The journal network and its role in collecting and communicating advances in science
continues to be a source of debate and challenge to understanding. The network illustrates
) argument that systems are shaped in hierarchies in order to deal
(Boyack et al. 2014)
. The journal structures provide order and improve the
efficiency of the search for new information. Eugene Garfield enhanced this role by
creating additional categories for the evaluation of journals
Although citations are paper-specific
(Waltman and van Eck 2012)
constructed the Science Citation Index (SCI) and its derivatives (such as the Social Science
Citation Index) at the journal level
. By aggregating citations at that level,
one obtains a systems view of the disciplines as they are linked to the subjects covered by
the respective journals
(Narin et al. 1972)
. The Institute of Scientific Information (ISI)
developed a journal classification system—the so-called ‘‘Web-of-Science subject
categories’’ (WC)—that is often used in scientometric evaluations. Three decades later,
however, Pudovkin and Garfield (2002, p. 1113) stated that journals had been assigned to
these categories by ‘‘subjective and heuristic methods’’ that did not sufficiently appreciate,
or perhaps allow for the visibility of, the relatedness of journals across boundaries
(Leydesdorff and Bornmann 2016)
. As boundaries are drawn to enhance efficiency, new
developments, especially those that bring together disparate ideas in original ways
et al. 2013)
, can be disadvantaged by a scheme that relies on incremental additions to the
conventional subject categories
(Rafols et al. 2012)
The categorization of research in terms of disciplines has often been commented upon
in the history of science. For example,
, p. 78) noted that: ‘‘From their very
nature there must be a certain amount of overlapping….’’ In 1972, the Organization for
Economic Cooperation and Development
proposed a systematization of the
distinctions between multi-, pluri-, inter-, and trans-disciplinarity as categories for research
and higher education
(Klein 2010; Stokols et al. 2003)
‘‘Multidisciplinary’’ is used for
juxtaposing disciplinary/professional perspectives, which retain separate voices;
‘‘interdisciplinary’’ integrates disciplines; and ‘‘transdisciplinary’’ synthesizes disciplines into
larger frameworks (Gibbons et al. 1994). We adopt these definitions in this study.
We return to a question which
Leydesdorff and Rafols (2011)
raised, but did not answer
conclusively at the time, namely, how to distinguish and if possible rank journals in terms
of their ‘‘interdisciplinarity’’ in such a way as to identify where creative combinations are
indicated. In this previous study we used the 8707 journals included in the Journal Citation
Reports (JCR) 2008, and explored a number of measures of interdisciplinarity and
diversity, also detailed in
Wagner et al. (2011)
. In this study, we build on the statistical
decomposition of the JCR data 2015 (11,365 journals) using VOSviewer
et al. 2017)
. A statistical decomposition, however, does not have to be semantically
(Rafols and Leydesdorff 2009)
. The advantage of this approach, however, is
that the two problems—of decomposition and interdisciplinarity—can be separated
analytically. Furthermore, we exploit advances made in recent years:
At the time, we did not sufficiently distinguish between cosine-normalization of the
data as more or less standard in the scientometric tradition
(Ahlgren et al. 2003; Salton
and McGill 1983)
and the use of graph-analytical measures such as betweenness
centrality that presume binary networks. The distance measures in the two topologies,
however, are very different: graph-analytically, one can distinguish shortest paths in
the network of relations; but the vector space is spanned in terms of correlations—that
is, including non-relations. Proximity can be expressed in this topology, for example,
as a cosine value; and distance accordingly as (1-cosine).
Betweenness centrality—the relative number of times that a node is part of the shortest
distance (‘‘geodesic’’) between other nodes in a network—is an obvious candidate for
the measurement of interdisciplinarity; it scored as best for this purpose in the previous
comparison. Leydesdorff and Rafols (2011, p. 93) noted that weighted betweenness
could be further explored using the citation values of the links as the weights; but at
that time, this concept was still under development
(Brandes 2001; Newman 2004)
not yet implemented for larger-sized matrices. In the meantime, Brandes (2008)
comprehensively discussed betweenness and the measure for valued networks was
implemented, for example, in the software package visone (available at http://visone.
Diversity measures have been further developed into ‘‘true’’ diversity measures by
Zhang et al. (2016)
; ‘‘true’’ diversity can be scaled at the ratio level so that one can
consider percentages in increase or decrease of diversity
(Jost 2006; Rousseau et al.
2017, in preparation)
. Furthermore, Cassi et al. (2014) proposed that diversity can be
decomposed into within-group and between-group diversity. Using a general
approximation method for distributions, these authors have developed benchmarks
for institutional interdisciplinarity
(see also the further elaboration in Cassi et al. 2017;
cf. Chiu and Chao 2014)
. However, we shall argue that one can decompose diversity in
terms of the cell values of (pipjdij) because it is a summation. Differences among
aggregates of these values can be tested for statistical significance using ANOVA with
Bonferroni correction ex post (e.g., the Tukey test).
