# Differences in collaboration structures and impact among prominent
researchers in Europe and North America

Lluís Danús1,∗, Carles Muntaner2, Alexander Krauss3,4,
Marta Sales-Pardo1,∗, and Roger Guimerà5,1,∗
1Department of Chemical Engineering, Universitat Rovira i Virgili, Tarragona,
Catalonia
2Dalla Lana School of Public Health, University of Toronto, Toronto, Canada
3London School of Economics, London, UK
4Universitat de Barcelona, Barcelona, Catalonia
5ICREA, Barcelona, Catalonia

∗Corresponding author(s). E-mail(s):
<EMAIL_ADDRESS><EMAIL_ADDRESS>roger.guimera@urvcat

> Scientists collaborate through intricate networks, which impact the quality
> and scope of their research. At the same time, funding and institutional
> arrangements, as well as scientific and political cultures, affect the
> structure of collaboration networks. Since such arrangements and cultures
> differ across regions in the world in systematic ways, we surmise that
> collaboration networks and impact should also differ systematically across
> regions. To test this, we compare the structure of collaboration networks
> among prominent researchers in North America and Europe. We find that
> prominent researchers in Europe establish denser collaboration networks,
> whereas those in North-America establish more decentralized networks. We
> also find that the impact of the publications of prominent researchers in
> North America is significantly higher than for those in Europe, both when
> they collaborate with other prominent researchers and when they do not.
> Although Europeans collaborate with other prominent researchers more often,
> which increases their impact, we also find that repeated collaboration among
> prominent researchers decreases the synergistic effect of collaborating.

Keywords : Science of science, Complex networks, Collaboration networks,
Research impact, Computational social science

## Introduction

Science is a social endeavor that progresses through the concerted effort of
many individuals, who exchange ideas and interact through intricate
collaboration networks (?, ?, ?, ?). Due to the increasing complexity involved
in the most pressing problems in science and society, and the advantage of
diverse groups at solving complex tasks (?, ?), the role of these
collaboration networks is becoming more and more important to achieve
scientific excellence and advance research fields (?, ?). Additionally, the
structure of collaboration networks affects the quality and scope of research
outcomes in different ways, some of which have been well described. In
particular, networks with more recurrent collaborations have been linked to
research with lower impact (?, ?). Also, centralized scientific communities
(those with a highly connected cluster in which the same group of scientists
repeatedly co-author articles) are more likely to propagate non-replicable
claims, and vice versa for decentralized communities with less overlap in co-
authorship and more diverse methods (?). The structure of the collaboration
network also has an impact on the career of researchers. For example, network
structure is predictive of who produces groundbreaking ideas, and who wins
scientific prizes and awards (?).

At the same time, there is mounting evidence that different research
environments, such as different funding and institutional arrangements or
different scientific and political cultures, leave measurable fingerprints in
collaboration networks (?, ?, ?, ?). For example, we know that resource-
intensive fields (such as astrophysics or high energy physics) typically have
collaborations involving a large number of researchers (more than 100) and,
therefore, denser collaboration networks (?, ?). Resource demands also result
in gender imbalance: women tend to be excluded from resource-intensive fields
that require large collaborations (for example, genomics versus plant sciences
in biology) and therefore end up working in smaller teams (?). Since funding
and institutional arrangements and scientific and political cultures differ
across regions in the world in systematic ways, we surmise that collaboration
networks should also differ systematically across regions, independently of
other factors such as research field. Additionally, because of the effect of
collaboration network structure on research outcomes, we expect to observe
systematic differences in the impact of research produced in North America and
Europe. Such differences have indeed been observed (?, ?); we explore whether
they are affected by collaboration-related factors.

