# Static and Dynamic Aspects of
Scientific Collaboration Networks

Christian Staudt<EMAIL_ADDRESS>Andrea Schumm
<EMAIL_ADDRESS>Henning Meyerhenke<EMAIL_ADDRESS>Robert Görke
<EMAIL_ADDRESS>Dorothea Wagner<EMAIL_ADDRESS>Institute of
Theoretical Informatics, Karlsruhe Institute of Technology (KIT), Am
Fasanengarten 5, 76131 Karlsruhe, Germany

###### Abstract

Collaboration networks arise when we map the connections between scientists
which are formed through joint publications. These networks thus display the
social structure of academia, and also allow conclusions about the structure
of scientific knowledge. Using the computer science publication database DBLP,
we compile relations between authors and publications as graphs and proceed
with examining and quantifying collaborative relations with graph-based
methods. We review standard properties of the network and rank authors and
publications by centrality. Additionally, we detect communities with
_modularity_ -based clustering and compare the resulting clusters to a ground-
truth based on conferences and thus topical similarity. In a second part, we
are the first to combine DBLP network data with data from the _Dagstuhl
Seminars_ : We investigate whether seminars of this kind, as social and
academic events designed to connect researchers, leave a visible track in the
structure of the collaboration network. Our results suggest that such single
events are not influential enough to change the network structure
significantly. However, the network structure seems to influence a
participant’s decision to accept or decline an invitation.

##  I Introduction

In scientometrics, the quantitative study of science, network analysis has
become a prominent tool. _Coauthorship networks_ have attracted interest both
as _social networks_ and as _knowledge networks_ : They display the social
structure of academia, while their bibliographic aspect allows conclusions
about the structure of scientific knowledge. Accordingly, networks of this
kind are the objects of ongoing research: Newman ([1, 2, 3, 4]), for example,
studies properties of coauthorship networks in the realm of physics (Los
Alamos e-Print Archive, SPIRES), mathematics (Mathematical Reviews),
biomedical research (Medline) and computer science (NCSTRL), summarizing many
statistical properties of coauthorship networks. Aspects like _connectedness_
, _distance_ , _degree distribution_ , _centrality_ and _community structure_
are recurring themes in such studies. Where we follow up on these topics, we
cite relevant related work in the respective sections of this paper.

Based on the extensive publication database _DBLP_ [5], we model relations
between authors and publications as graphs, mapping almost the entire field of
computer science. This allows us to examine and quantify the collaborative
relations between researchers using graph-based methods. We compile a graph in
which edges link coauthors, as well as a bipartite author-paper graph. In the
first part, we review standard properties of the network, rank authors and
publications by centrality, and detect communities with _modularity_ -based
clustering. In the second part, we combine the network with seminar data
provided by the _Schloss Dagstuhl_ [6] conference center: The _Dagstuhl
Seminars_ assemble researchers with the goal of fostering (collaborative) work
in cutting-edge areas of computer science. We examine whether such events
leave a track in the structure of the collaboration network. For this purpose,
we apply appropriate measures to a time-resolved version of the _authorship
graph_.

We are the first to perform a joint analysis of the Dagstuhl and DBLP
datasets, which allows us to study the impact of social/academic events on the
time-evolution of the network structure. Our results suggest that a
participant’s decision to accept or decline an invitation can be predicted
from the network data to some extent. While our analysis of the DBLP data
mostly confirms properties of similar networks, the distribution of the number
of coauthors differs from data reported in [4]. We also describe an approach
to finding central researchers based on _eigenvector centrality_ in the
bipartite authorship graph, a combination that to our knowledge has not been
used before. Additionally, we apply _modularity_ clustering and compare the
detected communities to a ground-truth defined by conferences, from which we
infer distinct areas of research.

