Scientific collaboration patterns vary with scholars’ academic ages Wei Wang 1,2 • Shuo Yu 1,2 • Teshome Megersa Bekele 1,2 • Xiangjie Kong 1,2 • Feng Xia 1,2 Received: 28 November 2016 / Published online: 19 April 2017 Ó Akade ´miai Kiado ´, Budapest, Hungary 2017 Abstract Scientists may encounter many collaborators of different academic ages throughout their careers. Thus, they are required to make essential decisions to commence or end a creative partnership. This process can be influenced by strategic motivations because young scholars are pursuers while senior scholars are normally attractors during new collaborative opportunities. While previous works have mainly focused on cross- sectional collaboration patterns, this work investigates scientific collaboration networks from scholars’ local perspectives based on their academic ages. We aim to harness the power of big scholarly data to investigate scholars’ academic-age-aware collaboration patterns. From more than 621,493 scholars and 2,646,941 collaboration records in Physics and Computer Science, we discover several interesting academic-age-aware behaviors. First, in a given time period, the academic age distribution follows the long-tail distri- bution, where more than 80% scholars are of young age. Second, with the increasing of academic age, the degree centrality of scholars goes up accordingly, which means that senior scholars tend to have more collaborators. Third, based on the collaboration fre- quency and distribution between scholars of different academic ages, we observe an obvious homophily phenomenon in scientific collaborations. Fourth, the scientific col- laboration triads are mostly consisted with beginning scholars. Furthermore, the differ- ences in collaboration patterns between these two fields in terms of academic age are discussed. Keywords Scientific collaboration Academic age Collaboration pattern & Xiangjie Kong [email protected]1 School of Software, Dalian University of Technology, Dalian 116620, China 2 Key Laboratory for Ubiquitous Network and Service Software of Liaoning Province, Dalian, China 123 Scientometrics (2017) 112:329–343 DOI 10.1007/s11192-017-2388-9
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Scientific collaboration patterns vary with scholars’academic ages
Fig. 2 Proportions of different academic ages over time. (Color figure online)
0 5 10 15 20 25 30 35 40 45
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
Junior SeniorBeginning
Prod
uctiv
ity
Academic Age
APS
Fig. 3 Scholars’ annual productivity at different academic ages
Beginning Junior Senior(b)(a) (c) (d)
Fig. 4 Examples of scientific ego networks
Scientometrics (2017) 112:329–343 333
123
Beginner–Beginner–Beginner (BBB) triads or cross-age relationships, i.e., Beginner–Ju-
nior–Senior (BJS) triads. Similar statistical analysis also can be performed on other aca-
demic triads on the junior ego network (Fig. 4b) and the senior ego network (Fig. 4c).
Figure 4d depicts an example of an interconnected component of authors and their
respective neighborhoods.
We present a comprehensive analysis between scholars’ academic age and their col-
laboration behaviors to observe how scholars of different academic ages collaborate with
each other to meet their specific academic needs. Inspiring by the idea of exploring ego
network structure in previous work (Dong et al. 2014) the following four network prop-
erties are considered. These features can illustrate the network properties of a given
scholar.
Degree Centrality (DC) the number of collaborators upon a scholar i in the network
(Opsahl et al. 2010; Badar et al. 2016), which is calculated as:
DC ¼ Ni ð1Þ
where Ni is the number of neighbors of scholar i.
Neighbor connectivity (NC) the average degree of neighbors of a specific scholar i
(Zhao et al. 2013), which is calculated as:
NC ¼ 1
jNijX
v�Ni
Nv ð2Þ
where Nv is the neighbors of scholar i.
Local clustering coefficient (CC) the measure of how closely a scholar’ neighbors relate
with each other (Newman 2001a; Leskovec et al. 2008), which is calculated as:
CC ¼ 2Ei
NiðNi � 1Þ ð3Þ
where Ei is the number of edges.
EmbeddedNess (EN) the extent that scholars are enmeshed in scientific collaboration
network (Granovetter 1985), which can be calculated as:
EN ¼ 1
jNijX
v�Ni
jNi \ NvjjNi [ Nvj
ð4Þ
where Ni is the neighbor of scholar i and Nv is the neighbor of scholar v.
All the features are extracted and calculated with Python. The network is constructed
with the NetworkX package (Schult and Swart 2008) in Python which is a high-produc-
tivity software for complex networks. After the construction of the network, these features
can be calculated directly based on their definitions. All experiments are performed on a
64-bit Windows based operation system, with a 4-duo and 2.6-GHz Intel Xeon CPU,
128-G Bytes memory.