We address the lack of comparative studies on collaboration networks across
regions by collecting data on field-specific collaboration networks for eight
different fields and classifying prominent researchers based on their
institutional affiliation in one of these two regions. We do not observe
systematic differences between prominent researchers in Europe and North
America if we look exclusively at the publication output and the overall
number of collaborators. However, consistent with our hypothesis, we find that
collaboration networks in North America and Europe do have distinctive
features that are robust across fields. Specifically, we find that prominent
researchers in Europe build denser collaboration networks with each other, and
those in North America build more decentralized networks, with researchers in
these two regions thus fulfilling different structural roles. Also consistent
with our expectations, we observe differences in the impact of the
publications of each community, and find that these differences are
collaboration-dependent. In particular, the impact (normalized by publication
year) of the publications of prominent researchers in North America is
significantly higher (12% overall) than for those in Europe, when they do not
collaborate with other prominent researchers in the field. When prominent
researchers collaborate with each other, which Europeans do more frequently,
normalized impact tends to increase, overall, by 10% for Europeans and 21% for
North Americans, broadening the impact difference to 22% overall.

## Results

### Collaboration networks between prominent researchers in different fields

We start by collecting data on the scientific collaboration networks between
roughly 100 prominent researchers in eight different scientific fields:
genetics, development economics, cognitive psychology, philosophy of science,
network science, metabolomics, network ecology, and social inequalities in
health. We focus on prominent researchers for two main reasons. First, elite
researchers are responsible for much of the impact and research focus in any
field (?, ?, ?, ?, ?). Second, since they also receive a disproportionate
share of the funding in their field, they are more likely to be sensitive to
institutional arrangements, scientific cultures and funding strategies.

We choose these eight fields because they provide a broad scope of fields
spanning across the natural and social sciences and they are sufficiently
small and well-defined for prominent researchers to collaborate with one
another, while being sufficiently established to have a consistent track
record of collaborations between prominent researchers, and of the impact of
these collaborations. Moreover, these fields are diverse in terms of the
topics covered, their scientific cultures, and how established they are. In
particular, the first four fields have longer traditions, whereas the latter
are relatively young and have evolved for shorter times. Finally, three of
these fields have a majority of prominent researchers based in Europe whereas
five have a majority based in North America, with overall 40% of researchers
based in Europe and 60% in North America (Supplementary Fig. S10).

For the field of inequalities in health, we used the list of prominent
scientists assembled by another research group (?). For the other seven
fields, we compiled data for the top 100 researchers using different criteria
depending on the nature of the field (for example, some fields have well-
defined conferences that we used, whereas others do not; see Methods). We
identified the 100 with the highest H-index (?), according to the Scopus
database. We excluded a few researchers who were not based in Europe or North
America and a few who did not have any collaboration with the others (these
were typically prominent researchers in other fields with only a few
publications in the fields we study). See Materials and Methods section in the
appendix for further details. The results we report in what follows are
consistent across fields, which provides assurance that our findings are
robust and not dependent on the methods used to compile the networks.

Collaboration patterns, and their outcomes in terms of publications, do not
appear, at first glance, to be vastly different for prominent researchers in
North America and Europe (Fig. 1). In both cases, we observe large variability
in the total number of collaborators and the total number of publications of
prominent researchers. Because of this variability, in what follows we
consider the logarithm of the number of collaborations, the number of
collaborators and the impact of publications (?). As expected, we observe that
the number of collaborators grows with the number of publications; but we
observe no consistent significant differences between Europe and North-America
(Fig. 1A-H) (except in the case of network ecology, $p=0.02$, and genetics,
$p=0.01$). By analyzing all papers of the prominent researchers, we also find
no evidence that researchers in either of the two geographic regions engage in
systematically larger collaborations, as measured by the number of authors per
article (Supplementary Fig. S1A-H).