The availability of virtually unlimited memory resources using a 64-bit operating
system and the further development of software for network analysis (Gephi, ORA,
Pajek, UCInet, visone, VOSviewer, etc.) enables us to address questions that were
previously out of reach.
Interdisciplinarity has remained a fluid concept fulfilling various functions at the interfaces
between political and scientific discourses
(Wagner et al. 2011)
. Funding agencies and
policy makers call for interdisciplinarity from a normative perspective based upon their
expectation that boundary-spanning produces creative outputs and can contribute to
solving practical problems. For example, in 2015 Nature devoted a special issue to
interdisciplinarity, stating in the editorial that scientists and social scientists ‘‘must work
together … to solve grand challenges facing society—energy, water, climate, food,
health.’’ On this occasion,
van Noorden (2015
) collected a number of indicators of
interdisciplinarity showing a mixed, albeit optimistic picture; interdisciplinary research, by
some measures, has been on the rise since the 1980s. According to this study,
interdisciplinary research would have long-term impact ([ 10 years) more frequently than
disciplinary research (p. 306). Asian countries were shown to publish interdisciplinary papers
more frequently than western countries (p. 307).
On the basis of a topic model, Nichols (2014, p. 747) concluded that 89% of the
portfolio of the Directorate for Social, Behavioral, and Economic Sciences (SBE) of the
US National Science Foundation is ‘‘comprised of IDR (interdisciplinary research)—with
55% of the portfolio identified as having external interdisciplinarity and 34% of the
portfolio comprised of awards with internal interdisciplinarity. When dollar amounts are
taken into account, 93% of this portfolio is comprised of IDR (…).’’ Although this result
may be partly an effect of the methods used
(Leydesdorff and Nerghes 2017)
impressive percentages show, in our opinion, the responsiveness of (social) scientists to
calls for interdisciplinarity by funding agencies.
Is this commitment also reflected in the output of research? Do scientists relabel their
research for the purpose of obtaining funds
(Mutz et al. 2015)
? On the output side, the
journal literature can be considered as a selection environment at the global level.
However, the journal literature has recently witnessed important changes in its orientation
toward ‘‘interdisciplinarity.’’ Using a new business model, PLOS ONE was introduced in
2006 with the objective to cover research from all fields of science without disciplinary
criteria. ‘‘PLOS ONE only verifies whether experiments and data analysis were conducted
rigorously, and leaves it to the scientific community to ascertain importance, post
publication, through debate and comment’’
MacCallum 2006, 2011)
. Although this model is multi-disciplinary, it creates room for the
evolution of new standards at the edges of existing disciplines.
It remains difficult to define interdisciplinarity, when disciplines cannot be demarcated
clearly. Most if not all of science is a process of seeking diverse inputs in order to create
innovative insights. Labels as to whether the results of research are classified as
‘‘chemistry’’ or ‘‘physics’’ are added afterwards. Yet, such classifications structure expectations,
behavior, and action. A physicist hired in a medical faculty, for example, has to fulfill a
different range of expectations and thus faces another range of options than his/her
colleague in a physics department.
The journal literature is mostly structured in terms of specialties because its main
function has been to control quality, particularly in the case of specialized contributions.
The launch of a new journal and its incorporation into the quality control system of the
relevant neighboring journals and databases (including the bibliometric ones) provide
practicing scientists with new options. The emergence of a new specialty is often
associated with the clustering of journals supporting new developments at the field level
Leydesdorff and Goldstone 2014; van den Besselaar and Leydesdorff 1996)
. However, the
demarcation of disciplines in terms of journals has remained a major problem. As noted,
one uses WCs in scientometrics as a proxy, but this generates error
Interdisciplinarity can also be considered as a variable; neither journals nor departments
are mono-disciplinary. The system is operational and therefore in flux. But how could one
measure the interdisciplinarity of a journal, a department, or even an individual scholar
‘‘while a storm is raging at sea’’
? Is physical chemistry more or less
‘interdisciplinary’ than biochemistry? Or are both parts of chemistry? Does it matter when
a laboratory for biochemistry is relabeled as molecular biology, and thereafter classified as
When interviewed, for example, physicists who attended the emergence of
nanotechnology and nanoscience during the 1990s considered the nano domain as just another
domain in physics, whereas material scientists experienced this same development as
(Wagner et al. 2015)
. A new set of research questions became possible and
new journals emerged at relevant interfaces, while existing journals changed their
orientations; for example, in terms of what is admissible as a contribution. The material
scientists considered nanotechnology and nanoscience as a new discipline, while the
physicists did not. As
states: ‘‘It is two disciplines, one might say, divided by
a common subject’’ (p. 79).
Unlike hierarchical classifications, a network representation of the relations among
disciplines and specialties provides room for operational definitions of interdisciplinarity
and measurement. Dense areas in the networks can overlap into areas that are less dense;
new densities can emerge in the less dense areas because of recursive interactions;
densities at interfaces can be approached from different angles, and then other characteristics
may prevail in the perception and hence categorization.
