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OCR for page 18
Colloquium
Coauthorship networks and patterns of
scientific collaboration
M. E. J. Newman*
Center for the Study of Complex Systems and Department of Physics, University of Michigan, Ann Arbor, Ml 48109
By using data from three bibliographic databases in biology,
physics, and mathematics, respectively, networks are constructed
in which the nodes are scientists, and two scientists are connected
if they have coauthored a paper. We use these networks to answer
a broad variety of questions about collaboration patterns, such as
the numbers of papers authors write, how many people they write
them with, what the typical distance between scientists is through
the network, and how patterns of collaboration vary between
subjects and over time. We also summarize a number of recent
results by other authors on coauthorship patterns.
I t has long been realized that the coauthorship of articles in
~ learned journals provides a window on patterns of collabora-
tion within the academic community. Coauthorship of a paper
can be thought of as documenting a collaboration between two
or more authors, and these collaborations form a "coauthorship
network," such as that depicted in Fig. 1, in which the network
nodes represent authors, and two authors are connected by a line
if they have coauthored one or more papers. The structure of
such networks turns out to reveal many interesting features of
academic communities.
Networks are not new to bibliometrics; the field has a long history
of the study of citation networks (1, 2), the networks formed by the
citations between papers. These are quite distinct, however, from
coauthorship networks; the nodes in a citation network are papers,
not authors, and the links between them are citations, not coau-
thorship. The coauthorship network is as much a network depicting
academic society as it is a network depicting the structure of our
knowledge. And, perhaps because of this, it has received far less
attention than have citation networks. Nonetheless, it has much of
value to tell us, as recent work has shown.
During the l990s (and possibly earlier), a number of authors
pointed out the potential utility of coauthorship data and in
some cases performed small-scale statistical analyses of such
things as frequency of coauthored articles by particular authors
or authors at particular institutions (3-74. But it was with the
advent of comprehensive online bibliographies that construction
of complete or near-complete coauthorship networks for entire
fields became a realistic possibility. Starting around 2000, several
researchers began the construction of large-scale networks rep-
resenting research in mathematics (8-10), biology, physics, and
computer science (11) and neuroscience (10~.
In this paper, we look in detail at three particular networks of
scientific collaborations and describe some of the patterns they
reveal. The networks are:
(i) A network of coauthorships of papers in the Medline
bibliographical database from 1995 to 1999, inclusive. Medline
is a widely used and compendious database of papers covering
biomedical research. Biomedical research accounts for the larg-
est part of civilian scientific research by far, dwarfing research in
all other subjects put together in terms of expenditure. Any study
that excluded biomedicine could not claim to be representative
of science as it is practiced today.
5200-5205 1 PNAS 1 April 6, 2004 1 vol. 101 1 suppl. 1
(ii) A network of coauthorships of physicists assembled from
papers posted on the widely used Physics E-print Archive at
Cornell University (formerly at the Los Alamos National Lab-
oratory) between 1995 and 1999. Physics has led the way in
moving from journal publication to author self-publication in
online preprint databases, with preprint publication largely
replacing journal publication in some subfields. Preprint data-
bases provide a useful source of up-to-the-minute publication
records, although their coverage is less complete than that of
professionally maintained databases like Medline.
(iii) A collaboration network of mathematicians compiled
from databases maintained by the journal Mathematical Reviews.
Of the networks yet studied, this is probably the most complete
and accurate, covering the period from 1940 to the present
without any break.
Networks i and ii were constructed by the author from
bibliographic data supplied by the maintainers of the corre-
sponding databases. Network iii was constructed by J. Grossman
and P. Ion (8) and graciously supplied by J. Grossman.
A number of other papers in this volume describe bibliometric
studies of a database of papers that appeared in PNAS over the
period 1997-2002. Although it would be possible to construct a
coauthorship network from these data, such a network would be
less satisfactory for the study of collaboration patterns than the
networks studied here. Most authors publish in more than one
journal, so that data on publications in a single journal would give
an incomplete picture of their authorship patterns. The data-
bases studied in this paper are more complete, although certainly
they do not claim to document every paper.
