RESEARCH ARTICLE

Citations driven by social connections?
A multi-layer representation of
coauthorship networks

Keine offenen Zugänge

Tagebuch

Chair of Systems Design, ETH Zurich, Zurich, Schweiz

Christian Zingg

, Vahan Nanumyan

, and Frank Schweitzer

Schlüsselwörter: citation network, citation rate, collaboration network, collective attention, Netzwerk
centrality, two-layer network

ABSTRAKT

To what extent is the citation rate of new papers influenced by the past social relations of their
authors? To answer this question, we present a data-driven analysis of nine different physics
journals. Our analysis is based on a two-layer network representation constructed from two
large-scale data sets, INSPIREHEP and APS. The social layer contains authors as nodes and
coauthorship relations as links. This allows us to quantify the social relations of each author, prior
to the publication of a new paper. The publication layer contains papers as nodes and citations
between papers as links. This layer allows us to quantify scientific attention as measured by the
change of the citation rate over time. We particularly study how this change correlates with the
social relations of their authors, prior to publication. We find that on average the maximum value
of the citation rate is reached sooner for authors who have either published more papers or who
have had more coauthors in previous papers. We also find that for these authors the decay in the
citation rate is faster, meaning that their papers are forgotten sooner.

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1.

EINFÜHRUNG

The availability of large-scale data sets about journals and scientific publications therein, their
authors, institutions, cited references, and citations obtained in other papers has boosted sciento-
metric research in recent years. They allow us to address new research questions that go beyond
the calculation of mere bibliographic indicators. These particularly concern the role of social
influences on the success of papers, for example coauthorship relations (Sarigol, Pfitzner,
et al., 2014) or the relations between authors and handling editors (Sarigol, Garcia, et al.,
2017). Such investigations have contributed to a new scientific discipline, the science of success
(Jadidi, Karimi, et al., 2018; Sinatra & Lambiotte, 2018).

But such data also allow us to redo traditional scientometric analyses on a much larger scale.
In Parolo, Pan, et al. (2015), the dynamics of the citation rate (d.h., the change in the number of
citations during a fixed time interval) is analyzed. The authors find that the change of the average
citation rate follows two characteristic phases: first a growth phase and then a decay phase.
Interessant, the duration of the first and the speed of the second phase have changed over
the years. This allows us to draw conclusions about how the collective attention of scientists
towards a given paper has evolved between early and recent times.

Allgemein, the dynamics of citations are extensively studied in the bibliometric literature. Für
Beispiel, the relation between the current number of citations and the citation rate was studied

Zitat: Zingg, C., Nanumyan, V., &
Schweitzer, F. (2020). Citations driven
by social connections? A multi-layer
representation of coauthorship
Netzwerke. Quantitative Science
Studien, 1(4), 1493–1509. https://doi
.org/10.1162/qss_a_00092

DOI:
https://doi.org/10.1162/qss_a_00092

zusätzliche Informationen:
https://doi.org/10.1162/qss_a_00092

Erhalten: 18 Oktober 2019
Akzeptiert: 27 September 2020

Korrespondierender Autor:
Christian Zingg
czingg@ethz.ch

Handling-Editor:
Ludo Waltman

Urheberrechte ©: © 2020 Christian Zingg,
Vahan Nanumyan, and Frank
Schweitzer. Published under a Creative
Commons Attribution 4.0 International
(CC BY 4.0) Lizenz.

Die MIT-Presse

Citations driven by social connections?

in Jeong, Néda, and Barabási, (2003). Citations were found to occur in bursts, with large bursts
within a few years after publication (Eom & Fortunato, 2011). Concerning the scientific field of a
Papier, citations from papers in the same field tend to be obtained earlier than citations from papers
in other fields (Rinia, Van Leeuwen, et al., 2001). Citation rates have also been used to classify
Papiere (Avramescu, 1979; Li & Ye, 2014). Such classes often identify papers that receive citations
earlier or later than the majority of papers (Ciotti, Bonaventura, et al., 2016; Colavizza &
Franceschet, 2016; Costas, van Leeuwen, & van Raan, 2010). Papers in the second class (d.h., welche
receive their citations only a long time after publication) are often called sleeping beauties or de-
layed (Burrell, 2005; van Raan, 2004). Their citation rate and how it differs from other papers was
studied extensively in Lachance and Larivière (2014). This class has also been thoroughly studied
outside paper classification settings. It was found that “sleeping beauties” are extremely rare, Und
nur 0.04% of papers published in 1988 were identified as such (van Raan, 2004). They were also
found to occur especially often in multidisciplinary data sets (Ke, Ferrara, et al., 2015).