In this study, these larger questions about the (inter)disciplinary dynamics of science are
reduced to the seemingly trivial question of the measurement of interdisciplinarity of
scholarly journals in a specific year. Can we sharpen the instrument so that an operational
definition and measurement of interdisciplinarity become feasible? Using the aggregated
journal–journal citation network 2015 based on JCR data, we test two measures which
have been suggested for measuring interdisciplinarity. By moving from the top level of ‘‘all
of science’’ (11 k ? journals) to ten broad fields and then to lower levels of specialties, we
hope to be able to say more about the quality of the instruments as well as about the
problems of measuring interdisciplinarity. In other words, we entertain two research
questions: one substantial, about measuring the interdisciplinarity of journals at different
levels, and one methodological, about problems with this measurement.
The measurement instruments
The focus will be on two measures of interdisciplinarity: betweenness centrality and
(Brandes 2001, 2008; Freeman 1978/1979)
and its derivatives such
as ‘‘structural holes’’
are readily available in software packages as measures
for brokering roles between clusters. A high betweenness measure at the node level
indicates that the node has a higher than average likelihood of being on the shortest path
from one node to another. This position may enable the agent at the node to control the
flow between other vertices
(Brandes 2008, p. 137)
. Investigators with high betweenness
are, for example, better positioned to relay (or withhold) information between research
(Freeman 1977; Abbasi et al. 2012)
. They are advantaged in terms of search.
Algorithms for variants of betweenness centrality were notably implemented in the
software package visone. Among these variants is the possibility to use weighted networks
(Freeman et al. 1991)
. The combination of betweenness centrality with the disparity notion
in diversity studies—to be discussed below—is also the subject of ongoing research on
Qor Gefura measures
(Flom et al. 2004; Rousseau and Zhang 2008; Guns and Rousseau
. However, this further extension is not studied here.
Following a series of empirical studies by Alan Porter and his colleagues
(Porter et al.
2006, 2007, 2008; Porter and Rafols 2009)
, on the one hand, and Stirling’s (2007)
mathematical elaboration, on the other,
Rafols and Meyer (2010)
aspects of interdisciplinarity: (1) variety, (2) balance, and (3) disparity. Variety can be
measured, for example, as Shannon entropy. The participating disciplines in specific
instances of interdisciplinarity can be assessed in terms of their balance: a balanced
participation can be associated with interdisciplinarity, whereas an unbalanced one suggests a
(Nijssen et al. 1998)
. In the extreme case, the one discipline is
enrolled by the other in a service relationship.
On the basis of animations of newly emerging journal structures,
showed that interdisciplinary developments occur often at specific
interfaces between disciplines, but are initially presented as—and believed to
be—interdisciplinary. From this perspective, interdisciplinarity can be associated with the idea of a
preparadigmatic phase in the development of disciplines and specialties
(van den Daele et al.
. New and initially interdisciplinary developments may crystallize into new
(van den Besselaar and Leydesdorff 1996)
or they may dissipate as the
core disciplines absorb the new concepts.
The measurement of ‘‘disparity’’ provides us with an ecological perspective: a
collaboration between authors in biology and chemistry, for example, can be considered as less
interdisciplinary in terms of disparity than one between authors in chemistry and
anthropology. The cognitive distance between latter two disciplines—being a natural and a social
science discipline is much larger than that between two neighboring fields in the natural
. The disparity thus reflects a next-order structure in terms of
ecological distances and niches among journal sets.
Disparity and variety can be combined in the noted measures of diversity
In this formula, i and j represent different categories; pi represents the relative frequency or
probability of category i, and dij the distance between i and j. The distance, for example,
can be the geodesic (that is, shortest path) in a network or (1-cosine) in a vector space by
using the cosine as a proximity measure
(Ahlgren et al. 2003; Jaffe 1989; Salton and
. The multiplication of the measures of distance and relative occupation has
led to the characterization of this measure as ‘‘quadratic entropy’’
(e.g., Izsa´ki and Papp
suggests developing a further heuristics by weighing the two
components; for example, by adding exponents. However, one then obtains a parameter
space which is infinite
(Ricotta and Szeidl 2006)
The first part of Eq. 1 (that is, the measure of variety P ij pipj is also known as the
Gini–Simpson diversity measure in biology or the Herfindahl–Hirschman index in
. Note that this term is measured at the level of a vector. Using a
citation matrix, two different distance matrices can be constructed among the citing and
cited vectors, respectively. In the citing dimension, Rao–Stirling diversity has been
considered as a measure of integration in interdisciplinary research
(Porter and Rafols 2009;
Rousseau et al. 2017, in preparation; Wagner et al. 2011, p. 16)
. Variety and disparity are
combined and integrated in a citing paper by the citing author(s). In the cited dimension,
one measures diversity (in terms of variety and disparity) in the structures from which one
cites. The structures operate as selection environments. Rousseau et al. (2017, in
preparation) suggests that diversity in the cited dimension should be considered as diffusion:
diffusion can be interdisciplinary to various extents.