##  II Preliminaries

###  II-A Collaboration Network Model

As of 2011, DBLP covers about 1.5 million publications by 0.8 million authors.
The earliest work dates from 1936, and we include all works up to 2009 in our
analysis. We describe briefly how a coauthorship network is extracted from the
publication database and represented as different types of graphs. The
database associates publications and authors and thus provides two main
relations, _authorship_ and _coauthorship_ , formalized as follows:

######  Def. 1.

Given the sets of authors $\mathbf{A}$ and publications $\mathbf{P}$, the
_authorship_ relation is defined as

$\forall\\{a,p\\}\in\mathbf{A}\times\mathbf{P}:\quad a\smile p\iff\text{$a$ is
author of $p$}$

The _coauthorship_ relation between two authors from $\mathbf{A}$ is defined
as

$\forall\\{a,b\\}\in\mathbf{A}\times\mathbf{A}:a\frown b\iff\exists
p\in\mathbf{P}:a\smile p\wedge b\smile p$

From these, two graph representations of the network follow: A bipartite
_authorship graph_ (or author-paper graph) $G_{\mathbf{PA}}$, in which each
publication is connected by edges to its authors; and a _coauthorship graph_
$G_{\mathbf{A}}$, in which two authors are connected by an edge if they are
coauthors of a joint publication.

######  Def. 2.

The _authorship graph_ is a mapping from the sets of publications $\mathbf{P}$
and authors $\mathbf{A}$ to the node sets $V_{\mathbf{P}}$ and
$V_{\mathbf{A}}$, resulting in a bipartite graph
$G_{\mathbf{PA}}=(V_{\mathbf{A}},V_{\mathbf{P}},E)$, where

$\\{v_{a},v_{p}\\}\in E\iff a\smile p$

######  Def. 3.

The _coauthorship graph_ is a mapping from the set of authors $\mathbf{A}$ to
the node set $V_{\mathbf{A}}$, resulting in the graph
$G_{\mathbf{A}}=(V_{\mathbf{A}},E)$, where

$\\{v_{a},v_{b}\\}\in E\iff a\frown b$

While $G_{\mathbf{A}}$ is sufficient when focusing only on the social network
of coauthors, $G_{\mathbf{PA}}$ preserves the publications as the cause of
relations, as well as single-author publications. Table I shows the size of
the graphs constructed from the full publication data set.

graph | $n$ | $m$
---|---|---
$G_{\mathbf{PA}}$ | 2 296 586 | 3 775 881
$G_{\mathbf{A}}$ | 852 250 | 2 785 037
TABLE I: Size of resulting graphs

In order to determine whether events have effects detectable in terms of the
network (Section IV), we also track groups of authors over the course of time,
using a sequence of graphs in which each graph represents a current snapshot
of the authorship relations. This _time-resolved_ version of $G_{\mathbf{PA}}$
enables us to study the dynamics of the network: Let $t(p)$ denote the
publication date of publication $p$. Then the publications from a time segment
$[y,z],z>y$, are

$\mathbf{P}_{[y,z]}:=\\{p\in\mathbf{P}:y\leq t(p)\leq z\\}$

The respective authors of these publications are

$\mathbf{A}_{[y,z]}:=\\{a\in\mathbf{A}:\exists p\in\mathbf{P}_{[y,z]}:a\smile
p\\}$

The graph sequence is constructed on the basis of a sliding time segment, with
parameters width $w$ and increment $s$:

######  Def. 4.

The _time-resolved authorship graph_ is a sequence of graphs
$\mathcal{G}_{\mathbf{PA}}^{w,s}$ where each graph in the sequence is
constructed from the publications in $\mathbf{P}_{[y,y+w]}$ and the authors up
to $\mathbf{A}_{[y,y+w]}$ using a sliding time segment with width $w$ and
increment $s$.

Author nodes are aggregated over time, while publications are deleted for each
step in the sequence. A time segment and increment of 1 year was chosen for
the study in Section IV, the finest time resolution possible with DBLP data.

##  III Network Properties and Community Structure

###  III-A General Network Properties

We briefly review some general properties of the collaboration network:

#### Connectedness

$G_{\mathbf{A}}$ features a _giant connected component_ containing about 80%
of all authors. (Giant components connecting up to 90% of all authors have
previously been detected across scientific fields [3]). Aside from the 6% of
the authors without collaborations, about 14 % of author nodes are distributed
over a multitude of small components with few publications. We conclude that,
in general, authors who have worked on several publications and were part of
more than one collaborative team join the large connected component. In terms
of average distances between researchers (6.58 for a sample), we confirm the
previously reported _small world_ property for the field of computer science
[4] and DBLP in particular [7].