The outline of this paper is as follows. In Statistical Properties of
Coauthorship Networks, we describe a variety of results derived from
analysis of our networks and highlight some differences among the
three subjects studied. In Additional Results, we summarize some
recent additional results obtained by using the same or additional
data, induding a number of results due to other authors. In
Conclusion, we give our conclusions. Many of the results reported
here have appeared previously in refs. 11-15, as well as a number
of other papers, which are cited as appropriate.
Statistical Properties of Coauthorship Networks
A summary of the basic statistics of the three networks studied
here is Riven in Table 1. The largest of the networks, not
surprisingly, is the biomedical network, with >1.5 million au-
thors over a 5-year period. Even the mathematics network, which
covers a much longer period (~60 years), comes nowhere close
to this size. Clearly, biology dwarfs other subjects in terms not
only of spending but also of manpower. The number of papers
shows a similar pattern, although we do not have precise data for
This paper results from the Arthur M. Sackler Colloquium of the National Academy of
Sciences, "Mapping Knowiec~ge Domains," held May 9-11, 2003, at the Arnold and Mabel
Beckman Center of the National Acaclemies of Sciences and Engineering in Irvine, CA.
*E-maii: mejn~umich.eclu.
2004 by The National Acaclemy of Sciences of the USA
www.pnas.org/cgi/doi/10.1073/pnas.0307545100
OCR for page 19
, ~ Agent-based
Models
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~ Structure of RNA
Statistical Physics
Fig. 1. An example of a small coauthorship network depicting collaborations
among scientists at a private research institution. Nodes in the network
represent scientists, and a line between two of them indicates they coau-
thored a paper during the period of study. This particular network appears to
divide into a number of subcommunities, as indicated by the shapes of the
nodes, and these subcommunities correspond roughly to topics of research, as
discussed by Girvan and Newman (37).
the number of papers in the mathematics database. "Grossman
(9) cites a figure of "about 1.6 million authored items" in the
Mathematical Reviews database, for a slightly more recent ver-
sion of the network than that studied here.]
The number of papers per author is similar across the three
subject areas, between five and seven in each case. Because the
mathematics database covers a longer time period, however, this
may indicate that mathematicians are producing fewer papers
than their more empirically minded colleagues in the sciences.
Scientific productivity, measured by number of papers authored,
has had a long history of study in bibliometrics, with the articles
by Lotka (16) and Shockley (17) being famous early examples.
Both of these authors found that the number of papers produced
by scientists had a "fat-tailed" distribution, in which a small
number of scientists produced a very large number of papers, a
result that has since been confirmed by others (18, 19), and which
is seen in our own data as well (11, 12~.
The number of authors per paper, by contrast, varies substan-
tially among the subjects studied, with biology having the largest
number and mathematics the smallest. This presumably reflects
real differences in the way research is done in these fields, with
biological research consisting often of work by large groups of
laboratory scientists and mathematics consisting of theoretical
work done primarily by individuals alone or by pairs of collab-
orators. Grossman (9) says that 66% of mathematics papers are
written by a single author (although this number changes over
time; see Additional Results). In the Medline database, the
corresponding figure is 21%. These figures may offer some
explanation for the possible lower productivity of mathematics
in terms of papers published per unit time: with fewer coauthors
Newman
Table 1. Summary statistics for the three coauthorship networks
analyzed here
Biology
Number of authors
Number of papers
Papers per author
Authors per paper
Average collaborators
Largest component
Average distance
Largest distance
Clustering coefficient
Assortativity
1,520,251 52,909
2,163,923 98,502
6.4 5.1
3.75 2.53
18.1 9.7
92% 85%
4.6 5.9
24 20
0.066 0.43
0.13 0.36
Physics Mathematics
253,339
6.9
1.45
3.9
82%
7.6
27
0.15
0.12
The statistics are, from top to bottom, total number of authors appearing in
the corresponding databases; total number of papers appearing; mean number
of papers published by an author; mean number of coauthors on a paper; mean
number of different individuals an author collaborated with; largest connected
group of individuals in the network; mean vertex-vertex distance between
connected individuals in the network; largest such distance; the clustering coef-
ficient, which is the mean probability that two coauthors will also be coauthors
of one another; and the degree assortativity coefficient, which is the Pearson
correlation coefficient of the degrees (i.e., number of collaborators) of adjacent
vertices in the network. The material shown here is after Newman (12) and
Grossman (9).
on most publications, the production of a mathematics paper
involves more work per author.