Recent progress in the study of scientometric systems has very much relied on representing
them as networks. A first example is citation networks, representing papers as nodes and citations
as their (gerichtet) links. Such networks can be seen as a knowledge map of science (Leydesdorff,
Carley, & Rafols, 2013). They can be also used to predict scientific success (Mazloumian, 2012). A
second example is coauthorship networks, representing scientists as nodes and their coauthor-
ships as links. While sociological studies (Cetina, 2009) just report that communication between
coauthors can be very intricate, formal models of how such collaborations form on the structural
level have also been developed (Guimera, 2005; Tomasello, Vaccario, & Schweitzer, 2017). To
study collaboration patterns in a university faculty (Claudel, Massaro, et al., 2017), such coau-
thorship networks have been combined with a network encoding the physical distance between
the faculty members. It was also analyzed how communities detected on a coauthorship network
overlap with different research topics (Battiston, Iacovacci, et al., 2016).

These investigations have the drawback that they study citation networks and coauthorship
networks separately from each other. As already emphasized (Clauset, Larremore, & Sinatra,
2017; Schweitzer, 2014), this becomes a problem if one wants to study social influence on cita-
tion dynamics. Zum Beispiel, based on a data set of Physical Review, it was shown that scientists
cite former coauthors more often (Martin, Ball, et al., 2013). daher, a better approach is to
combine both the citation and the coauthorship network in a multilayer network. Links between
the citation and the coauthorship layer express the authorship of papers. Using such a represen-
Station, a method to detect citation cartels was proposed (Fister, Fister, & Perc, 2016). Weiter, Die
rate of citations dependence on the authors’ total number of citations was studied (Petersen,
Fortunato, et al., 2014). Jedoch, it has not yet been investigated how the position of authors
in the coauthorship network influences when their papers are cited. In this paper we study exactly
this question.

Our analysis extends recent studies that focus on the success of papers as measured by their
total number of citations. In Sarigol et al. (2014), this success was related to the position of the
authors in a coauthorship network. It was shown that authors of successful papers are consider-
ably more central (as quantified by various centrality measures) in the coauthorship network. Wir
extend this by an analysis of the dynamics of the citation rate over time (d.h., when their papers are
cited). To parametrize the citation dynamics, we resort to the phases identified in Parolo et al.
(2015). We extend this work by relating these phases to the social relations of the authors.

Our paper is structured as follows. In section 2.1 we explain how citation dynamics can be mea-
sured by means of citation histories, which represent the collective attention given to a paper. In
section 2.2 we describe the data sets used for our analysis. In section 3.1 we introduce the multilayer

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Citations driven by social connections?

network to combine social information about authors with citation data. We then turn to our
research question and study in sections 3.2 Und 3.3 how the social relations of authors in the coau-
thorship network influence the collective attention. zuletzt, in section 4 we conclude our findings.

2. METHODS AND DATA

2.1. Dynamics of Citation Rates

2.1.1. Measuring attention

Citations are often used as a measure of the success of a paper, accumulated over time. They have
the advantage that they are objective in the sense that they are protocolled in the reference lists of
citing papers. But the sheer number of citations does not utilize the temporal information (d.h.,
how many of these citations arrive at a given time). This is captured in the citation rate, welche
better estimates the attention a paper receives in a given time (interval). Individual attention (d.h.,
who cites a given paper at a given time), is not of interest for our study. We focus on collective
attention (d.h., the aggregate over all authors who cite this paper during a given time interval).
Obviously, the citation rate is only a proxy for this collective attention. One could additionally
consider other attention measures like the altmetric score. But such information is only
available for very recent publications and further is strongly biased against the use of social
media. daher, we decide to restrict our study to using only the citation rate as a proxy for
collective attention. Most papers are still cited because they have caught in some way the atten-
tion of the authors of the citing papers. Außerdem, citation counts were found to be a good
approximation of scientific impact as perceived by scientists from the same field as the paper
(Radicchi, Weissman, & Bollen, 2017).

2.1.2. Citation histories

We measure the collective attention of a paper by the number of citations it receives over a
particular time interval (d.h., its citation rate). More precisely, for paper i published at time (cid:1)
ich,
the citation rate at t = (cid:1) − (cid:1)i time units after publication is
δð Þ

D
δ þ Δt
Δt
ich ((cid:1)) denotes the total number of “incoming” citations the paper has received at time (cid:1).
where kin
The dynamics of the citation rate ci(T) is also called the citation history of paper i (Parolo et al.,
2015). To compare citation histories across papers we further normalize them by their respec-
tive maximum value cmax

ci tð Þ ¼ kin

Þ − kin
ich

= maxt{ci (T)}:

(1)

ich

ich

~ci tð Þ ¼ ci tð Þ=cmax

ich

:

(2)

2.1.3. Two phases in citation histories

Parolo et al. (2015) find two characteristic phases in the dynamics of normalized citation his-
tories ~ci (T) of a paper i. In the first phase, which lasts for 2–7 years, it grows and eventually
reaches a peak at a time tpeak
. After the peak there is the second phase, in which the citation
rate decays over time. For the majority of papers this decay was found to be well described by
an exponential function:

ich

~ci tð Þ / exp −t=τi

D

Þ;

(3)

The parameter τ
Ist, the faster is the decay. Figur 1 illustrates the two phases of ~ci (T).

i is called the “lifetime,” and it determines the speed of the decay. The larger τ

ich

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Citations driven by social connections?