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Results
Scholar academic age distribution
We observe that the number of scholars drops sharply with the increase of academic age
(see Fig. 5). For example, using APS data sets, there are more than 33,000 physics
scholars, whose academic ages are \4, which is more than 30% of the total scholars. In
other words, more than 30% of scholars stop publishing papers after the third academic
age. This shows that many scholars have a short academic career. At the academic age of
10, there are merely 2051 scholars, which is 1.8% of the total scholars. We can see from
this figure that the academic age distribution follows the long-tail distribution, where more
than 80% scholars are of young age. Meanwhile, even though DBLP has more scholars
than APS, we observe that there are more senior scholars in Physics than that in Computer
Science. We further consider academic age beyond 29 and find that scholars in Physics
exceed that of Computer Science, which strengthens our observation.
Network characteristics
We explore the extent to which academic age correlated to the four network structure
properties in Fig. 6. Our analysis shows that at the academic age of 35, the DC and NC of
both APS and DBLP reach peak values and then decrease slightly (see Fig. 6a, b). At the
same time, APS has higher values than DBLP at all academic ages. The DC and NC of
DBLP increase slowly before 25 academic age.
Furthermore, we find that both CC and EN values decrease smoothly, and reach the
lowest value around the academic age of 30 (see Fig. 6c, d). These two metrics have also
been used to analyze the correlation between human communication behaviors and ages
(Dong et al. 2014). The results show that both CC and EN increase when people get older.
By comparison, we discover that collaborating with more scholars makes scholar ego
network relatively unstable. Beginning and senior scholars have a relatively stable con-
nections. Similar to the first two network properties, i.e., DC and NC, APS has higher
values of CC and EN than DBLP at all academic ages. In the meantime, the CC and EN of
DBLP drop more quickly than that of APS before academic age 25.
0 10 20 30 40 50
100
1000
10000
Academic Age
Num
bero
fSch
olars
APSDBLP
60000Fig. 5 Number of Scholars atdifferent academic ages. Shownas the distributions of scholars atdifferent academic ages in APSand DBLP
Scientometrics (2017) 112:329–343 335
123
Meanwhile, we further calculate the assortativity of beginning, junior and senior
scholars to explore NC feature. In a given network, if the hubs tend to link each other and
the small-degree nodes tend to connect to other small-degree node, the network is assor-
tative (Barabasi 2016). The assortativity feature is similar with the NC feature because they
both explore the relationships between nodes’ degree and their neighbors’ degree. We can
see from Fig. 7 that these networks all are assortative. The scholars in APS are more
assortative than DBLP. Meanwhile, with the increase of academic age, scholars tend to be
more assortative.
(a) (b)
(d)(c)
Fig. 6 Correlations between academic age and network properties. a The degree centrality, b neighborconnectivity, c local clustering coefficient, and d embeddedness dynamics at each academic age in APS andDBLP
APSDBLP
APSDBLP
100 101 102 103100
101
102
APSDBLP
Knn(K
)
100
101
102
Knn(K)
100
101
102
Knn(K
)
K100 101 102 103
K100 101 102 103
K
(a) (b) (c)
Fig. 7 Assortativity of beginning, junior, and senior scholars. The K denotes the degree of target nodes andthe KnnK denotes the degree of their neighbors. a Beginner scholar, b junior scholar, c senior scholar
336 Scientometrics (2017) 112:329–343
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We can see from Figs. 6 and 7 that with the increasing of academic age, the degree
centrality goes up accordingly and the local clustering coefficient of junior scholars is lower
than beginning scholars and senior scholars. The overall trend is that with the increase of
academic age, both the DC and NC goes up slowly since beginning scholars will meet more
junior scholars who might have more collaborators. From a sociological perspective, the
above observation can be explained as the nature of academic society and academic
strategies that scholars adopt different collaboration strategies to meet their academic needs.
Beginning scholars have a few but stable connections which may result from the mentor-
student relationships. For instance, a Ph.D. candidate may frequently collaborate with his/her
mentors as well as lab members. Thus, this might show that early career age scholars who has
lower degree values, are more active in broadening their academic circles, while senior
scholars who have stable embeddedness scores tend to keep steady relationships. In other
words, young scholars have small but stable academic circles. When they extend their
academic circles, their co-authors may collaborate less with each other. Then, after certain
ages, they will meet few new collaborators and the coauthors’ connectivity will go up slowly.