A similar pattern is revealed in the average number of
collaborators an individual has in the three fields, which is more
than four times higher in biology than in mathematics. This again
is presumably a result of different modes of research, with
biology being primarily experimental, mathematics being en-
tirely theoretical, and physics being a combination of the two.
tThe quintessential example of scientific experiment on an
industrial scale is high-energy physics, for which it was previously
found, using the SPIRES (www.slac.stanford.edu/spires) database
of high-energy physics papers, that authors had an amazing 173
collaborators on average over the 5-year period from 1995 to
1999 (11~]
In addition to mean numbers of papers and coauthors, one can
look at the distributions of these quantities. In Fig. 2, for
instance, we show the distributions of the number of coauthors
that scientists have for the three subjects. The distributions are
quite similar, although the distribution for biomedicine (circles)
u,
o
D 1 04
~0
3
cot
o
o
so
loo
10°
10
In, ,
· ~ I::
i: ~ Id:
i: : ~ : N : ~
: : NK ;N :
lo 0 biology I \\
0 0 physics
mathematics
~ ~~ ~ 1
\~ - is.
.\ . ., ,,,,, , ,~
10 100 1000
number of collaborators k
Fig. 2. Histograms of the distribution of numbers of collaborators for
scientists in each of three fields studied.
PNAS 1 April 6, 2004 1 vol. 101 1 suppl. 1 1 5201
OCR for page 20
has a longer tail, reflecting the higher mean number of collab-
orators that individuals have in that field. In each case, the
distribution is fat-tailed, like the distribution of number of
papers written by scientists mentioned above, with a small
fraction of scientists having a very large number of collaborators,
up to thousands in the case of the biology network. (Recall that
the data for this network cover only a S-year period; publishing
papers with 1,000 coauthors in <2,000 days is an impressive
achievement by any measure.) Unlike some other networks, such
as the World Wide Web and the Internet, however, the distri-
butions for these networks do not follow power laws; they are not
"scale-free networks," in the jargon of the field. It has been
suggested that the distributions are actually power law in form
with an exponential cutoff (9, 11, 20), and this appears to be a
reasonable fit to the data. The cutoff may be produced by the
finite time window used in the study, a hypothesis that could, in
principle, be tested by varying the size of the window, although
we do not do that here.
Table 1 also gives the size of the largest component in each of the
networks. A component is a set of network nodes connected via
coauthorship, such that any node in the set can be reached from any
other by traversing a suitable path of intermediate collaborators.
For each of the networks studied here, the largest component fills
most of the network, occupying 82-92% of the network in the three
cases. Thus a large portion of each of these communities is
connected in a kind of linked research enterprise rather than
working separately in isolation. Overall, this seems a promising
picture; intellectual isolation from the mainstream of one's research
area cannot often be a good thing. Most scientists who do not
belong to the largest component are members of small discon-
nected components containing only a handful of others.
Many recent studies of networks of various types have focused
on network distance between nodes. This distance is defined as
the number of "hops" along links in the network that one needs
to make to move from one given node to another. A pair of
individuals who have coauthored a paper, for instance, are
distance 1 apart, whereas a pair who have not done so but who
share a common coauthor are distance 2 apart, and so forth. In
the late 1950s, Kochen and Pool (21) speculated on mathemat-
ical grounds that networks might show surprisingly small typical
distances between pairs of nodes, and in a famous experiment
some years later, Milgram (22, 23) demonstrated that this was
the case for acquaintance networks, at least in the U.S. Our
coauthorship networks appear to follow the same pattern. We
calculate the distance between all pairs of individuals in a
network using a breadth-first search or "burning" algorithm (24)
and then take the average to give the figures shown in Table 1.
For each of the networks, the result is very small, at least
compared with the size of the network. Mathematics has the
largest mean distance, possibly again as a result of the relative
sparsity of mathematics collaborations, but even its value of 7.6
is tiny compared with the quarter of a million mathematicians in
the network. This appears to indicate a close-knit cohesive
community in which most people are connected not only by some
path through the network but also by a short one.