Figur 1.
most papers.

Illustration of the two characteristic phases in the normalized citation histories ~ci (T) von

2.2. Bibliographic Databases

As we argued in section 2, citations are particularly suitable to quantify the collective attention
by scientists from the same field as a given paper. daher, in our analysis we study different
journals separately, because each describes a topic-related community of authors and their
Papiere. To obtain the data for our study we resort to large bibliographic databases which index
papers across journals. They collect information such as a paper’s title, the list of authors, the date
of publication, and also the list of references that a paper cites. We extracted this set of informa-
tion for nine journals from two such databases in the same way as in Nanumyan, Gote, Und
Schweitzer (2020) and as explained below.

2.2.1. APS database

This indexes papers published in journals by the American Physical Society (APS). Access to the
database can be requested for research purposes at https://journals.aps.org/datasets. We extracted
the journals Physical Review (PR), Physical Review A (PRA), Physical Review C (VR China), Physical
Review E (PRE), and Reviews of Modern Physics (RMP) to cover a wide range of physics sub-fields.

The APS database has the known issue of name disambiguation, because it indexes authors by
their name and not by a unique identifier. This means that different authors with the same name
are indexed as one author. Such a “multiauthor” then owns all papers and coauthorships that
were actually accumulated by multiple authors. Im Gegensatz, one author whose name can be
spelled in different ways may be indexed as different authors in the database. The consequence
for our study is that such undisambiguated authors bias measures involving (co)authorships. Das
problem has already been discussed in the scientific literature, and a disambiguation algorithm
specifically for authors in the APS database was proposed (Sinatra, Wang, et al., 2016). Wir
applied this algorithm to the APS database to lower the bias from undisambiguated authors.

2.2.2.

INSPIREHEP database

The second database, called INSPIREHEP, indexes papers relevant for the field of high-energy
Physik. This database can be downloaded at http://inspirehep.net/dumps/inspire-dump.html.
In this database authors are disambiguated, because each author is indexed by a unique identi-
fier. We extracted the journals Journal of High Energy Physics ( JHEP), Physics Letters (Phys. Lett.),
Nuclear Physics (Nuc. Phys.), and high energy physics literature in Physical Review journals
(PR-HEP) from this database. These were the four largest journals in terms of number of citations
from papers in the same journal (d.h., the citations which we will use to compute citation rates in
the later sections).

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Citations driven by social connections?

Tisch 1. Overview of the extracted journals from the APS database and the INSPIREHEP database
(IH). |V p| is the number of papers, |V a| is the number of authors, |E pc| is the number of citations
between papers, Und |Ea| is the number of authorships

Datenbank
APS

IH

Zeitschrift

PR

PRA

VR China

PRE

RMP

JHEP

PR-HEP

Phys. Lett.

Nuc. Phys.

|V p|
46728

69147

36039

49118

3006

15739

44829

22786

24014

|V a|
24307

41428

22672

36382

3788

7994

33908

18078

18733

|E pc|
253312

416639

253948

182701

5282

191990

213625

56332

125252

|E a|
87386

144806

108844

95796

5044

39056

115237

53089

60018

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In INSPIREHEP some indexed papers have exceptionally large lists of authors, which sometimes
even exceed 1,000 authors. Such large-scale coauthorships were termed hyperauthorships in
Cronin (2001). Concerns were raised that it is unclear which authors actually made substantial con-
tributions to such papers (Cronin, 2001), and that the coauthorship network is not an accurate
representation of the social network of authors (Newman, 2004). In der Tat, every author in such a
hyperauthorship gets possibly thousands of collaborators from just a single paper, despite likely not
having collaborated with all of them personally. This introduces a bias for measures involving
coauthorships, and thus for our study. It was found that hyperauthorships usually occur in papers
from large experiments (Newman, 2001), such as the ATLAS experiment at CERN. To avoid this
bias we remove experimental papers from the database. To identify experimental papers we used
meta-tags that INSPIREHEP provides, so-called XML-tags. These are essentially labels for papers
that provide additional information, such as arXiv identifiers, author affiliations, or sometimes esti-
mates of whether a paper is experimental or theoretical. We removed all papers from the database
that are explicitly tagged as experimental. But because this tag might be unavailable for a paper, Wir
further removed all papers that are not explicitly tagged as theoretical work or work in general
Physik.

To summarize, Tisch 1 provides summary statistics of the nine journals. It further also
shows how large these journals actually are. Zum Beispiel, there is only one journal, Abgeordneter, welche
contains fewer than 10,000 authors, and there are more than 400,000 citations between
papers in PRA.

3. SOCIAL INFLUENCE ON CITATION RATE

3.1. Multilayer Network Representation

3.1.1. Combining information about papers and authors

Our aim is to combine the information about collective attention, as proxied by the citation rate,
with information about the social relations between authors. For the latter, we specifically focus
on coauthorship, because this is the most objective and best documented relation. Wieder, this is a
proxy because it neglects other forms of social relationships, such as friendship, personal

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Citations driven by social connections?

encounters (z.B., during conferences), electronic communication, or relations in social media. Aber
we do not have this type of information available for all authors over long periods. Therefore we
restrict our analysis to the coauthorship network that can be constructed from the available
Daten, as described below.