### Roles of prominent researchers in Europe and North America

Despite the lack of systematic differences among geographical groups of
prominent researchers in terms of the total number of publications and
collaborations, a more nuanced analysis of the structure of the collaboration
network between prominent researchers (that is, excluding their collaborators
who are not prominent) reveals systematic and consistent differences between
North America and Europe. We start by modeling the network using a
hierarchical (?) stochastic block model (hSBM) (?, ?, ?) (Fig. 2A and
Supplementary Figs. S2-S9A). This approach partitions researchers into groups
according to their collaboration patterns (Methods). Researchers in the same
group occupy a similar position in the network and thus play a similar role
(?). Unlike other methods to identify groups, roles and/or positions in
networks, our approach (Bayesian maximum a posterior, or, equivalently,
minimum description length; see Methods) guarantees that the partition of the
network into groups is the most parsimonious.

The groups we obtain are markedly polarized in their composition (Fig. 2B,C),
with some groups containing mostly researchers in Europe and others containing
mostly researchers in North America, meaning that researchers with the same
structural role are typically based in the same continent. We quantify this
polarization by counting the number of same-continent researchers in each
group, and comparing those numbers to the null expectation obtained by
resampling researchers’ institutional affiliations (Methods). We find that
group polarization is highly significant in all fields except philosophy of
science, where the scarcity of collaborations leads to non-significant results
(Fig. 2C and Supplementary Figs. S2-S9C). This indicates that prominent
researchers in North America and Europe fulfill distinct structural roles in
collaboration networks between prominent researchers.

Group polarization could be naively attributed to geographic proximity, that
is, to the tendency of researchers based in the same continent to collaborate;
indeed, this would lead to polarized groups. However, deeper analysis of the
collaboration networks and the corresponding block models (Fig. 2A,B and
Supplementary Figs. S2-S9) reveals that this is not the only factor at play.
Rather, we observe genuinely different collaboration patterns across
continents. Groups with more Europe-based researchers tend to have more
within-group and between-group collaborations, whereas groups with more
researchers in North America tend to have fewer collaborations altogether. In
the following, we quantify these differences directly in the collaboration
networks between prominent researchers.

First, we measure the total number of collaborations between each researcher
and other prominent researchers (Fig. 3A-H). When counting collaborations,
several repeated collaborations with the same alter prominent researcher are
counted separately, so that one collaborator can give rise to several
collaborations. Across all fields, we find that the average number of
collaborations with other prominent researchers is always higher in Europe
than in North America even though in fields with lower collaboration rates
among prominent researchers the differences are not statistically significant
(Fig. 3). When all fields are combined (normalizing each field), the
difference is significant at the 1% level (Fig. 3I). Similarly, a significant
majority of researchers with above-median number of collaborations with other
prominent researchers are based in Europe, whereas the majority of researchers
with below-median number of collaborations with other prominent researchers
are based in North America (Fig. S10; Methods). Taken together with the fact
that the total number of collaborators does not differ significantly between
Europe and North America (Fig. 1 and Fig. S1), these results indicate that
researchers based in North America have a higher tendency to collaborate with
non-prominent researchers, whereas in Europe the research elite in a specific
field is more tightly knit.

Second, we measure, for each prominent researcher, the fraction of prominent
researchers in their continent with which the researcher has collaborated. We
call this the fraction of intracontinental collaborators (Fig. 3J-Q); a value
of 0.5 indicates that a prominent researcher has collaborated with half of the
prominent researchers in their continent. If we pool all fields together, we
find that the fraction of intracontinental collaborators normalized by field
is significantly higher in Europe than in North America at $1\%$ level (Fig.
3R). For individual fields, we find that the mean fraction of intracontinental
collaborators is always significantly higher in Europe than in North America
and that prominent researchers in Europe have significantly above-median
intracontinental collaborators for all fields (Fig. S10), except for
metabolomics (Methods).