Triads in collaborations
In order to better understand various collaboration triads, we investigate scholars’ col-
laborator components at different academic ages. Collaborators’ academic age distribution
of beginning, junior and senior scholars in APS is shown in Fig. 8a. Our analysis find that
the collaborators of beginning, junior and senior scholars are mainly consists of scholars
who are younger than four academic age. In particular, most collaborators are of three
academic age. Each group’s academic age distributions also show that (a) Beginning
scholars have more collaborators whose academic age falls between 1 and 9 compared to
that of junior and senior scholars; (b) Junior scholars have more collaborators whose
0.00
0.02
0.04
0.06
0.08
0.10
0.120
0 10 20 30 40 50
10 20 30 40 500.00
0.02
0.04
0.06
0.08
0.10
DBLP BeginningDBLP JuniorDBLP Senior
(b)Prop
ortio
n
APS BeginningAPS JuniorAPS Senior
(a)
Academic Age
Fig. 8 Collaborators’ academic age distribution of beginning, junior and senior scholars. Shown ascomponents of beginning, junior and senior scholars’ collaborators in a APS and b DBLP. (Colorfigure online)
Scientometrics (2017) 112:329–343 337
123
academic age falls between 10 and 15 compared to that of beginning and senior scholars;
and (c) Senior scholars have more collaborators whose academic age is more than 15.
Similar trends have also been found in DBLP as shown in Fig. 8b. However, in DBLP,
scholars with academic age between 1 and 3 share a large percentage of the distributions.
In the meantime, there are differences compared to APS as follows: (a) Beginning scholars
have more 1–5 academic age collaborators than that of junior and senior scholars; (b) Ju-
nior scholars have more 6–19 academic age collaborators than that of beginning and senior
scholars and (c) Senior scholars have more collaborators whose academic age is more than
20.
In addition, we analyze the percentage of different collaboration triads and depict it
using the pie chart in Fig. 9. The most common collaboration relationship in APS is BBJ
triad, which is 19.1% of the total collaborations. Each of BJS, BBB, BBS and BJJ triad
shares more than 10% of all triads. However, in DBLP, the most common collaboration
relationship is BBB with a share of a large portion, 46.5%, which is almost half of all the
triads. The second and third largest collaboration triads in DBLP are BBJ and BBS,
respectively. Since there are fewer old scholars both in APS and DBLP, there are fewer
SSS and JSS triads. This is probably because of Computer Science is a relatively a young
discipline compared to Physics, and more papers are published by beginning scholars. On
the one hand, Computer Science discipline develops fast, which makes it difficult for older
scholars to catch up with rapidly emerging applications, methodologies, and technologies
of computing. On the other hand, Physics is relatively more stable and senior scholars are
still active.
Based on analysis above, we can get the conclusions that scientific collaborations based
on academic age display a homophily phenomenon. This phenomenon delineates that
people tend to interact with those who are similar to them (Lazarsfeld and Merton 1954). It
has been comprehensively analyzed and verified in online social networks (Lou et al.
2013) and human communication networks (Dong et al. 2014). The academic age
homophily is much stronger for scholars aged from 1 to 5. For example,the BBB triad
shares large collaborations percentage in both Computer Science and Physics (see Fig. 9).
(a) (b)
Fig. 9 Proportions of different triads. Shown as the ratios of different collaboration triads in a APS andb DBLP. (Color figure online)
338 Scientometrics (2017) 112:329–343
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Collaboration frequency between AAs
Previous research has shown that incorporating collaboration times can help to improve the
accuracy of recommending collaborators (Xia et al. 2014). The heat map in Fig. 10 shows
the collaboration frequency distributions among academic ages. The X-axis and Y-axis
represent scholars’ academic ages. The spectrum color, which ranges from blue (low) to
red (high), shows the number of collaboration frequencies among different ages. It shows
that with the increasing of academic age, scholars tends to collaborate with each other
more frequently. In APS, we find that scholars with lower academic age, i.e., no more than
5, usually collaborate with others once, while scholars with high academic age, i.e., more
than 25, collaborate with others more than twice. Due to the rareness of very old scholars in
DBLP, there are some null points between academic age 33 and 43. Meanwhile, scholars in
Computer Science tend to collaborate with each other more frequently from a global
perspective. Another interesting phenomenon is a highlighted diagonal line in DBLP,
which suggests the academic-age homophily phenomenon that scholars tend to collaborate
with others of similar academic age.
Collaboration distribution between AAs
The spectrum color extending from blue (low) to red (high) in Fig. 11 represents the
proportions of collaborations between scholars in every academic age. Both Fig. 11a, b
show that with the increasing of academic age, the proportion of collaborations drops
accordingly. At the same time, there exists a relative highlighted diagonal line both in APS
and DBLP, which also demonstrates the existence of homophily phenomenon. Meanwhile,
connections among beginning scholars are more common to observe, which indicates that
beginning scholars are the main workforce in academia. However, the spectrum color in
DBLP changes more dramatically than that of APS. The possible reason may be that most
scholars have a short academic age. For example, a professor may supervise several doctor
and master students. These students may collaborate more frequently with each other.