To relate information about authorship and about papers in a tractable manner, multilayer net-
works come into play, because they allow us to represent such separate information in different
layers. The nodes on the first layer correspond to papers and the (gerichtet) links to their citations.
Different from this, the nodes in the second layer correspond to the authors and the links to their
coauthorships (d.h., there is a link between two authors if they wrote at least one paper together).
Dann, there are links that connect nodes on the first layer with nodes on the second layer. Diese
links correspond to the authorship relations (d.h., for every author, there is exactly one such link to
each of her papers). We construct such a two-layer network for each of the nine journals in our
data set to represent the information about citations between papers as well as about the
authorships.

To summarize the above, Figur 2 illustrates the two layers of citation and coauthorship net-
works and their coupling. It further displays the temporal dimension: The multilayer network
evolves over time because new papers are published, and hence new coauthors appear. Als
the timeline indicates, paper i is published at time (cid:1)
i and then accumulates citations in the future,
at times (cid:1) > (cid:1)
ich ((cid:1))
of papers that cite i until time (cid:1) (see Eq. 1 and Figure 2). Speziell, it is the in-degree, weil das
publication network is directed. The question is now how the citation rate of this paper evolves
im Laufe der Zeit, conditional on the social information about its authors at time (cid:1)
ich, which is the publi-
cation time of paper i. Mit anderen Worten, we analyze the impact of information from before this
Veröffentlichung.

ich. The publication layer allows us to define the degree of a paper i as the number kin

3.1.2. Quantifying authors’ social relations

The coauthorship layer allows us to define the degree of an author n as the total number of distinct
coauthors kn((cid:1)
ich. Degree is the simplest centrality measure for

ich) that the author had before time (cid:1)

Figur 2. Multilayer network illustrating the coupling between the coauthorship network and the citation network. Links between the two
layers represent the relation between authors and papers. The timeline on top indicates that links within the citation layer are directed and
point to papers already existing at the time when a paper is published.

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Citations driven by social connections?

networks and reflects the local information about the embedding of an author in the social
Netzwerk. We use it here because it was shown recently (Nanumyan et al., 2020) that this measure
is a particularly good predictor for the future citation rate.

We characterize a paper i at time (cid:1)

i as the number of distinct coauthors of its authors before

Zeit (cid:1)

ich. This means that we sum over the authors’ individual degrees kr

sNC
ich

δið Þ ¼

X

kr δið Þ − C δið Þ

R

(4)

and subtract a correction term C((cid:1)ich) to not count multiple times those coauthors who collab-
orated with more than one author in the past. The derivation of this correction term can be
found in the Supplementary Material, Section S1. The index NC refers to number of coauthors.
Außerdem, the paper i published at time (cid:1)

i is not counted in sNC

((cid:1)

ich).

ich

ich

((cid:1)

ich). First we define the interlayer-degree

We also make use of the coupling between the two layers to define a second measure, welche
we can later compare with sNC
ich) of an author n as
the total number of distinct papers written by n before time (cid:1)
ich. This measure allows us to quan-
tify the experience of author n that she gained before a given point in time. To characterize a
paper i at time (cid:1)i by using this information about its authors r before time (cid:1)ich, we compute
X
~
kr δið Þ − ~

δið Þ ¼

C δið Þ

~
kn((cid:1)

(5)

sNP
ich

ich) is again a correction term used to only count unique papers
by analogy with Eq. 4. Hier
(if some authors had written a paper together in the past already). Its derivation can again be
found in the Supplementary Material, Section S1.

~
C((cid:1)

R

3.1.3. Parametrizing citation rates

((cid:1)

((cid:1)

ich

ich

ich) and sNP

The quantities sNC
ich) are based on the information of the authors of paper i. Our goal is
to determine how they influence the citation dynamics of paper i (d.h., we need an analytically
tractable parametrization of the citation rates). To parametrize the citation dynamics we resort
to the two characteristic phases of citation histories mentioned in section 2.1. The first phase
corresponds to increasing citation rates, and we parametrize by its duration tpeak
, weil wir
have no more precise knowledge about a general functional form of this phase. The second phase
corresponds to an exponential decay, and we parametrize it as the parameter τ
i in Eq. 3 (d.h., Die
so-called lifetime). Both parameters, tpeak

ich, are illustrated in Figure 1.

and τ

ich

ich

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We now have four parameters to summarize the information about paper i. The first two
ich), which characterize the authors of paper i. The other two

((cid:1)

parameters are sNC
parameters are tpeak

ich

((cid:1)
ich) and sNP
and τ

ich

ich

ich, which characterize the citation history.