### Collaboration-dependent differences in impact

If, as we have shown, collaboration patterns are different across continents,
and if collaboration network structure affects research performance (?, ?, ?),
then we expect systematic collaboration-dependent differences in impact across
continents. To investigate this question, we analyze the impact of
publications of prominent researchers, both when they publish with and without
other prominent researchers (Fig. 4 and Supplementary Fig. S11). We quantify
the value added by collaboration by means of the normalized logarithmic
impact, which measures the (logarithmic) impact of papers relative to the
(logarithmic) impact of papers written by single prominent researchers in the
same year (Methods). We find that, in general, researchers in North America
publish significantly more impactful papers than those in Europe when they
publish without other prominent researchers in their field (in philosophy of
science and cognitive psychology the differences are not significant). Since,
as we have seen earlier, prominent researchers in Europe collaborate more with
other prominent researchers (Fig. 4), this may provide a mechanism to
compensate, by means of collaboration, for the lower impact of their work
without other prominent researchers.

We also find that collaborating with other prominent researchers increases, by
15% on average across all fields, the impact of publications (differences not
significant for Europe-based researchers in philosophy of science and
genetics, and North America-based researchers in inequalities in health). The
prominent researchers in Europe and North America who benefit the most, in
terms of higher publication impact, by collaborating with other prominent
researchers are those in the fields of network science, with an increase of
25% and 33%, and development economics, with 20% and 30%, respectively.

However, previous results linking collaboration network structure to outcome
quality (?, ?) have generally indicated that repetitive collaborations with
the same researchers and largely closed collaboration networks (as those
observed in Europe) result in lower reproducibility and impact. Given the
observed differences in collaboration patterns between continents, we
investigate in more depth the effect of repeated collaborations (collaboration
number) on the value added by collaboration (Fig. 5 and Supplementary Figs.
S11-12). Specifically, we analyze the normalized logarithmic impact for the
first two collaborations among each pair of prominent researchers, the third
to fifth collaborations, and the sixth collaboration and higher. Although the
numbers in each field are small, often leading to non-significant differences,
when all fields are pooled together a clear and significant pattern emerges:
the more times a collaboration is repeated, the lower the impact (with
collaborations between prominent researchers in North America always having
higher normalized logarithmic impact). The first two collaborations among
prominent researchers increase (on average) the impact with respect to papers
with a single prominent researcher by 34% for North America based and 23% for
Europe based researchers. For 3-5 (and 6 or more repeated collaborations) the
increase in impact is lower: 29% (21%) and 22% (12%) for North America and
Europe, respectively. Trends among Europeans and North Americans follow
similar patterns within all fields (with Europeans having overall slightly
lower impact). Nonetheless the increase and subsequent decrease varies across
all fields. This suggests that the nature of the returns to repeated
collaborations are also influenced by field-specific features and not just the
overall research environment and the number of times researchers collaborate.

## Discussion

In studying complex systems like the scientific process or collaboration
networks, we are often constrained in precisely measuring causal relations.
Here, we surmised that collaboration networks and scientific impact differ
systematically across regions, and we found that the empirical evidence indeed
supports this hypothesis. This does not prove that the research environments
in Europe and North America are directly responsible for the observed
differences in collaboration structure (and, indirectly, impact); but
considering that research environment is known to affect collaboration network
structure in some cases (?, ?, ?, ?), we can conjecture about causal
mechanisms that could potentially lead to some of the observed differences.

In Europe, relative scarcity of research funds, collaboration-by-design in
framework programs, and the European Commission’s funding schemes can in part
account for the larger number of collaborations among Europeans and the
formation of a close-knit network of prominent scientists (?, ?). This
collaborative strategy has resulted in EU15 competing with the US as the
world’s largest scientific producing block in the last decades (?, ?),
although East Asia is catching up quickly. Paradoxically, even if
collaborative productivity increases, this does not necessarily imply greater
impact since largely closed networks of prominent scientists in Europe could
result in less original and impactful research (?). Indeed, as illustrated
above, the US has systematically been found to be more impactful across
scientific fields (?, ?).

Nonetheless, the observation that for Europe-based scientists there is an
advantage to collaborating with prominent Europe-based scientists suggests
that there might be other mechanisms at play that go beyond funding agency
norms. Europeans for example have shorter average travel distances and live in
similar time zones, and North Americans are commonly viewed as slightly more
competitive and self-confident in their work (?, ?). Citations, famously
referred to by Merton as “pellets of recognition,” contribute to appointment
and promotions decisions (?, ?). A growing supply of scientists and a stagnant
number of tenured positions in the last three decades has led to greater
competition for good jobs among scientists in Europe, vis-à-vis North America
(?).

