# Author Multidisciplinarity and Disciplinary Roles in Field of Study Networks

EEoghan Cunningham  BBarry Smyth  DDerek Greene  School of Computer Science,
University College Dublin, Ireland  Insight Centre for Data Analytics,
University College Dublin, Ireland

###### Abstract

When studying large research corpora, “distant reading” methods are vital to
understand the topics and trends in the corresponding research space. In
particular, given the recognised benefits of multidisciplinary research, it
may be important to map schools or communities of diverse research topics, and
to understand the multidisciplinary role that topics play within and between
these communities. This work proposes Field of Study (FoS) networks as a novel
network representation for use in scientometric analysis. We describe the
formation of FoS networks, which relate research topics according to the
authors who publish in them, from corpora of articles in which fields of study
can be identified. FoS networks are particularly useful for the distant
reading of large datasets of research papers when analysed through the lens of
exploring multidisciplinary science. In an evolving scientific landscape,
modular communities in FoS networks offer an alternative categorisation
strategy for research topics and sub-disciplines, when compared to traditional
prescribed discipline classification schemes. Furthermore, structural role
analysis of FoS networks can highlight important characteristics of topics in
such communities. To support this, we present two case studies which explore
multidisciplinary research in corpora of varying size and scope; namely, 6,323
articles relating to network science research and 4,184,011 articles relating
to research on the COVID-19-pandemic.

Network analysis,

Scientometrics,

Multidisciplinarity,

###### keywords:

Research

##  1 Introduction

With the increased recognition of the benefits of multidisciplinary and
interdisciplinary collaboration [1, 2], a trend has recently been established
towards greater levels of interdisciplinary research [3]. A common approach
for understanding these research processes is through the lens of network
analysis. For instance, given a corpus of research papers and their associated
metadata, we can construct a variety of network representations to reveal
different aspects of the underlying data, such as co-authorship networks [4,
5], citation networks [6], and co-citation networks [7]. These different
representations can help us to identify collaboration patterns between
individual researchers at a micro level. In other cases we might be more
interested in examining collaboration patterns between researchers coming from
different disciplines at the macro level. For example, we might wish to study
how these patterns evolve over time in response to a changing research funding
landscape or impactful exogenous events, such as the COVID-19 pandemic.

In this work, we propose a practical “distant reading” approach to help reveal
collaboration patterns in large scientific corpora in order to understand
better the nature and implications of these patterns. Distant reading has been
used in other contexts, such as digital humanities, as a means of exploring
large volumes of data from a macro level view, in order to identify specific
areas of interest for closer examination [8]. As the core contribution of this
work, we present a novel graph representation, referred to as the _Field of
Study_ (FoS) network, which facilitates the investigation of multidisciplinary
and interdisciplinary research in corpora of scientific research articles at
the macro level. A key aspect of field of study networks is the use of author-
topic relations. Specifically, a FoS network is populated by fields of study
(or research topics), which are related to one another according to the
authors who publish in them. In Section 3 we describe how these networks can
be constructed from the topics/fields of study that have been assigned to
research papers. Later in Section 4 we describe two cases studies, which
analyse the FoS networks arising from datasets of differing scope and size.
The first case study in Section 4.1 relates to multidisciplinary research in
the area of applied network science, while the second study in Section 4.2
pertains to the changing nature of author multidisciplinarity in response to
the COVID-19 pandemic. These case studies demonstrate that FoS networks can
provide a useful tool for the distant reading of large collections of research
articles. In particular, we show how simple characteristics computed on a FoS
network can highlight important topics in the research corpus. Further, we use
community detection methods to identify specific multidisciplinary schools
within a larger body of research, and we conduct a ‘role analysis’ of the
topics within these communities to understand the role that they play in
multidisciplinary collaborations. Crucially, we demonstrate our methods using
datasets or varying size and scope, and, finally, we discuss some techniques
that may be employed to drill-down on interesting interactions in the graph
for further “close-reading”.

##  2 Related Work

While a range of different definitions exist for _multidisciplinary research_
, it is most commonly characterised as work which draws on expertise, data or
methodology from two or more distinct disciplines. Most formal definitions
distinguish _interdisciplinary_ research as an extension of multidisciplinary
research, which involves the _integration_ of methods from the contributing
disciplines [9]. There are numerous analyses which have explored multi- or
interdisciplinary research, and investigated the relationship between
different scientific disciplines. Many of these studies proposed metrics to
quantify research interdisciplinarity, either at the author or at the paper
level [10, 11], often in order to investigate a correlation between
interdisciplinarity and research impact [1, 2], productivity or visibility
[12]. Typically, works which integrate methods and ideas from a diverse set of
disciplines are found to have greater research impact and visibility compared
to those that do not [2, 12]. Notably, there are several examples of works
which have investigated cross-disciplinary collaboration, often drawing on
representations and methods from network science [4, 6, 13, 14, 15].