Zhang et al. (2016)
further developed D into 2D3 as a ‘‘true’’ diversity measure; true
diversity has the advantage that the measure is scaled so that a 20% higher value of 2D3
indicates 20% more diversity
. Conveniently, the two measures relate
monotonically as follows
(Zhang et al. 2016, p. 1260, Eq. 6)
2D3 ¼ 1=ð1
True diversity varies from one to infinity when D varies between zero and one. Note that
these diversity measures do not include ‘‘balance’’ as the third element distinguished in the
definition of interdisciplinarity by
Rafols and Meyer (2010)
. One can envisage adding a
third probability distribution (pk) to Eq. 1 as a representation of the disciplinary
. Alternatively, ‘‘balance’’ can be operationalized using, for example,
Cassi et al. (2014)
developed a methodology for the decomposition of
diversity into within-group and between-group diversity
(see also the further elaboration in
Cassi et al. 2017; cf. Chiu and Chao 2014)
. In our opinion, the Eqs. 1 and 2 are valid for
each subset since the operation is a straightforward summation. Consequently, one can
decompose diversity in terms of the cell values (pipjdij). Differences among aggregated
subsets can be tested using ANOVA with Bonferroni correction ex post (e.g., the Tukey
test). For the exploration of this decomposition, we use the WoS Category Library and
Information Science (86 journals in the JCR 2015) instead of the set of 62 journals
Leydesdorff et al. (2017)
into a single group on statistical grounds. The
results are then easier to follow.
Units of analysis
In addition to the various aspects of interdisciplinarity that can be distinguished, the choice
of the system of reference will make a difference. Interdisciplinarity can be attributed to
departments, journals, oeuvres, emerging disciplines, etc. In science studies, it is customary
to distinguish between the socially organized group level and the level of intellectually
organized fields of science
. The interdisciplinarity of a group (e.g., a
department) can be important from the perspective of team science. The dynamics of
interdisciplinary at the field level are relatively autonomous
(‘‘self-organizing’’; van den
Daele and Weingart 1975)
For example, the interdisciplinary development of nano-technology in the 1990s
required contributions from chemistry (e.g., advanced ceramics), applied physics, and
materials sciences. A group in a chemistry faculty will be positioned for the challenge of
participating in this new development differently from a group in physics. The group
dynamics, in other words, can be different among groups and from the field dynamics. New
fields of science may develop at the global level, whereas groups are localized. One can
also consider the fields as the selection environments for groups or, more generally,
individual or institutional agency. Selection mechanisms can reflexively be anticipated.
Furthermore, one can attribute interdisciplinarity as a variable to units of analysis such
as authors, groups, texts at the nodes of networks, or second-order units of analysis such as
2,848,736 (11,049 loops)
links. (Factor loadings, for example, are attributes of variables.) One can expect different
dynamics at the first-order or second-order level. Whereas interdisciplinarity can a political
or managerial objective in the case of first-order units (e.g., groups), interdisciplinarity
attributed at the level of second-order units (e.g., fields) is largely beyond the control of
decision makers or individual scientists. Second-order units can be rearranged and thus
develop resilience against external steering.
Note that these distinctions are analytical: journals, for example, are organized in terms
of their production process, but can be self-organizing in terms of their content to variable
extents. The interdisciplinarity of a journal or a department is also determined by the
sample and the level of granularity in the analysis. A journal, for example, may appear
interdisciplinary in the context of a large set of journals, but when this set is decomposed,
the interdisciplinarity may be lost since the borders are drawn differently. For example,
important ties to other domains may be cut by decomposition. In sum, one unavoidably
entertains a model when measuring ‘‘interdisciplinarity;’’ and by using this model, the
concept is (re)constructed.
We use the directed (asymmetrical and valued) 1-mode matrix among the 11,365 journals
listed in the Science and Social Sciences Citation Index in 2015. Table 1 provides
descriptive statistics of the largest component of 11,359 journals. (Six journals are not
In the first round of the decomposition, ten clusters were distinguished. These are listed
in Table 2. At http://www.leydesdorff.net/jcr15/scope/index.htm the reader will find a
hierarchical decomposition in terms of maps of science.