In this context, for aspiring Europe-based scientists, co-authorship with
prominent scientists might be a dominant and effective social mechanism of
professional advancement to secure access to scarce tenured positions (?, ?).
On the other hand, in North America the existence of individual soft money for
career promotion coupled with less secure and influential tenured positions
(?, ?) could lead to permeable networks which are more open to newcomers and
with fewer incentives for social closure through collaborations with respect
to Europe. In fact, in North America the competition for resources through
soft-money positions, prestige of first and last-authorship (to which
researchers often renounce in large collaborations), and individual rewards
could be a deterrent for prominent scientists to engage in systematic
collaborations with other prominent scientists (?). Social stratification is
well known to play an important role in student acceptance and hiring
inequalities (?, ?, ?) and could also play an important role in shaping the
collaborations that prominent scientists establish. Further studies based on
our findings could examine which forms of social stratification result in
differential access to networks of prominent scientists in North America and
Europe.

More generally, statistical analysis of network structures linked to impact of
the scientific output can be limited in providing a precise causal mechanism
given factors that are not easily measurable such as researchers’ personality
traits (such as being more competitive and self-confident) and individual
motivations towards collaboration (?), and the social norms that shape
differences in scientific cultures across continents. Nonetheless, our finding
that research that involves several prominent researchers has larger impact,
which however wanes in repeated collaborations, holds across regions and
scientific fields can have important implications. On the one hand, the share
of research funding allocated to teams (and to repeating teams) may need to be
reassessed for existing funding schemes. On the other, early career
researchers may need, given different hiring criteria across fields, to strike
a balance between work they do by themselves and in collaboration.

## Materials and methods

### Data acquisition

For constructing the lists of prominent researchers, we used the following
procedures. The list for social inequalities in health was previously
collected by another research group in Ref. (?). For the four more established
fields in our analysis (genetics, development economics, philosophy of
science, and cognitive psychology) we selected the 100 researchers with the
highest h-index in their field using Google Scholar in January 2021. We then
confirmed our initial list using Scopus’ citation and h-index data. To ensure
that all researchers commonly viewed as the most influential were included in
the top 100 lists, we checked common rankings of the most influential
researchers for each of these fields. We incorporated the few top researchers
in these ranked lists, who were not already among the top researchers
according to Google Scholar. As these four fields have a longer tradition than
the other four fields, we only included researchers with publications between
1960 and 2021.

For the four younger fields, for those with well defined conferences and
scientific societies (network science and metabolomics) we identified the main
conferences (NetSci, NetSciX and CompleNet, for network science; and events of
the Metabolomics Society for metabolomics) and societies (Network Science
Society and Metabolomics Society), and considered all researchers who gave
talks, are in scientific committees and scientific boards, and received awards
in these venues. The authors in this list were identified in the Scopus
database and ranked by their h-index. For the field of network ecology, we
assembled the initial list by querying the Scopus database using a series of
keywords (Ecologi* Network*, Food Web*, Environment* Network*, Trophic*
Network*, Trophi* Web*) and focusing on top interdisciplinary and ecology
journals. We then refined and ranked the list using the h-index, as before.

For all fields, we used Scopus database to extract all publications and
bibliometric data for each author. In all cases, we excluded the few
researchers (a total of 6%) not based in Europe or North America, or who did
not collaborate with any other prominent researchers in the network. We also
checked manually that all researchers in the network really have a significant
body of work in the field, and excluded a few scientists that are prominent in
other fields and have only made a small contribution to the field under
consideration.

Note that we consider all the publications of authors that are prominent in
each field, including publications in other fields. This is because we are
interested in all the collaborations between these researchers. Additionally,
we assign each prominent researcher to their main current affiliation,
although some of them have developed parts of their careers in North America
and Europe.