Most frequently, _co-authorship networks_ have been used as a means of
representing the collaborations between different researchers, both in small-
scale studies and when analysing large-scale bibliographic collections [16].
In this type of network, researchers are represented by nodes and
collaborations (i.e., articles jointly authored by a pair of researchers) are
encoded by the undirected edges between them. Thus, research teams are
identified as fully-connected components of the graph. In cases where research
backgrounds can be identified among the authors in the network, this can be
used to measure the extent to which authors engage in multidisciplinary
collaborations. The analysis of co-authorship networks has often revealed a
strong disciplinary homophily between researchers, despite the fact that those
with diverse neighbourhoods in these networks tend to have a higher level of
research impact [4].

Another common representation used to investigate interdisciplinary research
is the _citation network_ , which is typically constructed at the article or
journal level [17]. Analyses of citation networks can highlight influential or
“disruptive” articles in interdisciplinary research [13], as well as
“boundary” papers which span multiple disciplines [6]. Indeed community
finding approaches have been employed to automatically group articles in
citation networks into their respective fields of study [14], so that
interdisciplinary interactions can then be explored at the macro level.

An alternative strategy for analysing research collections is to apply text
mining to article abstracts or full-texts in order to group articles together
which relate to similar research themes, using techniques such as document
clustering or topic modelling [14, 15, 18]. This is typically based on word
co-occurrence patterns, rather than based on article citation patterns. Of
course, the patterns which emerge from textual analysis can be quite different
from those generated using network-based approaches, as fields of study which
are distant in their authorship or citation representations may still
potentially be closely linked semantically.

Here we propose an alternative network representation, which relates fields of
study according to the authors who typically publish in those fields. This
kind of network may be used in conjunction with more conventional network
representations — in much the same way that semantic networks have been shown
to complement citation networks [14]. However, later in Section 4.2 we show
that, on their own, FoS networks can provide an effective means of exploring
large scientific collections, particularly in revealing aspects around author
multidisciplinarity.

##  3 Methods

In this section we formalise the definition of a Field of Study (FoS) network
and explain how such a network can be generated from existing research
resources. In Sections 3.2 and 3.3 we describe two FoS variations: the
_static_ FoS network and the _temporal_ FoS network respectively.

###  3.1 Field of Study Networks

Formally, a _Field of Study_ network is defined as a general graph
representation of a collection of research articles ($R$), written by a set of
authors ($A$), and denoted $F=(N,E)$. The nodes ($N$) represent identifiable
research topics (i.e. the fields of study) and the edges ($E$) represent
authorship relations between pairs of topics. These relations are aggregated
across multiple associated research papers. Below we describe how a FoS
network can be constructed from a more conventional authorship graph and we
argue that FoS networks are particularly well-suited to analysing the nature
of collaboration within the scientific literature, especially as they relate
scientific fields of study according to the researchers/authors who publish in
them.

The formation of a FoS network depends on the availability of appropriate
fields of study labels for a given set of research papers. These could be
derived via manual annotations by domain experts, the application of automated
text mining methods, or some combination of the two. For instance, topic
modelling techniques have been shown to be successful in extracting research
topics from corpora of research articles and assigning papers to those fields
[15, 19].

In fact, many research databases and search engines employ these techniques
(or manual classification) to assign articles or academic journals to fields
of study. For example, the Microsoft Academic Graph
(MAG)111https://www.microsoft.com/en-us/research/project/microsoft-academic-
graph/ maintains a deep hierarchy of _Fields of Study_ which they assign to
papers; Web of Science
(WOS)222https://clarivate.com/webofsciencegroup/solutions/web-of-science/
group journals in 258 _Subject Categories_ ;
Scopus333https://www.scopus.com/home.uri employs experts to assign _All
Science Journal Classification (ASJC)_ codes to all journals covered by their
index. For the purpose of the case studies described later in Section 4, we
use MAG fields of study to categorise research papers and construct FoS
networks. The deep MAG field of study hierarchy is desirable as it supports
the construction of FoS networks at varying levels of detail, from the
broadest research disciplines (level 0) to the specific topics and sub-topics
that exist within a particular discipline (levels 4 and 5).

It is important to note that the Microsoft Academic Graph may not always be an
appropriate source for field of study data. For instance, the corpus does not
provide full coverage of all research disciplines and the corresponding
hierarchy of fields may contain some spurious connections due to its size and
the semi-automated nature of its construction. However, the methods that we
propose are not specific to the MAG hierarchy. Rather, they are agnostic in
the sense that they are designed to generalise to any case where fields of
study can be identified at an appropriate level of detail.