3.1.4. Excluding incomplete citation histories

Obviously, our data sets only contain papers published before the release date of the respective
database. Somit, the time-span on which we can compute a given paper’s citation history is also
limited by this date. This introduces an issue, especially for recent papers: The observable period
of the citation history can be so short that the decay phase has not yet started at all. To account
for this, we omitted all papers that were published within the last 5 years before the release of the
respective database. Somit, for all papers in our study the citation histories are covered over at

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Citations driven by social connections?

least 5 Jahre. Zusätzlich, we also removed those papers whose citation rate is nondecreasing in
the latest year, as this is a sign that the respective paper has not yet reached its decay phase.

3.2. Time to the Peak Citation Rate

3.2.1. Regressions

ich

ich

ich

, or publications, sNP

Our aim is to study the dependence between peak-delays, tpeak
, and the number of previous
coauthors, sNC
. At first, linear regression seems applicable to determine such
a dependence. It would allow a straightforward interpretation of fitted coefficients. Jedoch,
peak-delays are essentially counts, because we count in which year after publication the peak
citation rate occurs (d.h., whether this is in year 0, or in year 1, or in year 2). For such data, classical
linear regression can give wrong conclusions, Zum Beispiel, because it can predict negative
Werte, which are impossible for counts. Stattdessen, we apply a negative binomial regression, welche
is a standard model for count data (Hilbe, 2011). We chose this model over the simpler Poisson
regression, because we found that the variance of peak-delays across papers is larger than
their mean. We test this so-called overdispersion for our data in the Supplementary Material,
Section S3. Overdispersion violates an assumption of Poisson regression, while the negative
binomial regression becomes applicable. Somit, the model we fit is

tpeak
ich

D
¼ negbin α þ β (cid:2) si

Þ

(6)

where si is the number of previous coauthors, sNC
and tpeak
is measured in years ( Venables & Ripley, 2002). negbin stands for a negative binomial
ich
regression. The parameters (cid:3) Und (cid:4) are to be fitted. We use the function glm.nb in the R-package
MASS to fit them.

, or the number of previous publications, sNP

,

ich

ich

3.2.2.

Fitted parameters

In Table 2 we show the fitted parameters for all journals. Except for one coefficient, all parameters
(cid:4) are negative, which means that peak delays get smaller for increasing numbers of previous co-
authors or publications. The exception is JHEP, which has a positive (cid:4) for the number of previous
publications. Jedoch, this coefficient is not significant, meaning that it is likely not different from
null, and therefore does not contradict the discovered trend. To conclude, we find that the larger
the number of previous coauthors or publications is, the sooner the peak citation rate is reached.

3.2.3. Size of the effect

ich

, or publications, sNP
i and sNP

We also study the size of the dependence between a paper’s peak-delay, tpeak
previous coauthors, sNC
average peak-delay for given sNC
first focus on the number of previous coauthors sNC
except RMP the predicted average tpeak
is always less than 4 Jahre, irrespective of the number of
previous coauthors. For RMP, papers with no authors take around 7.5 years on average to reach
the peak, but this number then also decreases to 4 years at roughly 150 previous coauthors.

, und die Anzahl der
. Zu diesem Zweck, we use our fitted models to predict the
for each journal. Figur 3 shows these predictions. Let us
in Abbildung 3 (links). We see that for all journals

ich

ich

ich

ich

ich

We further point out the differences in speed across journals at which the peak-delays
decrease for increasing numbers of previous coauthors. Zum Beispiel, papers in the journal
PR-HEP reach the peak citation rate on average after 3.75 years for zero previous coauthors.
This duration changes to roughly 2.5 years for papers with 100 previous coauthors. This is dif-
ferent from the journal PRE. Dort, a paper reaches the peak citation rate on average after