The names of the prominent researchers are provided in Supplementary Figs.
S2-S9. Note that our criteria guarantee that all scientists in the network are
prominent, although different criteria may result in somewhat different
prominent researchers. Overall, all 100 researchers identified in each field
are among the most highly cited and influential researchers with the highest
h-index in their given field. We validated the data set by using an
alternative method based on a Scopus search by keywords. The overlap with the
network identified here, in network science for example, was 90% and all
results in the study remained the same.

### Hierarchical stochastic block model for the analysis of network positions
and roles

Stochastic block models (SBM) are a class of generative models for networks
(?, ?, ?). In SBM, nodes are assumed to belong to groups, and node-to-node
connectivity is defined by the group memberships alone. In particular, if
nodes $i$ and $j$ belong to groups $g_{i}$ and $g_{j}$, respectively, then the
probability that they are connected is given by a fixed number
$p_{g_{i}g_{j}}$, which is identical for all other pairs in $g_{i}$ and
$g_{j}$. The degree-corrected stochastic block model (SBM-DC) (?) is a variant
of the SBM that allows for each node to have a different propensity to create
links with others, thus allowing nodes in the same group to have broad degree
(connectivity) distributions despite having the same connectivity patterns.

Because group memberships are typically unknown, it is necessary to infer them
from the observed connections in a given network. The most plausible partition
of the nodes into groups (the partition that maximizes the Bayesian posterior
over partitions (?)) is also the one with the minimum description length
(MDL), that is, the one that most compresses the observed connections (?). To
obtain the MDL partition, one needs to specify a prior distribution over
partitions. A hierarchical prior, in which groups of nodes are assumed to be
nested hierarchically, tends to yield shorter descriptions lengths than more
uninformative priors. The SBM with such hierarchical priors is often referred
to as the hierarchical SBM (hSBM) (?).

We obtain the MDL partition of the nodes in a collaboration network by using
the graph-tool Python module. For each network, we fit the regular as well as
the degree-corrected SBM, both with non-informative and hierarchical priors.
In all cases (Supplementary Tables S1,2), the degree-corrected hSBM yields the
shortest description length, so all results reported in the manuscript
correspond to this model. In Fig. 2, we use the groups at the second level of
the hierarchy.

### Group polarization and statistical significance of North America-Europe
differences

To quantify the affiliation imbalance of the groups identified by the hSBM, we
defined group polarization $g_{p}$ as follows. For each researcher $i$ in a
group of prominent researchers, we calculated the fraction of others in the
group that belong to the same continent as $i$. Then, the mean group
polarization $g_{p}$ is calculated as a mean over all researchers in all
groups:

$g_{p}=\frac{1}{N}\sum_{g=1}^{G}\sum_{i=1}^{n_{g}}\frac{c_{ig}-1}{n_{g}-1}$
(1)

where $N$ the number of researchers in the network, $G$ is the number of
groups, ${c_{ig}}$ the number of researchers in group $g$ (other than $i$)
belonging to the same continent than node $i$, and $n_{g}$ the total number of
nodes in group $g$. Thus, the polarization of the network is $g_{p}=1$ if all
groups comprise researchers only from North America or only from Europe, but
no group contains researchers from both.

To assess the statistical significance of the group polarization of a given
partition of the collaboration network into groups, we used resampling. In
particular, we randomly reassigned the affiliations of all researchers in the
network and calculated $g_{p}$ maintaining the same groups, and repeated this
operation many times to obtain the null distribution of $g_{p}$ (Fig. 2C and
Supplementary Figs. S2-9C).

To estimate the significance of the differences between North America and
Europe we used, in all cases, resampling. In particular, for a given metric
(number of authors per paper, log number of prominent researcher
collaborations, fraction of intracontinental collaborators) we used the
difference in the means as our statistic, and then obtained the expected null
distribution of the statistic (and the p-value) by randomly reassigning
affiliations to authors many times. Similarly, to establish the significance
of the differences between fractions of above- and below-median researchers
(for log number of prominent researcher collaborations and fraction of
intracontinental collaborators) we calculated the actual value of such
differences and compared them to the null expectation obtained by, again,
reshuffling affiliations.