###  3.2 Static FoS Networks

The formation of a static FoS network from a collection of research articles
is best described as the two-step process illustrated in Figure 1. In the
first step, an unweighted bipartite graph is generated from identifiable
fields of study and their contributing authors; see Figure 1(a). In the second
step, this graph is used to generate a projection (the FoS Network) in which a
weighted undirected edge exists between two fields if and only if at least one
author has published research in both fields; see Equation 1 for all $a\in A$,
where $N$ is the set of fields identifiable in $R$. The resulting edge weights
correspond to the number of such authors who publish in both fields (Equation
2).

$E=\big{\\{}(n_{i},n_{j})~{}:~{}published(a,n_{i})~{}\land~{}published(a,n_{j})\big{\\}}$
(1)
$w\big{(}n_{i},n_{j}\big{)}=|\big{\\{}a~{}:~{}published(a,n_{i})~{}\land~{}published(a,n_{j})\big{\\}}|$
(2)

###  3.3 Temporal FoS Networks

It is further possible to encode temporal information in a FoS Network as
_directed_ edges, which allows us to study changes in multidisciplinarity
research patterns over time. Temporal FoS networks can be visualised in a
time-unfolded representation, where the data is divided into a sequence of two
or more discrete _time steps_ , as frequently employed in dynamic network
analysis tasks. Nodes are duplicated for each time step so that authors can be
connected to any fields in which they publish research during a given time
step.

As an example, Figures 2(a) and 2(b) illustrate the two stages in the
formation of a temporal FoS network, showing an instance of a temporal FoS
network with respect to two time-points ($t_{n}$ and $t_{n+1}$) on either side
of some event ($e$); thus $t_{n}<t_{e}<t_{n+1}$). The temporal FoS network in
Figure 2(b) contains a directed edge between two fields $(n_{i},n_{j})$ if an
author published in field $n_{i}$ at time $t_{n}$ (before event $e$) and in
field $n_{j}$ at time $t_{n+1}$ (after event $e$), as given by

$E^{\prime}=\big{\\{}(n_{i},n_{j})~{}:~{}published(a,n_{i},t_{n})~{}\land~{}published(a,n_{j},t_{n+1})\big{\\}}$
(3)

In the next section we present two illustrative examples which demonstrate the
utility of static and temporal FoS representations, as described above.

##  4 Case Studies

In our first case study, presented in Section 4.1, we consider the use of
static FoS networks to explore aspects of multidisciplinary research in the
area of network science. The second case study, described in Section 4.2,
considers the use of both static and temporal FoS networks in the context of a
large-scale dataset of research publications relating to the COVID-19
pandemic.

###  4.1 Multidisciplinary Research in Network Science

Network construction. Firstly, we focus on research published in the journal
Applied Network Science (ANS)444https://appliednetsci.springeropen.com, to use
as a smaller case study with which we can highlight our methods. We choose ANS
as it is a journal with multidisciplinary implications, and we consider the
year 2019 as the period with the best coverage in our data source. Figure 3
presents two resulting static FoS networks, which we create to explore author
multidisciplinarity in our data. These networks are produced using Microsoft
Academic Graph metadata for 6,323 research articles. This set of articles
represents 131 papers published in the journal Applied Network Science,
supplemented by any additional research published by the same authors in the
three years prior (2016-2018 inclusive). We use MAG _fields of study_ metadata
to categorise these research papers. The MAG uses hierarchical topic modelling
to identify and assign research topics to individual papers, each of which
represents a specific field of study [20]. To produce a more useful
categorisation of articles, we consider only those topics at the first two
levels of the MAG hierarchy:

  1. 1.

The 19 field labels at level 0, which we refer to as ‘disciplines’.

  2. 2.

The 292 field labels at level 1, which we refer to as ‘sub-disciplines’

Thus, each article is associated with at least one discipline (e.g.
‘Medicine’, ‘Physics’, ‘Engineering’) and at least one sub-discipline (e.g.
‘Virology’, ‘Particle Physics’, ‘Electronic Engineering’). Note some MAG sub-
disciplines belong to more than one discipline. For example, ‘Biochemistry’ is
a child of both ‘Chemistry’ and ‘Biology’.

To center the FoS networks in Applied Network Science research, we include
only those edges that originate from ANS papers. We apply weight thresholding
to represent the FoS network as unweighted graphs. All analysis is completed
on the unweighted graph produced with threshold 5 (the mean edge weight in the
weighted network). In order to provide the clearest visualisations, we further
prune the networks with threshold 10 before plotting. Figure 3(a) illustrates
the resulting FoS network when network science articles are categorised at the
_discipline_ level. Each node (or discipline) in this FoS network can then be
decomposed into its _sub-disciplines_ , as shown in Figure 3(b).