We pursue the analysis for the complete set (n = 11,359) and for the first cluster
(n = 3274). Within this latter subset, 62 journals are classified as Library and Information
Science (LIS) in the second round of decomposition. We use the LIS set as an example at
the (next-lower) specialty level.2
1 Avian Res, EDN, Neuroforum, Austrian Hist Yearb, Curric Matters, and Policy Rev.
2 For the delineation of the LIS set, see the appendix of Leydesdorff et al. (2017, pp. 1611f).
As noted, we focus in this study on betweenness centrality and diversity as two main
candidates for measuring interdisciplinarity in journal citation networks. The betweenness
centrality (BC) of a vertex k is equal to the proportion of all the geodesics between pairs
(gij) of vertices that include this vertex
(gijk; e.g., de Nooy et al. 2011, p. 151)
. The BC for a
vertex k can formally be written as follows:
X gijk ;
i 6¼ j 6¼ k
introduced several variants of this betweenness measure when proposing
it. In their study of centrality in valued graphs,
Freeman et al. (1991)
flow centrality, which includes all the independent paths contributing to BC in addition to
the geodesics. In the meantime, a number of software programs for network analysis have
adopted Brandes’ (2008) algorithm for valued graphs.3 We use Pajek and UCInet for
nonvalued graphs and visone for analyzing valued ones.4
While BC can be computed on an asymmetrical matrix, Rao-Stirling diversity and 2D3
are evaluated along vectors in either the cited or citing direction of a citation matrix. Both
the proportions and the distances have to be taken in the one direction or the other. One
thus obtains two different—but most likely correlated—measures. The proportions are
straightforward relative to the sum of the references given by the journal (citing) or the
citations received (cited).5 The distance measure, however, provides us with another
In line with the reasoning about BC, one could consider using geodesics as a measure of
distance. However, the average geodesic in the network under study is 2.5 with a standard
deviation of 0.6 (Table 1). In other words, the variation in the geodesic distances is small:
3 Non-valued BC can be obtained by first binarizing the matrix.
4 UCInet offers also a number of options such as ‘‘attribute weighted betweenness centrality,’’ but the
results are sometimes very similar to ordinary BC.
5 The ‘‘total citations’’ provided by the JCR can be considerably larger than the citations included in the
matrix. Probably, citations by other sources such as the Arts and Humanities Citation Index are also
included. We correct for this by recounting the total citations (and total references) in each set.
most of them are 2 or 3.6 The choice of another distance measure—or equivalently
(1proximity)—provides us with a plethora of options. We chose (1-cosine) as the distance
measure because Euclidean distances did not work in our previous project
and Rafols 2011)
. The cosine has been used as a proximity measure in technology studies
Ahlgren et al. (2003)
suggested using the cosine
(Salton and McGill 1983)
as an alternative to the Pearson correlation in bibliometrics.
The computation of diversity is computationally intensive because of the permutation of
the i and j parameters along the vector in each case. A routine for generating diversity
values on the basis of a Pajek file is provided in the Appendix. Note that pi and pj along a
vector can both be larger than zero, but the cosine between the vectors i and j in the same
direction may be zero. For example, if a journal n is cited by two marginal journals (i = 5
and j = 6 in Fig. 1), the co-occurrence in the vertical direction is larger than zero; but in
the horizontal direction the cosine value can be zero and the distance therefore one. The
cosine values between marginal journals may thus boost diversity as measured here.
(Given the skew in scientometric distributions, one can expect relative marginality to
prevail in any delineated domain.)
The full set of 11,365 journals in JCR 2015
Table 3 lists the top-25 journals when ranked for betweenness, valued betweenness, and
diversity measured as 2D3 in both the citing and cited directions. Not surprisingly, PLOS
ONE ranks highest on BC in both the binary and the valued case. The Pearson correlation
for the two rankings across the file is larger than .99 (Table 4), but differences at the top of
the list are sometimes considerable. PLOS ONE and, for example, Psychol Bull gain in
score when BC is based on values, but Nature and Science lose.
Interestingly, Scientometrics ranks 11th on BC in the binary case, but only in the 15th
place using valued BC. Typically, this journal cites and is cited by journals in other fields
incidentally and unsystematically in addition to more dense citation in its own intellectual
environment. Citations to and from Psychol Bull in contrast are more specific. Annu Rev
Psychol and Psychol Rev show the same pattern as Psychol Bull of increasing BC when
Most of the journals with high BC values are multi-disciplinary journals. In accordance
with its definition, BC measures the extent to which the distance between otherwise
potentially distant clusters is bridged. Note that some journals in the social sciences score
high on BC, among which is Scientometrics. In our opinion, Scientometrics can be
considered as a specialist journal with a specific disciplinary orientation. As noted, however,
its citation patterns and being cited patterns span across different disciplines because a
variety of disciplines can be the subject of study and indicators are used in other fields. In
other words, BC does not teach us about the nature of the knowledge production process,
but about patterns of integration and diffusion across disciplinary boundaries
et al. 2017, in preparation)
Table 4 shows that BC and 2D3 measure different things. Diversity in the citing
direction is not correlated to BC. In the cited direction the rank-order correlation is still
6 A transformation to a measure between zero and one could be (1 - 1/N) leading to a distance of
case of a distance of two and 0.67 in the case of three.
substantial. This correlation can be explained as follows: the disparity factor (dij) indicates
the distances that have to be bridged between different domains. The (multi-disciplinary)
structure of science is reflected in both this distance and BC. However, variety
[P ijði6¼jÞ pipj]—as the second component of diversity—is based on a different principle. In
the citing dimension, particularly, one may cite across disciplinary boundaries
(‘‘transdisciplinarily’’; Gibbons et al. 1994)
and generate variety. This source of variation is also
reflected in the cited dimension, since the cited can be considered as the archive of a
timeseries of citing relations. Not incidentally, therefore, we find journals in the right-most
column of Table 3 from the periphery, or with a specific national background that may be
problem- or sector-oriented (e.g., agriculture).