For the joint distribution of Fig. 1 we used the 2D Kolmogorov-Smirnov
statistic (?) and, once more, we obtained the significance levels by
repeatedly reshuffling the affiliations of each researcher.

### Distribution of the logarithmic number of citations

Fig. 4 shows the mean log number of citations for papers published by one or
multiple prominent researchers, and by researchers in North America, Europe,
or both. Supplementary Fig. S11 shows the whole distribution of the
logarithmic number of citations for the same papers. This distributions were
compared using the Kolmogorov-Smirnov statistic and, as everywhere else, the
significance of the observed differences was calculated by repeatedly
reshuffling researchers’ affiliations.

### Normalized logarithmic impact

To measure how research impact varies when prominent researchers collaborate
(Figs. 4 and 5), we use normalized logarithmic impact as defined next. The
normalized logarithmic impact $I_{i}$ of a paper $i$ is the logarithmic number
of citations (plus 1) $\log(k_{i}+1)$ of the paper divided divided by the mean
of the logarithmic number of citations (plus 1) of papers with no prominent
researcher collaboration in the same publication year

$I_{i}=\frac{\log(k_{i}+1)}{\langle\log(k+1)\rangle_{y_{i}}}\,.$ (2)

Here $\langle\dots\rangle_{y}$ is the mean over all papers published in year
$y$ by single prominent researchers (and, possibly, other non-prominent
researchers, but not multiple prominent researchers). Comparison to
publications in the same year is necessary to avoid the artifact of later
collaborations being less impactful just because they have had less time to
accrue citations.

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## Acknowledgments

We acknowledge Louise Boucchard for sharing her complete list of authors with
CM. This project has received funding from the Spanish Ministerio de Economía
y Competitividad (PID2019-106811GB-C31) and from the Government of Catalonia
(2017SGR-896).

### Authors contributions

CM, MS-P, RG formulated the overarching research goals and aims. LD and AK
collected the data. LD developed the computer code for data analysis and
visualization, and conducted the experiments. All authors analyzed and
discussed the data and wrote the manuscript.

### Competing interests

The authors have no competing interests.

#### Data and materials availability

All data are publicly available, and the lists of prominent researchers and
their publications will be provided upon request.

## Supplementary materials

Figs. S1 to S12
Tables S1 and S2

## Figures

Figure 1: Total number of collaborators and publications for prominent
researchers. (A) -(H) Logarithm of the total number of collaborators as a
function of the logarithm of the total number of publications for each
prominent researcher in: (A) inequalities in health, (B) network science, (C)
metabolomics, , (D) network ecology, (E) development economics, (F) philosphy
of science, (G) genetics and (H) cognitive psycology. Red circles and blue
triangles correspond to prominent researchers based in North-America and
Europe, respectively. We test whether the points are distributed differently
using the 2D Kolmogorov-Smirnov statistic (?), and calculate the significance
by resampling the researchers’ affiliations. At the 5% confidence level, we
can only reject the null hypothesis (that both subsets are drawn from the same
distribution) in the case of network ecology.