Network characterisation. From Figure 3, we can begin to understand the
multidisciplinarity of authors publishing in Applied Network Science, as the
nodes represent a diverse set of sub-disciplines, coloured according to their
parent-disciplines. Highly central in Figure 3(b) are the fields which
represent the technical and methodological foundations of network science
research. Sub-disciplines of Mathematics and Computer Science, such as
‘Theoretical Computer Science’ and ‘Topology’, have high degree centrality
(ranked 1st and 4th respectively), because they are identified across the
majority of network science research papers. Modern network science methods,
such as ‘Artificial Intelligence’, ‘Machine Learning’ and applications, such
as ‘Information Retrieval’, have similarly high degree centrality (ranked 2nd,
3rd, and 6th respectively). Some fields beyond the disciplines of Computer
Science and Mathematics, such as ‘Applied Psychology’, ‘Econometrics’, and
‘Neuroscience’ have high betweenness centrality in the FoS Network (ranked
3rd, 5th and 8th, respectively). This is likely because they represent
interdisciplinary applications of network science published by authors who
have backgrounds in other, more distant topics. For example, in the bottom of
Figure 3(b) we can see a group of medical fields which are linked to topics in
Mathematics and Computer Science through ‘Applied Psychology’ and ‘Social
Psychology’.

Community detection. The MAG FoS hierarchy offers one possible definition of
science’s traditional disciplinary taxonomy, grouping fields (or sub-
disciplines) into broader schools of research. We can explore an alternative
categorisation of the topics in the ANS graph by employing community detection
methods. Figure 4 shows the network from Figure 3(b), but with the nodes
colour-coded to show cluster memberships identified using the Louvain method
[21] (with resolution parameter value 1.0). This technique identified 7
clusters which maximise modularity in the graph, and group topics according to
authorship relations. Table 1 provides descriptive statistics for the
communities. Such communities represent multidisciplinary clusters of fields
across which authors – in particular, those authors who contributed to ANS in
2019– are likely to publish. Louvain found clusters containing as few as 2,
and as many as 26 topics. Broadly, the clusters can be categorised as: (i)
central applied network science topics and applications (ii) networks in
machine learning and neuroscience, (iii) psychology, biology and medicine,
(iv) mathematics, statistics and natural language processing, (v) product
development and process management, (vi) physics and economics, (vii)
transport networks and microeconomics.

Role analysis. In addition to categorising ANS-related topics according to (i)
a traditional disciplinary hierarchy (Figure 3(b)), and (ii) author-related
communities (Figure 4), it is also possible to group fields according to the
“role” they play within the Field of Study network. Using the popular
_struc2vec_ algorithm [22], we learn dense vector representations for the
fields in the FoS network, which preserve _structural equivalence_ between
nodes. That is, nodes having similar structural features in the graph will
have similar representations (commonly known as their role embedding) [23]. We
then cluster the embedding space to identify a discrete set of disciplinary
roles. Figure 5 illustrates the role assignments learned in the ANS graph
according to a $k$-means clustering ($k=9$) of struc2vec role embeddings,
where $k=9$ represents the elbow of the curve when silhouette scores are
plotted for clusterings of increasing values of $k$. Table 2 shows the mean
network centrality scores computed for the different clusters such that we can
explain the roles that they represent. Fields in cluster #1 exhibit “hub-like”
behaviour, as they score highly for all centrality measures. For each of the
largest Louvain communities (i.e. excluding communities (v) and (vii)), the
most central node was assigned to role #1. We will refer to these as the
“core” nodes since they represent the fields most commonly identified in ANS
research and are the most central in the FoS graph. Clusters #6, #7, #8 and #9
all represent peripheral/leaf nodes with degree 1 and very low centrality
scores. None of the topics in the peripheral clusters can be identified in ANS
published research. Instead, these topics appear in the 2016–2018 portion of
the data and we refer to them as “distant background” topics.

Clusters #5, #4 and #3 are made up of increasingly prevalent background
topics. Similar to the distant background roles, a majority of the topics in
these clusters never appear in ANS research published in 2019. However, with
greater degree than the more peripheral nodes, topics in clusters #5, #4 and
#3 appear more frequently in author backgrounds. In the particular case of
cluster #3, we identify a set of “ANS-adjacent” disciplines, i.e. the fields
in which ANS authors publish the most readily. Finally, cluster #2 includes
non-core topics that have high degree and betweenness centrality. The set of 9
fields in this cluster are separate to the dense communities at the core of
the graph. Instead topics like ‘Applied Psychology’, ‘Computational Biology’
and ‘Regional Science’ link distant background subjects to the rest of the
network. With all fields in cluster #2 represented in ANS research published
in 2019, we anticipate that the research assigned to these topics offer
multidisciplinary applications of network science research, published by
authors with diverse research backgrounds. The roles identified in clusters
#1, #2 and #6 are apparent in clusterings with 5 $\leq k\leq$ 10 (i.e.,
identical clusters are found for those parameter values).