Leydesdorff and Bihui (2005)
found such a
non-disciplinary orientation in the case of Chinese journals that are institutionally based.
The Journal of the Chinese Institute of Engineering (with 2D3 = 20.13 at the top of this
list), for example, was cited in 2015 in articles published in 56 journals, but it cites from
230 journals. It can therefore be considered a net importer of knowledge
(Yan et al. 2013)
Figure 2 shows this environment of 230 journals as a map based on aggregated citation
relations. Using BC as the values for the nodes, Fig. 2a first shows the structure of the
journals as a map. In Fig. 2b, diversity in the citing direction is used as the parameter for
the node sizes. This brings engineering journals more to the fore then physics journals. The
J Chin Inst Eng itself is not visible in Fig. 2a, but most pronouncedly in Fig. 2b. Note that
there is further nothing special about this journal: its 2-year Journal Impact Factor (JIF) is
.246 and the 5-year JIF is .259.
Journals in the social sciences
The largest subset of journals distinguished in the decomposition (Table 2) is a group of
3274 journals in the social sciences. We pursue the analysis for this subset in order to see
whether the patterns found above can be considered general. In a next section we zoom
further into the subset of journals classified as LIS within this set.
Table 5 shows that Soc Sci Med is ranked highest in terms of BC in both the valued and
non-valued analysis. This journal was ranked in the third position in the full set—after
PLOS ONE and PNAS. The rank of Scientometrics has now decreased from the 11th to the
21st position using non-valued BC and from the 15th to the 31st position using valued BC.
A large proportion of its betweenness is in connecting social science disciplines with the
natural and medical sciences. These relations across disciplinary divides are cut by the
decomposition (Table 6).
ivn i-aTw lsae -cS ita nE
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The pattern described above for the full set is also found in this subset. Two factors
explain 78.6% of the variance in the four variables: BC versus the variation-factor in the
diversity citing (Table 7). The Pearson correlations between BC (binary and valued) and
2D3 citing are .010 and .008, respectively. Note the negative sign of 2D3 citing on factor 1
in Table 7. The two mechanisms thus stand orthogonally.
The journals in the right-most column of Table 6 are recognizably trans-disciplinary or,
in other words, reaching out across boundaries. On the cited side, the pronounced position
of sociology journals is noteworthy. Major sociology journals such as Am J Sociol, Brit J
Sociol, and Am Sociol Rev figure in this top list as they did in Table 3, but other sociology
journals such as Soc Sci Inform also rank high on this list (#9), while this journal was
ranked only at position 1363 in the total set.
In Fig. 3, we try to capture the differences visually. Figure 3a first provides a map of
these 3274 journals. In Fig. 3b, the node sizes are proportional to the BC scores of the
journals. One can see a shift to the applied side. For example, the Am Rev Econ comes to
the foreground in the left-most cluster (pink) in Fig. 3a, while this most-pronounced
position is assumed by Appl Econ and World Dev in Fig. 3b. Similarly, J Pers Soc
Psychology—the flagship of this field—is overshadowed by Psych Bull in the top-right cluster
(turkois) of Fig. 3b. This journal is also read outside the specialty. The J Bus Ethics is most
pronounced in terms of BC values among the business and management journals in the
light-blue cluster top-left.
In Fig. 3c, the node sizes are proportional to the diversity scores (citing). The picture
teaches us that highly diverse journals are spread across the disciplines as variation. All
disciplines have portfolios of journals of which some are more diverse than others.
Library and information sciences (LIS)
We first pursued the analysis using the 62 journals that were classified as LIS, but for
reasons of presentation, here we use the results of the analysis based on citations among the
86 journals classified in terms of SC as LIS in the JCR 2015. Otherwise, the discussion
about the differences between the two samples would lead us away from the objectives of
(cf. Leydesdorff et al. 2017)
In Table 8, Scientometrics is the journal with the highest BC in both analyses. JASIST
follows at only the 12th position, while one would expect the latter journal to be more
integrative among the different subjects studied in LIS. In terms of knowledge integration
indicated as diversity in the citing dimension, JASIST assumes the third position and
Scientometrics trails in 45th position. In the cited dimension, the diversity of
Scientometrics is ranked 70 (among 86). Thus, the journal is cited in this environment much more
specifically than in the larger context of all the journals included in the JCR, where it
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assumed the 339th and 6246th position among 11,359 observations, respectively. In the
latter case the quantile values are 97.0 and 45.0, respectively, versus 47.7 and 7.0 in the
smaller set of LIS journals (Table 10).