####  $k$-Core Structure

Figure 1: Histogram of _core numbers_ in $G_{\mathbf{A}}$ (x-axis: _core
number_ , logarithmic y-axis: frequency)

A $k$-core is a maximal subgraph in which each node is adjacent to at least
$k$ other nodes. $k$-cores refine the concept of connected components (which
form the 1-core); _$k$ -core decomposition_ reveals nested, successively more
cohesive layers of the graph. We assign each node a _core number_ , the
highest $k$ for which there is a $k$-core containing the node. Figure 1 shows
a histogram of the resulting _core numbers_ in $G_{\mathbf{A}}$ with two
logarithmic axes. The rather uniform sequence indicates uniform density and
cohesiveness of the graph, showing that the network does not have strongly
cohesive groups of authors embedded in shells of weakly connected authors [8].
A more extensive $k$-core analysis of a DBLP-based coauthorship network is
presented in [9].

#### Degree Distribution

Figure 2: Degree distribution in $G_{A}$ (logarithmic x-axis: degree,
logarithmic y-axis: frequency)

Node degree in $G_{\mathbf{A}}$ corresponds to the number of coauthors of each
author. The degree distribution is highly skewed. It indicates a _scale-free
network_ , in which the frequency $P(k)$ of nodes with degree $k$ follows a
power law, i.e. $P(k)\sim k^{-\gamma}$, with coefficient $\gamma=2.889$.
Newman [3] reports a differing power-law degree distribution in the number of
coauthors with $\gamma=3.41$ for computer science, based on NCSTRL.

#### Summary

General properties indicate that the network of collaborations in computer
science is in many respects a typical social network: It shows participation
inequality (visible as a power-law degree distribution), with a few highly
prolific authors and many smaller contributions. It also features a high
degree of connectedness, a giant component, and mostly short paths between
arbitrary pairs of nodes. Our observations are in agreement with the results
of related studies (except for the degree power-law exponent), indicating that
these properties are universal features of scientific collaboration networks.

###  III-B Centrality

_Centrality measures_ were formulated to identify nodes which are structurally
prominent or influential, due to their position in the center of a network.
_Betweenness_ and _closeness centrality_ have previously been applied to
coauthorship graphs with the goal of identifying influential scientists in
their respective fields ([4, 10]). Elmacioglu et al. report a ranking of
prominent scholars by _closeness_ and _betweenness_ centrality [7]. As a
rationale, it has been stated that authors with high _betweenness_ are
important intermediates for interactions or information flows, as it allows
them to control such flows; high closeness is assumed to be an advantage for
accessing or disseminating information [7]. However, it is not clear why
academic influence should be understood mainly as the ability to mediate
interactions. Furthermore, the network of information flow in academia and the
network of coauthorship relations may be quite distinct. We therefore follow a
different approach based on _eigenvector centrality_ [11] in the bipartite
authorship graph: It assumes that an author’s influence is first of all
proportional to the amount of publications. Additionally, the contribution of
a paper to an author’s centrality should be weighted depending on the
centrality of the coauthors.

######  Def. 5.

_Eigenvector centrality_ : Given a graph $G$ with adjacency matrix $A$, we
require a centrality score $x_{i}$ of node $v_{i}$ to be proportional to the
scores of its neighbors:

$x_{i}=c\sum_{j=1}^{n}A(i,j)\ x_{j}\qquad c\neq 0$

By the Perron-Frobenius theorem, there exists a nonnegative eigenvector $x$ of
$A$ (satisfying $Ax=\frac{1}{c}x=\lambda x$) which corresponds to the largest
eigenvalue $\lambda$. An entry $x_{i}$ constitutes the desired centrality
score for vertex $v_{i}$.

Modeling the collaboration network as the bipartite graph $G_{\mathbf{PA}}$
has the benefit that it allows us to assign a centrality score to a
publication as a node, rather than just account for a publication as an edge
attribute or weight in $G_{\mathbf{A}}$ [12]. Thus, our centrality scores
express the concept that authors are central in the collaboration network to
the extent that they have collaborated on central publications with other
central authors. In this respect, the approach is similar to ranking webpages
with the PageRank algorithm, where hyperlinks are treated as votes to the
relevance of the target page and are weighted by the relevance of the source
page.