A certain amount of attention has focused also on the distances
from particular scientists to others in the coauthorship network.
Mathematicians have long discussed the "Erdos number," the
distance through the mathematics network from a given mathe-
matician to Paul Erdos, an influential Hungarian number theorist
of the 20th century who was renowned for his prolific publication
and collaboration. Erdos numbers have been studied in depth by a
number of authors by using the Mathematical Reviews data (8, 9, 25,
26~. It is found, for instance, that the mean distance from Paul
Erdos to other mathematicians is much lower than the mean
distance in the network as a whole, taking a value ~4.7. tMean
distances from other individuals, most of which are significantly
higher than Erdos' mean, are sometimes called "Doe numbers"
5202 1 www.pnas.org/cgi/doi/10.1073/pnas.0307545100
| Newman, M. E. J. |
| Ziff, R. M. ~ "Farmer, J. D. | | Snappy, Al
~ ELI
| Havlin, S.1
| Stanley, H. E. | |Amaral, L. A. N. | 1Cuerno, R. |
| Barabasi, A.-L. |
Fig. 3. The shortest paths through the collaboration network of physics
papers from the author of this paper to A.-L. Barabasi, who also publishes on
networks.
(9~.] The largest distance in a network, which is called the "diam-
eter," is also occasionally of interest; it is between 20 and 30 for each
of the networks studied here.
It is straightforward to create a computer algorithm to find the
shortest path between two particular scientists, again using
breadth-first search, and it has been suggested by Kautz et al. (27)
that such algorithms could be of use for providing "referral
chains," links of acquaintances that individuals could use to
establish contact with other scientists. In the simplest case, for
example, it might be useful to know that one shared a common
collaborator with another scientist if one wished to arrange an
introduction. Note that the shortest path between two individ-
uals need not be unique, and in fact, it happens quite frequently
that there are two or more shortest paths of equal length. Fig. 3
shows shortest paths in the network of the Physics E-print
Archive between the present author and A.-L. Barabasi of the
University of Notre Dame, who also publishes on networks. As
Fig. 3 shows, there are several different paths from one scientist
to the other, all with length four. This particular case is inter-
esting, because it shows that scientists working in the same field
need not be linked through others in their field. The shortest
paths in this case are established via my collaborations with J. D.
Farmer, J. P. Garrahan, K. Sneppen, and R. M. Ziff, only the last
of which collaborations involved work on networks (and then
only peripherally).
Another interesting network measure related to shortest paths
has been suggested by S. H. Strogatz (personal communication),
who asks how many of the shortest paths from a particular
individual to others pass through each of their collaborators. Is it the
case that most of our connections to others are via just one or two
of our best-connected collaborators, or are they distributed evenly
among our collaborators? For the networks studied here, it turns
out that the former is the case, as is evident in Fig. 4, which shows
for the physics network what percentage of shortest paths pass
through each of a scientist's coauthors, on average. Thus, Fig. 4
reveals that on average ~64% of an individual's shortest paths to
others pass through the best-connected of their collaborators, and
most of the remainder pass through the next-best connected. This
may indicate that a small number of scientists are playing the role
of broker for communications among others. (See also the discus-
sion of betweenness centrality in Additional Results.)
Two other quantities of interest, both previously studied for
many networks, are also given in Table 1. The first is the
"clustering coefficient" (28), which measures network "cluster-
ing" or "transitivity," the probability that two of a scientist's
coauthors have themselves coauthored a paper. In topological
terms, it is a measure of the density of triangles in a network, a
Newman
OCR for page 21
0 60
at_
cut
o
5
~ 40
o
ce
~ 20
o
n-
~r _
1 2 3 4 5 6 7 8 9 10
rank of collaborator
Fig. 4. The average percentage of paths from other scientists to a given
scientist that pass through each collaborator of that scientist, ranked in
decreasing order. The plot is for the physics network, although similar results
are found forthe others. [Reproduced with permission from ref. 13 (Copyright
2001, American Physical Society)].
triangle being formed every time two of one's collaborators
collaborate with each other. The clustering coefficient is highest
for physics (43%) and lowest for biology (7%), and it is unclear
why there is so much variation among fields. Presumably the
numbers reflect substantial differences among collaboration
patterns in the sciences, but what these differences are is far from
obvious. Part of the clustering in each network can be accounted
for by papers with three or more coauthors. Such papers
introduce triangles of collaborating authors and hence increase
the clustering coefficient. This effect can account for only about
one-half of the clustering seen in coauthorship networks, how-
ever (29~; the rest must be due to sociological or organizational
effects of some kind.