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Fitted parameters (cid:4) for the negative binomial regression in Eq. 6, computed for each
Tisch 2.
journal individually. Four fits are displayed for each journal, depending on whether the predictor
is sNC
(NP), and whether time is measured in years (vgl. section 3.2) or in publications
ich
(vgl. section 3.4). The stated significance levels of the estimated parameter (cid:4) are given as
*** (< 0.001), ** (< 0.01), * (< 0.05) (NC) or sNP i si PR NC NP PRA NC NP PRC NC NP PRE NC NP RMP NC NP JHEP NC Time years pubs years pubs years pubs years pubs years pubs years pubs years pubs years pubs years pubs years pubs years pubs (cid:3) 0.768 0.903 0.721 0.922 1.055 0.637 1.095 0.625 1.141 1.132 1.130 1.141 0.907 0.971 0.941 0.992 1.987 1.482 2.022 1.534 0.050 −0.251 (cid:4) −0.022*** −0.003* −0.010*** −0.006*** −0.001*** 0.000 −0.005*** 0.001 −0.000* 0.000 −0.000 −0.000 −0.001*** −0.000 −0.004*** −0.002** −0.004* −0.003 −0.008* −0.008* −0.002 −0.001 1501 Quantitative Science Studies l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u q s s / a r t i c e - p d l f / / / / 1 4 1 4 9 3 1 8 7 1 0 2 3 q s s _ a _ 0 0 0 9 2 p d / . f b y g u e s t t o n 0 8 S e p e m b e r 2 0 2 3 Citations driven by social connections? Table 2. (continued ) si NP PR-HEP NC NP Phys. Lett. NC NP Nuc. Phys. NC NP Time years pubs years pubs years pubs years pubs years pubs years pubs years pubs (cid:3) 0.035 −0.286 1.292 1.870 1.321 1.907 0.813 1.088 0.824 1.094 1.156 1.199 1.211 1.239 (cid:4) 0.000 −0.000 −0.005*** −0.000* −0.004*** −0.001*** −0.007*** −0.009*** −0.004*** −0.005*** −0.007*** −0.005*** −0.005*** −0.004*** l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u q s s / a r t i c e - p d l f / / / / 1 4 1 4 9 3 1 8 7 1 0 2 3 q s s _ a _ 0 0 0 9 2 p d . / f b y g u e s t t o n 0 8 S e p e m b e r 2 0 2 3 Figure 3. Relation between peak-delays tpeak i measured in years, and the number of previous coauthors sNC (right) according to Eq. 6. The solid lines are the estimated responses, and the respective colored areas are 95% confidence bands from the negative binomial regres- sions. Estimated responses are plotted at most until the largest observed number of previous coauthors or publications in the respective journal. (left) or publications sNP i i Quantitative Science Studies 1502 Citations driven by social connections? 2.5 years for zero previous coauthors, which stays almost the same even at 100 previous coauthors. This means that journals have a large impact on the time when citations occur, espe- cially with respect to the prospective decrease as the number of coauthors grows. Figure 3 also shows confidence bands for the predicted average tpeak . These are narrow for all journals except one, because of the large numbers of papers used in the model fits. For the exception, RMP, only 214 papers were used, which is why its confidence bands are wider. i i Figure 3 (right) shows the average tpeak predicted by the number of previous publications, sNP . The main difference from Figure 3 (left) is that now also the peak-delays for the journals PRA and PRE decrease noticeably for increasing numbers of previous publications. For example, tpeak is on average equal to 3 years for zero previous publications, but this number drops to 1 year for 200 previous publications. This means that, to receive citations earlier in these journals, increasing the number of publications appears to be a more successful strategy than increasing the number of coauthors. i i To summarize, the negative binomial regression models show that for increasing numbers of previous coauthors or publications the highest citation rate is reached sooner. They also identify differences in the benefit of high numbers of coauthors or publications across journals: For journals such as PRC there is almost no decrease in peak delay, even with 200 previous coauthors. But for journals such as PR, papers that already have 50 previous coauthors reach their peak on average in less than half the time of papers with zero previous coauthors. 3.3. Characteristic Decay Time 3.3.1. Regressions We now analyze the relationship between characteristic decay time τi of paper i and the social relations of its authors. To find whether there is a significant relationship, we perform a linear analysis for log-transformed variables: log10 τi ¼ ατ þ βτ (cid:2) log10 si (7) i or the number of previous publications , and the time unit is again chosen as years. In the Supplementary Material, Section S2, we where again si is the number of previous coauthors sNC sNP i show that Eq. 7 reasonably fulfils the assumptions of linear regression models. Fitted parameters 3.3.2. These are presented in Table 3. There, we see that all fitted parameters (cid:4)τ are negative and significantly different from 0 (on a significance level of 0.05). To interpret the effect of si on τ i, one can exponentiate Eq. 7 to obtain τi (cid:3) si½ (cid:4)(cid:4)τ : (8) i becomes. From Eq. 3 we know that the smaller τ Because (cid:4)τ is negative, this means that the more previous coauthors the authors have, the smaller the value of τ i is, the faster the decay of the normalized citation rate ~ci(t). This in turn means that such a paper faces a quicker and stronger shortage in new citations. Again, we also find significantly negative parameters (cid:4)τ when using the number of previous publications sNP in Eq. 7. To conclude, we find that the larger the number of previous coauthors or publications is, the quicker and stronger the shortage in new citations after the peak. i Quantitative Science Studies 1503 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u q s s / a r t i c e - p d l f / / / / 1 4 1 4 9 3 1 8 7 1 0 2 3 q s s _ a _ 0 0 0 9 2 p d / . f b y g u e s t t o n 0 8 S e p e m b e r 2 0 2 3 Citations driven by social connections? Parameters (cid:4)τ Table 3. fitted according to Eq. 7 for each examined journal in our APS data set (left) and in our INSPIREHEP data set (right). Four fits are displayed for each journal, depending on whether