###  4.2 Author Multidisciplinarity in COVID-19 Research

Field of Study networks generated on yearly data snapshots have been
implemented to quantify author multidisciplinarity, according to the extent to
which authors publish across different disciplines [24, 25]. They show a
stable trend with author multidisciplinarity increasing year-on-year, with a
much larger than expected increase for COVID-19-related research. In
particular, these analyses grouped research topics (sub-disciplines) according
to the MAG disciplinary hierarchy. In the following case study, we explore
richer groupings of COVID-19 related research topics in an FoS network, to
identify modular communities of sub-disciplines, and to explore their
disciplinary roles.

Network construction. Using a large dataset of COVID-19 related research –
COVID-19 Open Research Dataset
(CORD-19)555https://www.semanticscholar.org/cord19 – we identify all authors
who published COVID-19 related research in 2020, and collect MAG metadata for
their COVID-19-related articles, along with any available articles that they
published between 2016 and 2019, inclusive. This result is 4,184,011 articles,
with 166,356 related to COVID-19. We then construct a FoS network using MAG
sub-disciplines identified in the papers. Similar to the ANS example in
Section 4.1, we consider the graph induced by only those edges which originate
in COVID-19 research. That is, we do not consider authorship relations between
the topics in the pre-COVID-19 portion of the data (2016-2019). Again, we
apply thresholding to produce an unweighted graph where edges with weight
greater than or equal to the mean edge weight (50) are preserved.

Community detection. When applied to the COVID-19-related FoS network, the
Louvain [21] method (with resolution 1.0) identifies 7 communities, leaving 42
nodes unassigned to any community. Summary statistics for these communities
are provided in Table 3. Community (i) groups the core topics in Medicine. It
is a dense community with many authors publishing across almost all pairs of
topics. ‘Surgery’, ‘Pathology’ and ‘Radiology’ are the most central fields.
Community (ii) is more multidisciplinary than community (i). In addition to
many medical fields (‘Intensive Care Medicine’, ‘Emergency Medicine’, etc.),
it contains a number of sub-disciplines in Engineering (e.g. ‘Engineering
Management’ and ‘Electrical Engineering’). As such, the authors who link
topics in this community may represent those who tackled the medical emergency
posed by the pandemic and, in particular, the challenges associated with the
massive strain on intensive care units and relevant equipment like
ventilators. Community (iii) clearly demarcates those topics relevant to the
study of the socioeconomic implications of the pandemic. In addition to topics
in Economics, this community links many sub-disciplines of Business and
Sociology (e.g. ‘Financial Systems’ and ‘Demography’).

Topics in Biology, Chemistry, Physics and Engineering are linked in community
(iv). As the largest and least dense of the communities, (iv) represents the
many STEM research areas that are relevant to the study of epidemiology.
‘Virology’, ‘Immunology’, ‘Computational Biology’ and Pharmacology’ are among
the most central sub-disciplines in community (iv). Community (v) contains
topics relevant to Machine Learning and Mathematics and is likely formed as a
result of the sizeable effort to apply machine learning and data science
methods to detecting and tracking the spread of COVID-19 [26]. Finally,
communities (vi) and (vii) represent the smallest and most dense communities
in the FoS network.

The topics in community (vi) relate to studies of the environmental impact of
the COVID-19 pandemic and associated lockdowns, while nodes in community (vii)
are related to ‘Astrophysics’. Further inspection of the sub-disciplines in
community (vii) (‘Astrophysics’, ‘Astronomy’, ‘Classical Mechanics’, and
‘Computer Engineering’) highlights a portion of the CORD-19 dataset that is
unrelated to the COVID-19 pandemic. We believe these papers were included in
the collection in error. The modular FoS communities represent groups of
topics which are strongly related according to the authors who publish in
them. As such, these communities highlight the different schools/disciplines
which emerged in COVID-19 research, together with the different research
backgrounds and expertise with which authors contributed to them. Crucially,
these disciplines offer an alternative classification of sub-disciplines to
the more traditional MAG scheme, highlighting instead a more nuanced,
multidisciplinary set of topics, specific to the pandemic.