In this much smaller set, the diversity in the citing dimension is significantly correlated
to BC (Table 9). In other words, citing behavior is more specific at the specialty level. The
socio-cognitive structure of the field guides the variation. Table 10 shows the values of
diversity in the case of Scientometrics at the three levels, respectively. Diversity is larger in
** Correlation is significant at the 0.01 level (2-tailed)
* Correlation is significant at the 0.05 level (2-tailed)
Table 7 Varimax rotated factor
solution for the four variables;
n = 3264
Extraction method: Principal
component analysis. Rotation
method: Varimax with Kaiser
Rotated component matrix
the citing than cited dimension at the level of the full set. Limitation to the social sciences
leads to losing citation in the citing dimension more than in the cited. As a consequence,
diversity is larger in the cited than citing dimension at this level. Being at the edge of the
LIS set, the journal cites more than it is cited by other journals in this set.
In sum, diversity is dependent on the delineations of the sample in which it is measured.
Decomposition of the diversity
In a next step we decompose the LIS set of 86 journals (Table 11). Three journals
(Econtent, Restauror, and Z Bibl Bibl) are not part of the large component, and therefore
not included in this decomposition. Using VOSviewer, six groups are distinguished, of
which one contains only a single journal (Soc Sci Inform). Figure 4 shows this map. Mean
diversity values with standard errors for the five groups decomposed as sub-matrices are
provided in Fig. 5.
Based on the post hoc Tukey test, two homogenous groups are distinguished in the
citing dimension: library science and bibliometrics with relatively high citing scores, on
the one side, and the other three with significantly lower scores, on the other. However, the
distinction is not significant. In the cited direction, the entire set is statistically
Within the subsets, however, the diversity scores are based on sub-matrices with
corresponding cosine values. Table 12 provides the diversity values when all cell values are
normalized in terms of the grand matrix. The difference between the total diversity and the
sum of the within-group diversities is then by definition equal to the between-group
diversity. Using the Tukey test with this design between-group diversity is significantly
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** Correlation is significant at the 0.01 level (2-tailed)
* Correlation is significant at the 0.05 level (2-tailed)
different from diversity in all the subsets with the exception of citing diversity in the subset
of 19 journals labeled as ‘‘information science.’’ Both cited and citing, ‘‘information
science’’ and ‘‘library science’’ are considered as homogenous with between-group diversity.
The other three specialism are considered as significantly different.
Note that the total diversity is generated in a matrix of 82 times 81 or 6642 cells,
whereas the within-group diversity is generated in subsets which add up to 1648 cells
(24.8%).7 In other words, diversity is concentrated in these groupings since they generate
in 24.8% of the cells (100–53.3 =) 46.7% and (100–58.1 =) 41.9% of the total diversity in
the cited and citing directions, respectively.
Diffusion and integration
Bibliographic coupling among diverse sources by a citing unit has been considered as
(Wagner et al. 2011)
, whereas co-citation can be considered conversely as
(Rousseau et al. 2017, in preparation)
. Using the concepts of integration and
diffusion of knowledge for citing and cited diversity, however, one can directly draw
diffusion and integration networks by extracting the k = 1 neighbourhoods; for example in
Pajek. Figure 6a, b provide these networks for the journal Scientometrics in the LIS set
(JCR 2015) as an example: 38 journals constitute the diffusion network (Fig. 6a) and 51
the knowledge integration network (Fig. 6b).
For example, Fig. 6b shows that the Journal of the American Society for Information
Science and Technology plays a central role in the knowledge integration network. Articles
7 (32 9 31) ? (19 9 18) ? (14 9 13) ? (10 9 9) ? (7 9 6) = 1648 cells.
Fig. 5 Average 2D3 cited and citing for five subgroups of LIS journals (error bars with standard errors)
in this journal are cited in Scientometrics; but only the Journal of the Assocation for
Information Science and Technology—the current name of the same journal—is visible in
the diffusion network (Fig. 6a). Note that this analysis was pursued within the LIS set of 86
journals. Other journals outside the LIS field (e.g., Research Policy) are also important in
the citation environment of Scientometrics.
Conclusions and discussion
Using journals as units of analysis, we addressed the question of whether interdisciplinarity
can be measured in terms of betweenness centrality or diversity as indicators. We tried to
pursue these ideas in considerable detail. It seems to us that the problem of measuring
interdisciplinarity, however, remains unsolved because of the fluidity of the term
‘‘interdisciplinarity.’’ The very concept means different things in policy discourse and in science
studies. From a scientometric perspective, interdisciplinarity is difficult to define if there is
no operational definition of the disciplines. The latter problem, however, has remained an
unsolved problem in bibliometrics.
Bibliometricians often use the WoS Subject Categories as a proxy for disciplines, but
these categories are pragmatic
(e.g., Pudovkin and Garfield 2002; Leydesdorff and
Bornmann 2016; Rafols and Leydesdorff 2009)
. In this study, we build on the statistical
decomposition of the JCR data using VOSviewer
(Leydesdorff et al. 2017)
. The advantage
of this approach is that the two problems—of decomposition and interdisciplinarity—are
Our main conclusions are:
The analysis at different levels of aggregation teaches us that BC can be considered as a
measure of multi-disciplinarity more than interdisciplinarity. Valued BC improves on
binary BC because citation networks are valued; marginal links should not be
considered equal to central ones.