the predictor is sNC (NP), and whether time is measured in years (cf. section 3.3) or in publications (cf. section 3.4). The significance levels of the p-values for (cid:4)τ *** (< 0.001), ** (< 0.01), * (< 0.05) are encoded as (NC) or sNP i i si PR NC NP PRA NC NP PRC NC NP PRE NC NP RMP NC NP JHEP NC Time years pubs years pubs years pubs years pubs years pubs years pubs years pubs years pubs years pubs years pubs years pubs (cid:3)τ 0.714 0.859 0.687 0.866 0.978 0.833 0.964 0.827 0.996 1.017 0.986 1.013 0.779 0.808 0.768 0.789 1.328 1.281 1.305 1.224 0.573 0.512 (cid:4)τ −0.082*** −0.013 −0.032*** −0.020* −0.138*** −0.056*** −0.142*** −0.058*** −0.071*** −0.052*** −0.083*** −0.063*** −0.041*** −0.049*** −0.036*** −0.038*** −0.272*** −0.337*** −0.247*** −0.281*** −0.061*** −0.002 1504 Quantitative Science Studies l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u q s s / a r t i c e - p d l f / / / / 1 4 1 4 9 3 1 8 7 1 0 2 3 q s s _ a _ 0 0 0 9 2 p d . / f b y g u e s t t o n 0 8 S e p e m b e r 2 0 2 3 Citations driven by social connections? Table 3. (continued ) si NP PR-HEP NC NP Phys. Lett. NC NP Nuc. Phys. NC NP Time years pubs years pubs years pubs years pubs years pubs years pubs years pubs (cid:3)τ 0.524 0.490 0.917 1.284 0.902 1.269 0.846 0.918 0.849 0.916 0.971 0.997 0.997 1.012 (cid:4)τ −0.026*** 0.011 −0.159*** −0.054*** −0.135*** −0.039*** −0.080*** −0.123*** −0.070*** −0.102*** −0.117*** −0.116*** −0.119*** −0.111*** l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u q s s / a r t i c e - p d l f / / / / 1 4 1 4 9 3 1 8 7 1 0 2 3 q s s _ a _ 0 0 0 9 2 p d / . f b y g u e s t t o n 0 8 S e p e m b e r 2 0 2 3 Figure 4. Relation between decay exponents τ (left) or the number of previous publications sNP i and the number of previous coauthors sNC (right) according to Eq. 7. The solid lines are the estimated responses, and the respective colored areas are 95% confidence bands derived from the standard errors. Estimated responses are plotted at most until the largest observed number of previous coauthors or publications in the respective journal. i i Quantitative Science Studies 1505 Citations driven by social connections? 3.3.3. Size of the effect i i or publications sNP We also intend to study the size of the dependence between decay exponents τ i and the number of previous coauthors sNC . To this end, we visualize the estimated average decay parameters for the different journals in Figure 4. We focus on the description of the num- ber of previous coauthors, Figure 4 (left), because overall both plots convey a similar message. We see that for papers with zero previous coauthors, the decay exponents are below 10 for all journals, except for RMP, which attains a decay exponent below 30. We further point out that papers in the journal JHEP have the smallest decay exponents even for up to 1,000 previous coauthors. This in turn means that decays in this journal tend to be particularly fast compared to the other journals. 3.4. Rescaling Time by Counting Publications 3.4.1. Effect of the growing scientific output It is known that the number of papers published every year grows exponentially over time (Price, 1951). This means that in recent years there are more papers published in a given time interval than was the case longer ago. All of these new publications can potentially cite a given paper. This time dependence likely affects our regression results by confounding the respective response (tpeak ). In the past it was suggested that the de- pendence of the citation rate on the publication year of a paper can be weakened by counting time in terms of the number of published papers instead of absolute time (days, weeks, years, etc.; Parolo et al., 2015). Therefore we repeat our regressions from section 3.2 and 3.2, and while measuring time on this alternative timescale. Thereby we assess whether such a bias from the publication year of a paper is present in the relations that we found. i) and predictor variable (sNC or sNP i or τ i i 3.4.2. Results for the alternative timescale i The fitted parameters are listed in the pubs rows in Table 2 for the peak-delay models and in Table 3 for the decay models. They remain smaller than 0, except for three journals: PRA, PRC, and JHEP. For PRA and PRC the fitted parameters (cid:4) are positive for the peak-delay models with the number of previous coauthors, sNC , as predictor. However, neither of these parameters is significantly different from 0. For JHEP the fitted parameter, βτ 1, is positive for the decay model with the previous number of publications, sNP , as predictor. However, this parameter is also not significantly different from 0. Only one significantly positive parameter occurs in the whole study, namely for PRA with the number of previous publications, sNP , as predictor. The fitted parameters for all other journals are either negative or insignificantly different from zero, as was the case when measuring time in years. This means that, also according to the alternative timescale, for most journals the citation rate peak is reached faster for papers by authors with more previous coauthors or publications. Accordingly, the decay becomes steeper for papers by such authors. i i 4. CONCLUSIONS In this paper, we address the question of how the attention towards an academic publication is accumulated over time, depending on the social relations of its authors, as expressed in the coauthorship network. For example, does the attention mostly occur in an early phase right after publication? Or is it rather spread uniformly over time? Or might it even happen only after a long time has passed since publication? To obtain a tractable, objective characterization of attention, we proxy attention by the citation rate of a paper (i.e., the number of new citations obtained in a particular time interval). We argue that, in order for a citation to occur, the authors of the citing paper have to be aware of the cited paper. Quantitative Science Studies 1506 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u q s s / a r t i c e - p d