Role analysis. We also conduct a role analysis of the topics in the
COVID-19-related FoS network, using the methods described in the ANS case
study above. As before, we identify a discrete set of roles via k-means
clustering of struc2vec role embeddings. We consider an optimal clustering to
be the elbow of the silhouette score curve when plotted for increasing values
of $k$. Consistent with the greater scope of the COVID-19-related dataset
(when compared with that of the ANS dataset), we identify a larger set of
clusters in the COVID-19-related FoS network ($k$ = 21). Statistics for these
clusters are provided in Table 4. Although the clusters appear more numerous
and complex than in the ANS case study, a number of distinct roles are
evident. We now discuss the predominant roles in turn.

The disciplinary hubs in the graph are captured in role #1. ‘Internal
Medicine’, ‘Environmental Health’, ‘Virology’, and ‘Artificial Intelligence’
are clustered in role #1 as the core nodes in the network, with each topic
among the most central nodes in the Louvain communities (ii), (iii), (iv) and
(iv) respectively. Topics in role #4 have high betweenness scores, despite
being outside of the most the central core of the graph (according to
eigenvector centrality). Similar to role #2 in the ANS case study, these
topics likely play a bridging role, linking otherwise disconnected topics to
the rest of the graph. Role #4 contains topics such as ‘Economic Growth’,
‘Algorithm’, ‘Social Psychology’ and ‘Risk Analysis’, which all fall outside
of the scope of virology or epidemiology. These topics occur in
COVID-19-related research that is published by authors with research
backgrounds that are more peripheral in the graph. We hypothesise that topics
attributed to this bridging role occur in multidisciplinary applications of
one or more fields to a external problem. A similar bridging role may be
described by role #9, which has high betweenness centrality (ranked 4th), but
relatively low eigenvector centrality (ranked 9th). With lower eigenvector
centrality, it is unlikely that nodes in role #9 are adjacent to highly
central topics in the graph and, as such, likely represent more peripheral
“bridging” disciplines. Topics in role #9 are ‘Composite Materials’, ‘Computer
Network’, ‘Atmospheric Sciences’ and ‘Climatology’. The largest cluster in the
graph is role #15. With relatively low degree (mean = 3.2, median = 3) and
greater eigenvector centrality than nodes with similarly low degree, it is
likely that this cluster represents background topics which are adjacent to
two or more of the more central COVID-19-related topics. Although the topics
in this role are quite diverse, the cluster contains many sub-disciplines of
Engineering, Chemistry, and Physics.

Through the role analysis outlined above, it is possible to further categorise
the topics in the FoS graph according to the role they play within and between
the disciplines described by the Louvain clusters. In particular, we identify
those topics that (i) are at the core of the discipline(s) (i.e., hubs), (ii)
represent multidisciplinary applications (i.e., bridges), (iii) are relevant
in the research backgrounds of contributing authors (i.e., leaf or peripheral
nodes).

Close reading. For very large datasets, such as the COVID-19-related research
explored in this case study, it can be difficult to parse FoS network
visualisations. Thus, we rely on computational methods such as community
detection and role analysis to understand the relationship between fields of
study. Such methods describe the network structure and the multidisciplinary
role of the associated research topics as we have shown. Additionally, these
methods can highlight cases of multidisciplinary research which can be
explored in greater detail. For example, Figure 6 presents the FoS subgraph
containing the topics in Louvain community (iii). We highlight these topics as
they represent one of the larger, more multidisciplinary communities that were
identified in COVID-19-related research dataset. This community groups many
topics from the disciplines Medicine, Economics, Psychology, Sociology and
Political Science. The authors who link these topics likely represent those
who contributed research relating to the socioeconomic impact of the pandemic.
Highly central in the subgraph are sub-disciplines of Medicine such as ‘Family
Medicine’ and ‘Gerontology’ (the study of the social, psychological and
biological aspects of ageing), in addition to non-Medical topics like
‘Economic Growth’ and ‘Demography’ (the statistical study of populations).

Many topics from Psychology and Economics are present in the more peripheral
nodes in the graph, as are sub-disciplines of Mathematics and Computer Science
(e.g. ‘Internet Privacy’ and ‘Statistics’) and even topics from Political
Science (e.g. ‘Public Relations’ and ‘Public Administration’). The FoS
subgraph helps to illustrate the highly diverse school of research that
developed around the study of the socioeconomic impacts of the pandemic. We
can further investigate the multidisciplinary nature of the research in this
subset by using Temporal FoS networks to compare the pre-COVID (2016–2019) and
COVID (COVID-19 related research in 2020) time periods. For example, we might
ask the question – ‘What were the research backgrounds/expertise of the
authors who published COVID-19-related research in the field of Economics?’.