An alternative way to measure the clustering effect is to look
at the time evolution of a network. Among social networks,
coauthorship networks are unusual in having well-documented
time evolution. Because each paper comes with a date of
publication or submission, we can say approximately when each
connection was added to the network, and so we can reconstruct
the order in which the network grew. This allows us to ask the
probability of two scientists coauthoring a paper, given that they
have a third mutual collaborator and have not collaborated in the
past. By studying only scientists who have not previously collab-
orated, we eliminate any bias introduced by papers with three or
more coauthors. In ref. 14, we showed that scientists with a single
mutual collaborator are ~45 times more likely to coauthor a
paper than those with no mutual collaborators. Those with two
are >100 times as likely to coauthor a paper.
The last line in Table 1 gives the "assortativity coefficient" or
degree correlation for the networks (15~. This is the correlation
coefficient for the number of collaborators that coauthors have.
It lies in the range of -1 to 1, with positive values indicating that
people with many collaborators tend to collaborate with others
who have many collaborators and negative values indicating the
reverse. The coefficient is positive for all networks studied,
indicating that the most gregarious scientists tend to be con-
nected to each other. Again, it is an open question why this
should be the case.
It is also possible to extract from coauthorship data a measure
of the strength of the collaboration between pairs of individuals.
The simplest such measure would be just a count of the
frequency with which two scientists have coauthored papers, the
number of coauthored papers over a given interval, for instance.
However, this fails to take into account the number of other
coauthors on each paper. Presumably two authors who collab-
Newman
'1:5 1
~ + 1 +
3
1
2
11
6
Fig. 5. Authors A and B have coauthored three papers, labeled 1, 2, and 3,
which had, respectively, four, two, and three authors. The tie between A and
B accordingly accrues weight ]/3, 1, and '/2 from the three papers, for a total
weight of ]~/6. [Reproduced with permission from ref. 13 (Copyright 2001,
American Physical Society)].
orate on a 10-author paper are, in general, working less closely
with one another than two who produce a two-author paper with
no other help. To account for this effect, we proposed in ref. 13
the measure of collaboration strength illustrated in Fig. 5. Each
paper coauthored by a given author pair adds an amount
1/(n-1) to the strength of their collaboration, where n is the
total number of authors on the paper. The rationale behind this
choice is that an author divides his/her time between the n-1
other authors with whom he/she works on a paper, and hence the
strength of the connection to each of them varies inversely as
n-1. As an example of this measure, we show in Fig. 6 the
coauthors of G. Barkema, one of the author's most frequent
collaborators, with line thickness used to indicate the strength of
the connections. Clearly, there is considerable variation in
connection strength. Over the entire physics network connec-
tion, strengths range from a maximum of 34.0 to a minimum
of ~0.01.
it). 6, ~ icy
.~ cot
.S An'
|,Q,~ ~
· ha
or
c_
Fig. 6. G. Barkema and collaborators, with lines representing collaborations
whose thickness is proportional to the estimate of collaboration strength
defined in the text and illustrated in Fig. 5.
PNAS 1 April 6, 2004 1 vol. 101 1 suppl. 1 1 5203
OCR for page 22
Additional Results
The network of collaborations of mathematicians compiled by
Grossman and Ion (8) and studied here has also been analyzed
extensively by Grossman and collaborators (8, 9, 25) and by
others (26~. Grossman (9) gives a number of results about the
time evolution of the collaboration network. He notes that the
rate of publication has increased slightly over the last 50 years or
so, but there has been a much more striking increase in the level
of collaboration. From the start of the period covered by the
Mathematical Reviews data in 1940 until the end of the 1950s, less
than one-half of all mathematicians had ever coauthored a paper
with another writer; nowadays, virtually all of them have. Pre-
sumably this trend reflects some combination of changes in the
social organization of the mathematics community, better com-
munications, and possibly changes in the types of problems
studied and approaches used, making modern mathematics more
amenable to collaborative investigation.