Figure 2: Stochastic block model and group polarization for the collaboration
network in the field of inequalities in health. (See Supplementary Figs. S2-S8
for all other fields). (A) Collaboration network and best fit of the
hierarchical stochastic block model (hSBM). Each node in the network
represents a prominent researcher, and each edge represents a different
collaboration (coauthored paper) between a pair of researchers. Prominent
researchers in North America and Europe are represented as circles and
triangles, respectively. Different colors correspond to the groups identified
by the hSBM, so that nodes with the same color have a similar collaboration
pattern with other researchers and therefore fulfill a similar structural role
in the collaboration network. Node size represents the betweenness centrality
of the researcher in the network. We omit the names of the researchers so as
not to distract from the patterns we aim to explore; for reproducibility, we
provide the names of the prominent researchers in Extended Data Fig. 1, and in
Supplementary Materials Fig. S2-S8 for the other fields. (B) Block model of
the collaboration network. Each node represents a group of researchers with
similar collaboration patterns (that is, a different color in (A)), with node
size representing the number of researchers in the group. The width of the
edges represents the number of collaborations between groups, and loops
represent collaborations within each group. The color of each node indicates
the fraction of researchers in the group that are based in North America, so
that dark blue nodes represent groups with mostly Europe-based researchers,
and red nodes represent groups with mostly North America-based researchers.
(C) We define the polarization of a group as the number of same-continent
researchers in the group over the random expectation for such number
(Methods). The vertical line indicates the mean group polarization for the
observed collaboration network. We randomize authors’ affiliations and
calculate the distribution of expected (null) polarization values. The
empirical value is well above the null expectation, so that the group
structure of the observed network is significantly polarized.

Figure 3: Differences in collaboration patterns between prominent researchers
in North America and Europe. (A)-(H) Number of prominent researcher (PR)
collaborations. We plot the distribution of the logarithm of number
collaborations for prominent researchers in North America (red) and Europe
(blue). The vertical lines indicate the mean log-number of collaborations for
each subset. The significance of the difference between the European and North
American means was established by resampling researcher affiliations (one
sided test). (I) Aggregated distribution for all fields. The log-number of PR
collaborations are normalized by the mean in each field so as to make all
fields comparable. (J)-(Q) Fraction of intracontinental collaborators, defined
as the fraction of prominent researchers in the same continent with which a
prominent researcher collaborates. We plot the distribution of the fraction of
intracontinental collaborators in North America (red) and Europe (blue). The
vertical lines indicate the mean fraction of intracontinental collaborators
for each subset. The significance of the difference between the European and
North American means was established by reshuffling researcher affiliations
(one sided test). (R) Aggregated distribution for all fields. The fractions of
intracontinental collaborations in each field are normalized by the mean of
the field so as to make all fields comparable. Stars indicate significant
differences (***: 1%, **: 5%, *: 10%, n.s.: not significant).

Figure 4: Impact difference under different collaborative strategies. Mean
normalized logarithmic impact for articles authored by either a single
prominent researcher (PR) or multiple PR in: (A) inequalities in health, (B)
network science, (C) metabolomics, (D) network ecology, (E) development
economics, (F) philosophy of science, (G) genetics and (H) cognitive
psychology. The normalized logarithmic impact $I_{i}$ of a paper $i$ is the
logarithmic number of citations (plus 1) $\log(k_{i}+1)$ of the paper divided
by the mean of the logarithmic number of citations (plus 1) of papers with no
prominent researcher collaboration in the same publication year (Methods). (I)
Aggregated normalized logarithmic impact for all fields. Stars indicate
significant differences (***: 1%, **: 5%, *: 10%, n.s.: not significant). See
Extended Data Fig. 5 for the whole distributions of the logarithmic number of
citations.

Figure 5: Evolution of impact with repeated collaborations. Mean normalized
logarithmic impact of publications authored by a pair of prominent researchers
(PR) as a function of the collaboration number (the number of times two
prominent researchers have co-authored a paper: 1-2, 3-5, or $>$5; Methods).
The normalized logarithmic impact $I_{i}$ of a paper $i$ is the logarithmic
number of citations (plus 1) $\log(k_{i}+1)$ of the paper divided by the mean
of the logarithmic number of citations (plus 1) of papers with no prominent
researcher collaboration in the same publication year (Methods). (A)
inequalities in health, (B) network science, (C) network ecology, (D)
metabolomics, (E) development economics, (F) philosophy of science, (G)
genetics and (H) cognitive psychology. (I) Aggregated normalized logarithmic
impact for all fields, as a function of the number of collaboration.