l f / / / / 1 4 1 4 9 3 1 8 7 1 0 2 3 q s s _ a _ 0 0 0 9 2 p d / . f b y g u e s t t o n 0 8 S e p e m b e r 2 0 2 3 Citations driven by social connections? To study the time when this attention occurs, we compute the change in the number of cita- tions over a time interval (i.e., the citation rate). It is known that the citation rates of most papers have two characteristic phases over time, namely an increasing phase followed by a decay phase. We found that the first phase tends to get shorter and the decay in the second phase tends to get faster for papers written by authors who have many previous coauthors. We also found that for some journals the time to the peak citation rate is almost halved within the first 100 previous coauthors, while for other journals it stays almost unchanged. Such a difference is also present in the decay exponents for different journals. In terms of attention, our findings mean that papers written by authors with more previous coauthors attract attention faster, but are then also forgotten sooner. We also found this effect when measuring the number of previous papers of the authors instead of the number of previous coauthors. Furthermore, this effect also persisted when we controlled for the time when a paper was published. But most importantly, we found this effect in nine journals, based on hundreds of thousands of authors and papers and far more than a million citations. A study on such a large scale is a strong sign that we have uncovered a general trend that is not limited to the analyzed data sets. 4.1. A Speculative Explanation Which mechanisms could be responsible for this? One way how authors learn about the papers which they cite is through communication with other scientists. Hence, authors can use their (few or many) social contacts, proxied by coauthors, to “advertise” a paper. Our findings indicate that authors with many previous coauthors or papers tend to do so within a short period of time after publication. When a new publication is made, the authors “advertise” it to the scientific commu- nity by presenting it in conferences and seminars, by sharing it on social media, etc. This behav- iour happens within a finite time period, after which the authors stop actively promoting the given publication. However, this explanation is merely speculative at this point. 4.2. Regressions Not Suitable for Predictions Our performed regressions have low predictive power, as indicated by extremely small coeffi- cients of determination, R2. For instance, for some regressions the R2 is as low as 0.001, meaning that only 0.1% of the variance in the dependent variable is explained. However, while our regression models are not useful for prediction, our inferred relations are significant. In particular our regressions show that the time to the peak citation rate and the subsequent decay are not independent of the authors. 4.3. No Causal Relations Studied In our study, we focus on the detection of the dependence between citation rate and social rela- tions of the authors. However, we do not (yet) aim to understand the actual mechanisms behind it. In other words, we study associations between measures of social relations and citation histories, but we do not aim to detect causal relationships between them. For example, our study does not guarantee that a paper gets scientific attention faster simply by replacing its authors by scientists with larger publication or coauthor counts. Instead, we observe such faster attention among papers whose authors were not actively chosen based on their past social relations. 4.4. Future Work In the future, we also intend to study causal relationships. Such a study will allow us to determine why authors with many previous publications or coauthors tend to write papers that receive scientific attention faster. To this end, we can use generative modeling to learn more about these Quantitative Science Studies 1507 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u q s s / a r t i c e - p d l f / / / / 1 4 1 4 9 3 1 8 7 1 0 2 3 q s s _ a _ 0 0 0 9 2 p d / . f b y g u e s t t o n 0 8 S e p e m b e r 2 0 2 3 Citations driven by social connections? underlying mechanisms. For instance, hypotheses can be formulated and tested using the frame- work of coupled growth models presented in Nanumyan et al. (2020). We find that a paper receives attention from the scientific community faster, the more coau- thors the authors had prior to its publication. But we find as well that such a paper is also forgotten sooner again afterwards. Our findings indeed highlight that the citations of a paper can have substantially different dynamics depending on the social relations of the authors. Furthermore, our approach illustrates how such coupled dynamics can be studied by representing scientific collaborations in a multilayer network. ACKNOWLEDGMENTS The authors would like to thank all reviewers for their comments and Luca Verginer and Giacomo Vaccario for discussions concerning the negative binomial regression models. AUTHOR CONTRIBUTIONS Christian Zingg: Conceptualization, Data curation, Formal analysis, Software, Validation, Visualization, Writing—original draft, Writing—review & editing. Vahan Nanumyan: Conceptualization, Data curation, Formal analysis, Software, Validation, Visualization, Writing—original draft, Writing— review & editing. Frank Schweitzer: Conceptualization, Formal analysis, Project administration, Supervision, Visualization, Writing—original draft, Writing—review & editing. COMPETING INTERESTS The authors have no competing interests. FUNDING INFORMATION No funding has been received for this research. DATA AVAILABILITY We use two large bibliographic databases, APS and INSPIREHEP. Access to the APS database can be requested for research purposes at https://journals.aps.org/datasets. Access to the INSPIREHEP database is possible either as a download or through an API as explained on its website https://inspirehep.net/. For this paper, we downloaded the INSPIREHEP database. 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