After graduation, they may go to work where they will seldom write papers. Thus, mentors
(a) (b)
Fig. 10 Collaboration times among ages. Shown as the collaboration times between any two academic agesin a APS and b DBLP. (Color figure online)
Scientometrics (2017) 112:329–343 339
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will probably recruit new students. In this condition, there are more beginning scholars and
few senior scholars in academia. Therefore, we can conclude that the large percentages of
collaborations happen among young scholars.
(a) (b)
Fig. 11 Collaboration distribution between ages. Shown as the collaboration distribution between any twoacademic ages in a APS and b DBLP. (Color figure online)
(a) (b)
(d)(c)
Fig. 12 Network properties in different time periods. Shown as a the degree centrality, b neighborconnectivity, c local clustering coefficient, and d embeddedness dynamics at each academic age in APS atthree time periods. (Color figure online)
340 Scientometrics (2017) 112:329–343
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Comparisons in different time periods
Figure 12 shows the strength of the four network properties at different academic ages
during 1987–1989, 1999–2001, and 2011–2013 time periods. According to Fig. 3, where
the academic career of a scholar is divided into three stages based on productivity, the time
interval between two stages is 12 years. Thus, we choose 12 years to distinguish different
periods based on the idea that 12 years is long enough to have two generations of scholars.
From Fig. 12a, b, we can observe that the DC and NC increase with academic age for the
three time periods. In 1987–1989 and 1999–2001, the trend of DC and NC are almost the
same, while, in 2011–2013, the values of DC and NC are higher than that of previous two
periods. The advancement of science and communication platform can be accounted as a
reason for more publications with multiple authors. Thus, this result shows that collabo-
rations are getting more popular, which is confirmed with the study in Katz and Martin
(1997).
From Fig. 12c, it can be seen that the CC of the three time periods is practically the
same. Younger and senior scholars have higher CC while junior scholars have lower CC.
Figure 12d presents the EN of the three time periods. In 1987–1989 time periods, the
scholars’ EN value is the highest while it’s the lowest in 2011–2013. This indicates that as
the time goes on scholars tend to have an unstable academic condition, i.e. scholars are not
well embedded in collaboration networks.
Furthermore, the proportions of different collaboration triads in different time periods
are shown in Fig. 13. In 1987–1989 and 1999–2001, BBB triad shares the largest scientific
collaboration proportion, while, in 2011–2013, the largest proportion is BBJ triads. The
share of the top three triads i.e., BBB, BBJ, and BBS in 1987–1989 and 1999–2001 drops
sharply while the share of the top four triads i.e., BBB, BBJ, BBS and BJS in 2011–2013
have no obvious change. Meanwhile, more senior scholars are active in 2011–2013 than
other two periods.
BBB BBJ BBS BJS BJJ BSS JJS JSS JJJ SSS0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
Prop
ortio
n
2011-20131999-20011987-1989
Fig. 13 Proportions of different triads in different time periods. Shown as the ratios of differentcollaboration triads of APS in three time periods. (Color figure online)
Scientometrics (2017) 112:329–343 341
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Discussion
In this work, we study the collaborative strategies among scholars’ of different academic
ages during three distinct time periods. We examine academic-age-aware collaborations
from a scholar’s local perspective based on his/her ego network. We discover that the
academic age distribution follows the long-tail distribution. We explore the collaboration
pattern differences between Computer Science and Physics disciplines. The collaboration
patterns in different time periods are investigated. We further uncover that an obvious
homophily phenomenon exists in scientific collaboration on academic age.
We believe that academic age, which is a basic demographic characteristic of scholars,
should be analyzed extensively. Detecting and investigating academic-age-aware collab-
oration behaviors can shed new light on the scientific collaboration mechanisms. Policy
makers may establish new policies to promote scientific collaborations based on academic-
age-aware collaboration behaviors. Meanwhile, understanding the collaboration mecha-
nisms cross academic ages may benefit many practical issues such as team structure
optimization.
Despite the promising results of this work, there is still much room left for future work.
First, academic-age-aware behaviors can be used to explore team science, which might
require additional analysis of more social theories and collaboration patterns. Second,
studying academic-age-aware behavior impact on recommending collaborators and
scholars’ future success can be worth mentioning as future research directions.
Acknowledgements Funding was provided by the Graduate Education Reform Fund of DUT (Grant No.JG2016022).
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