Figure 7 presents COVID-19 related research in the field of Economics, with
pre-COVID nodes on the left (representing the authors’ research backgrounds)
and COVID nodes on the right (representing the FoS characterisation of the
COVID related research). To highlight the strongest trends that exist, the FoS
network shows only the top-30 edges by weight prior to thresholding. The
multidisciplinary nature of this research subset is apparent in the diverse
set of topics illustrated on the left hand side of the plot. In accordance
with the broad spectrum of factors (social, political and economic) which
influenced economic growth during the pandemic, we identify many authors who
have published previously in sociology, psychology and political science in
the graph. Additionally, those topics which may have useful, transferable
skills such as ‘Statistics’ and ‘Data Science’ are also found to contribute.

To conduct further close reading, we can filter the list of articles by
considering only those papers that contribute a particular edge to the FoS
network. For example, we can search for COVID-related papers which result in
the edge between ‘Social Psychology’ and ‘Economic Growth’. These will
correspond to COVID-related articles containing the topic ‘Economic Growth’,
in which the authors have previously published research in the field of social
psychology. To better understand the papers in this subset, we can explore the
lower-level MAG topics that are most commonly identified amongst them, or the
keywords which occur most frequently in their titles and abstracts.

##  5 Conclusions

In this work we have demonstrated that our proposed Field of Study (FoS)
networks provide a useful means of exploring author multidisciplinarity in a
body of research. The two case studies, provided in Sections 4.1 and 4.2, have
shown the utility of FoS networks for this purpose in mid- ($\approx 6,000$)
and large-sized ($\approx 5,000,000$) research corpora. Modular communities in
FoS networks offer an alternative categorisation strategy for research topics
and sub-disciplines, when compared to traditional prescribed discipline
classification schemes. Such communities represent the broader,
multidisciplinary trends in a body of research, together the different
backgrounds and expertise with which authors contribute to them. Furthermore,
role analysis, using methods such as struc2vec role embeddings, can be
employed to parse the respective roles of topics within and between these
communities. In particular, we have highlighted core and background roles,
which serves to distinguish the central topics in a field from the background
expertise of the authors. In addition, less central topics with high
betweenness centrality may highlight multidisciplinary applications in the
body of research. In the case of very large corpora, visualising FoS networks
can be challenging. As such, in Section 4.2 we have outlined methods for
drilling down to conduct closer reading of research corpora, at greater
detail, using dynamic FoS networks.

There are a number of avenues for potential further research in this area. For
example, in a corpus where full paper texts or abstracts are available, it may
be informative to explore semantic relationships between the fields of study
represented in the network. Similarly, citation information could be used to
explore the flow or diffusion of information between communities. Recent work
in [14] suggests that a multi-dimensional approach, which combines these
methods, may prove to be a useful tool for scientometric analysis.

## Declarations

### Funding

This research was supported by Science Foundation Ireland (SFI) under Grant
Number SFI/12/RC/2289_P2.

### Consent for Publication

Not applicable.

### Availability of data and materials

An archive of the relevant metadata for both case studies will be made
available online before any final publication.

### Ethics approval and consent to participate

Not applicable.

### Competing interests

The authors declare that they have no competing interests.

### Authors’ contributions

EC proposed the methods, implemented the code, and performed the experiments.
EC, DG and BS wrote, read, and approved the manuscript.

### Acknowledgements

Not applicable.

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## Figures

(a)

(b)

Figure 1: The formation of a _static_ Field of Study (FoS) network involving
two steps: (a) creation of a bipartite network of authors and fields; (b)
projection to an _undirected_ network of fields.

(a)

(b)

Figure 2: Illustrative example of a _temporal_ Field of Study (FoS) network,
involving two steps: (a) creation of a bipartite network of authors and
fields; (b) projection to a _directed_ network of fields.

(a) Disciplines or level 0 fields of study.

(b) Sub-disciplines or level 1 fields of study.

Figure 3: FoS Network for research published in related to the journal
“Applied Network Science” during 2016–2019. Node size encodes the number of
papers attributed to a field of study. In (b) nodes are coloured to represent
the parent discipline of the field of study. Edges are coloured to show the
parent discipline if the edge is within a discipline/community. Edges between
communities are not coloured. Figure 4: FoS Network for research published in
related to the journal “Applied Network Science” during 2016–2019. Nodes are
coloured to show clusters identified by Louvain. Figure 5: FoS Network for
research published in related to the journal “Applied Network Science” during
2016–2019. Nodes are coloured to show role assignments according to 9 clusters
generated on _struc2vec_ embeddings. Figure 6: FoS Network for a community of
COVID-19-related research published during 2015–2020. Louvain community (iii).
Nodes are coloured according to their MAG parent discipline. Figure 7:
Temporal FoS Network presenting COVID-19-related research in Economics,
produced from 1,355 COVID-related research papers which were attributed to the
MAG field ‘Economics’.