Diversity in the citing dimension is very different (and statistically independent) from
BC: it can also indicate non- or trans-disciplinarity. In local and applicational contexts,
for example, the disciplinary origin of knowledge contributions may be irrelevant. In
specialist contexts, however, citing diversity is coupled to the intellectual structures in
the set(s) under study.
Diversity in the cited dimension may come closest to an understanding of
interdisciplinarity as a trade-off between structural selection and stochastic variation.
Despite the absence of ‘‘balance’’—the third element in
Rafols and Meyer’s (2010)
definition of interdisciplinarity—Rao-Stirling ‘‘diversity’’ is often used as an indicator
of interdisciplinarity; but it remains only an indicator of diversity.
The bibliographic coupling by citation of diverse contributions in a citing article has
been considered as knowledge integration
(Wagner et al. 2011; Rousseau et al. 2017)
Analogously, but with the opposite direction in the arrows, diversity in co-citation can
be considered as diffusion across domains. Using an example, we have demonstrated
how these concepts can be elaborated into integration and diffusion networks.
The sigma (R) in the formula (Eq. 2) makes it possible to distinguish between
withingroup and between-group diversity. In this respect, the diversity measure is as flexible
as Shannon entropy measures (Theil 1972). Differences in diversity can be tested for
statistical significance using Bonferroni correction ex post. Homogenous and
nonhomogenous (sub)sets can thus be distinguished.
In other words, the problems of measurement could be solved to the extent that a
general routine for generating diversity scores from networks is provided (see the
Appendix). However, the interpretation of diversity as interdisciplinarity remains the
problem. Diversity is very sensititive to the delineation of the sample; but is this also the
case for interdisciplinarity? Is interdisciplinarity an intrinsic characteristic or can it only be
defined (as more or less interdisciplinarity) in relation to a distribution?
We focused on journals in this study, but our arguments are not journal-specific. Some
units of analysis, such as universities, are almost by definition multi-disciplinary or
nondisciplinary. Non-disciplinarity can also be called ‘‘trans-disciplinary’’
(Gibbons et al.
. However, the semantic proliferation of Greek and Latin
propositions—meta-disciplinary, epi-disciplinary, etc.—does not solve the problem of the operationalization of
disciplinarity and then also interdisciplinarity.
In summary, we conclude that multi-disciplinarity is a clear concept that can be
operationalized. Knowledge integration and diffusion refer to diversity, but not necessarily
to interdisciplinarity. Diversity can flexibly be measured, but the score is dependent on the
system of reference. We submit that a conceptualization in terms of variation and selection
may prove more fruitful. For example, one can easily understand that variation is generated
when different sources are cited, but to consider this variation as interdisciplinary
knowledge integration is at best metaphorical.
Given this state of the art, policy analysts seeking measures to assess interdisciplinarity
can be advised to specify first the relevant contexts, such as journal sets, comparable
departments, etc. Networks in these environments can be evaluated in terms of BC and
diversity. The routine provided in the Appendix may serve for the latter purpose and
network analysis programs can be used for measuring BC. (When the network can be
measured at the interval scale, one is advised to use valued BC.) The arguments provided
in this study may be helpful for the interpretation of the results; for example, by specifying
Acknowledgements We thank Wouter de Nooy for advice and are grateful to Thomson Reuters for JCR
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0
International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution,
and reproduction in any medium, provided you give appropriate credit to the original author(s) and the
source, provide a link to the Creative Commons license, and indicate if changes were made.
Appendix: A routine for the measurement of diversity in networks
The routine net2rao.exe—available at http://www.leydesdorff.net/software/diversity/
net2rao.exe—reads a network in the Pajek format (.net) and generates the files rao1.dbf
and rao2.dbf. Rao1.dbf contains diversity values for each of the rows (named here ‘‘cited’’)
and each of the columns (named ‘‘citing’’). Rao2.dbf is needed for the computation of cell
values (see here below).
The input file is preferentially saved by Pajek so that the format is consistent. Use the
standard edge-format. The user is first prompted for the name of this .net-file. The output
contains the values of both Rao-Stirling diversity and so-called ‘‘true’’ diversity
‘‘Zhang_ting’’ in the citing direction and ‘‘Zhang_ted’’ in the cited one; see Zhang et al.
2016; cf. Jost 2006)
By changing the default ‘‘No’’ into ‘‘Yes,’’ one can make the program write two files,
labeled res_ting and res_ted, containing detailed information for each pass. These files can
be used for detailed decompositions. However, the files may grow rapidly in size
([ 1 GB). All files are overwritten in later runs; one is advised to save them under other
names or in other folders.
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