The time evolution of coauthorship networks has also been
investigated by the present author (14) and others (10) in the
context of tests of the "preferential attachment" hypothesis. Price
(30) and later Barabasi and Albert (31) have suggested that
networks grow by the addition of connections in such a way that the
probability of an individual gaining a new connection is propor-
tional to the number they already have. Because coauthorship
networks are well time-resolved, as discussed in the preceding
section, one can test this hypothesis by measuring the probability
that a newly published paper contributes new connections to an
individual? as a function of the number of connections that indi-
vidual already has. Refs. 10 and 14 tackle this measurement in
slightly different ways, but both conclude that preferential attach-
ment of an approximately linear variety is indeed taking place in
collaboration networks.
A number of authors have also looked at "betweenness
centrality" in coauthorship networks (13, 32-34~. The between-
ness centrality of a node A in a network is defined to be the
number of shortest paths between other pairs of nodes that pass
through A (35~. It is regarded as a measure of the influence that
individuals have over information flow between others. Individ-
uals who act as brokers for information flow between their
colleagues will have high betweenness scores. In ref. 13, it was
shown that betweenness scores vary widely from one individual
to another in coauthorship networks, with a few having much
higher scores than the majority. Later work by Goh et al. (33)
showed that in fact the distribution of betweenness scores
approximately follows a power law. This appears to indicate that
collaboration networks contain a small number of influential
individuals and many peripheral actors, a conclusion bolstered
by the findings of Holme et al. (32), who showed that collabo-
ration networks are highly susceptible to the removal of the
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(2002) Physica A 311, 590-614.
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5204 1 www.pnas.org/cgi/doi/10.1073/pnas.0307545100
individuals with highest betweenness scores. One need only
remove a few such individuals from the network, it turns out, to
break the connection between others and fracture the network
into disconnected parts. In a recent paper, Goh et al. (34) have
extended their investigation of betweenness to the correlation
between the betweenness scores of collaborators. They find that
there is very little such correlation, implying that influential
scientists are not collaborating preferentially with other influ-
ential scientists to any significant extent; the probability of one's
collaborator having a high betweenness appears not to be
significantly greater if one has a high betweenness than if one
does not.
Conclusion
In this paper, we have discussed the structure of three networks of
scientific collaborations, as deduced from the pattern of coauthor-
ships of papers. The networks cover biomedical research, physics,
and ma~thematics, respectively, and the results reveal both similar-
ities and differences among the different fields. All fields appear to
have a broad distribution of the number of coauthors that an
individual has, with most individuals having only a few coauthors,
whereas a few have many, hundreds or even thousands in some
cases. Biological scientists tend to have significantly more coauthors
than mathematicians or physicists, a result that reflects the labor-
intensive, predominantly experimental direction of current biology.
Other differences are less easily explained. In biology, for instance,
it is far less likely than in mathematics that two of one's coauthors
will also be coauthors of one another, a result that has yet to receive
a clear explanation.
Coauthorship networks provide a copious and meticulously
documented record of the social and professional networks of
scientists. The results reported here represent only a small portion
of what could be done with these data. Possible future directions for
study might include tests for community structure or "invisible
colleges" within the networks (36, 37) or further investigations of
changes in collaboration patterns over time (9, 14), as well as other
measurements not yet thought of. Coauthorship data represent a
superb resource for the pursuit of questions such as these, and I look
forward to future developments with interest.
I thank particularly Paul Ginsparg for help in obtaining the data used for
this study. The data were generously made available by Oleg Khovayko,
David Lipman, and Grigoriy Starchenko (Medline); Paul Ginsparg and
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matical Reviews). I also thank Steve Strogatz for suggesting the "fun-
neling effect" calculation of Statistical Properties of Coauthorship Net-
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suggestions. This work was funded in part by the James S. McDonnell
Foundation, by the Intel Corporation, and by the U.S. National Science
Foundation under Grants DMS-0109086 and DMS-0234188.
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PNAS 1 April 6, 2004 1 vol. 101 1 suppl. 1 1 5205
Representative terms from entire chapter:
betweenness scores