## Tables

Table 1: Louvain communities in ANS-related research and their size, network density, most central topics (according to degree centrality) and the most frequent MAG disciplines that are identified in them ($\geq 20\%$ of topics). | size | density | most central nodes | MAG disciplines
---|---|---|---|---
(i) | 67 | 0.04 | theoretical computer science | computer science
(ii) | 15 | 0.39 | artificial intelligence, machine learning | computer science
(iii) | 16 | 0.23 | algorithm, applied psychology | medicine, biology
(iv) | 9 | 0.14 | statistical physics, pattern recognition | biology, computer science, medicine
(v) | 11 | 0.04 | process management, food science | physics
(vi) | 18 | 0.14 | econometrics, topology, industrial org | economics, physics
(vii) | 5 | 0.40 | computer network, regional science | economics
Table 2: Roles identified in Applied Network Science Research and their mean network attributes, including centrality scores, cluster size (count), and the proportion of topics in the cluster identified in ANS research (ANS prop). role | degree | betweenness | closeness | eigenvector | ANS prop | count
---|---|---|---|---|---|---
#1 | 28.7 | 0.025 | 0.279 | 0.503 | 1.00 | 15
#2 | 12.2 | 0.014 | 0.223 | 0.171 | 1.00 | 9
#3 | 7.2 | 0.002 | 0.245 | 0.220 | 0.29 | 21
#4 | 2.9 | 0.002 | 0.229 | 0.108 | 0.15 | 27
#5 | 1.7 | 0.000 | 0.187 | 0.038 | 0.10 | 31
#6 | 1.0 | 0.000 | 0.221 | 0.061 | 0.00 | 25
#7 | 1.0 | 0.000 | 0.148 | 0.005 | 0.00 | 4
#8 | 1.0 | 0.000 | 0.159 | 0.011 | 0.17 | 6
#9 | 1.0 | 0.000 | 0.169 | 0.011 | 0.00 | 3
Table 3: Louvain communities in COVID-19-related research and their size, network density, most central topics (according to degree centrality) and the most frequent MAG disciplines that are identified in them ($\geq 10\%$ of topics). | size | density | most central nodes | MAG disciplines
---|---|---|---|---
(i) | 23 | 0.69 | surgery, pathology, radiology | medicine
(ii) | 22 | 0.26 | intensive care medicine, emergency medicine | medicine
(iii) | 70 | 0.30 | public relations, economic growth, demography | economics
(iv) | 82 | 0.18 | virology, nanotechnology, cell biology | biology
(v) | 42 | 0.27 | artificial intelligence, algorithm, data science | computer science, mathematics
(vi) | 5 | 0.90 | atmospheric sciences, climatology | geography
(vii) | 4 | 0.83 | astrophysics, astronomy, classical mechanics | physics, engineering
Table 4: Roles identified in COVID-19 related research and their mean network attributes, including centrality scores and cluster size (count). role | degree | betweenness | closeness | eigenvector | count
---|---|---|---|---|---
#1 | 132.2 | 0.076 | 0.570 | 0.951 | 4
#2 | 112.2 | 0.025 | 0.534 | 0.925 | 5
#3 | 84.3 | 0.005 | 0.495 | 0.811 | 29
#4 | 65.2 | 0.013 | 0.474 | 0.570 | 12
#5 | 49.3 | 0.000 | 0.446 | 0.535 | 24
#6 | 45.5 | 0.003 | 0.437 | 0.418 | 22
#7 | 19.8 | 0.001 | 0.380 | 0.128 | 26
#8 | 15.0 | 0.000 | 0.384 | 0.154 | 21
#9 | 13.5 | 0.006 | 0.384 | 0.074 | 4
#10 | 9.2 | 0.001 | 0.350 | 0.042 | 19
#11 | 8.2 | 0.000 | 0.303 | 0.016 | 4
#12 | 5.8 | 0.000 | 0.324 | 0.031 | 6
#13 | 4.7 | 0.000 | 0.306 | 0.011 | 3
#14 | 3.7 | 0.000 | 0.300 | 0.011 | 3
#15 | 3.2 | 0.000 | 0.329 | 0.036 | 51
#16 | 2.4 | 0.000 | 0.264 | 0.001 | 7
#17 | 2.0 | 0.000 | 0.249 | 0.000 | 2
#18 | 1.0 | 0.000 | 0.306 | 0.007 | 2
#19 | 1.0 | 0.000 | 0.332 | 0.014 | 5
#20 | 1.0 | 0.000 | 0.319 | 0.013 | 2
#21 | 1.0 | 0.000 | 0.323 | 0.013 | 2