$\begin{array}[]{|c|c|}\hline\cr\text{centrality}\cdot
10^{-5}&\text{author}\\\ \hline\cr 9.76232&\text{Diane Crawford}\\\
9.45441&\text{Robert L. Glass}\\\ 9.08697&\text{Chin-Chen Chang}\\\
8.30777&\text{Edwin R. Hancock}\\\ 7.91401&\text{Grzegorz Rozenberg}\\\
7.82901&\text{Joseph Y. Halpern}\\\ 7.75409&\text{Sudhakar M. Reddy}\\\
7.69387&\text{Philip S. Yu}\\\ 7.50894&\text{Moshe Y. Vardi}\\\
7.47370&\text{Ronald R. Yager}\\\ \hline\cr\end{array}$ TABLE II: Top segment
of author ranking by centrality

(a) authors

(b) publications

Figure 3: Centrality scores (logarithmic y-axis), sorted

Figure 3 shows the distributions of centrality scores for authors and
publications. Extreme values are less frequent, and the distribution does not
exhibit a power law. Table II contains the top segment of an author ranking by
our approach to centrality. (See [13] for a comparison to a purely
productivity-based ranking of DBLP authors.) The respective ranking of
publications places papers with unusually high author counts at the top, e.g.
work on large supercomputing and database projects, and further study would be
needed to interpret publication centrality properly. With respect to the
evaluation in Section IV, it should also be noted that Dagstuhl seminar
invitees have a significantly higher median _eigenvector centrality_ score
than other authors ($3.8\cdot 10^{-6}$ versus $2.4\cdot 10^{-7}$). We
therefore propose that _eigenvector centrality_ in bipartite author-paper
networks is a promising approach for studying the role and impact of
collaborating individuals in science, and might serve as an objective measure
of influence in scientific publishing.

###  III-C Modularity-driven Clustering

_Graph clustering_ comprises a variety of methods for detecting natural
communities in networks. Formally, it is concerned with partitioning the node
set into disjoint subsets (clusters), the result of which is called a
_clustering_. The notion of a cluster is usually based on the _intra-cluster
density versus inter-cluster sparsity_ paradigm, according to which a
clustering should identify groups of nodes which are internally densely
connected, while only sparse connections exist between the groups. One of the
primary measures of clustering quality based on this paradigm is _modularity_
[14].

######  Def. 6.

For a graph $G=(V,E)$ and a clustering $\zeta=\\{C_{1},\dots,C_{k}\\}$ of $G$,
_modularity_ is defined as

$\displaystyle\mathit{mod}(G,\zeta):=\sum_{C\in\zeta}\frac{|E(C)|}{|E|}-\sum_{C\in\zeta}\frac{\left(\sum_{v\in
C}deg(v)\right)^{2}}{(2\cdot|E|)^{2}}$

The measure considers the clustering’s _coverage_ (the fraction of edges
placed within a cluster) on the actual graph and subtracts the _coverage_ it
would achieve on a randomly connected version of the graph (preserving degree
distribution). _Modularity_ -based clusterings often agree with human
intuition, although criticism has emerged recently [15]. Since maximizing
_modularity_ is an $\mathcal{N}\mathcal{P}$-hard problem [16], we use a
heuristic based on _local greedy agglomeration_. The base algorithm, commonly
referred to as the Louvain Method [17], starts with a singleton clustering,
considers nodes in turn, moves them to the best neighboring cluster and
contracts the graph for the next iteration. This yields a hierarchy of graphs
with increasing coarseness where the clustering in the coarsest level induces
the resulting clustering in the original graph. Rotta et al. [18] enhance
this algorithm by a refinement phase that iteratively projects this clustering
to lower levels of the hierarchy and further improves modularity by local node
moves. We use this modified algorithm.

It is a common approach to apply a clustering method to a real world network
and then compare it to a ground-truth partition of the node set in order to
interpret the result. For example, Rodriguez et al. [19] study sensor
networks research groups and apply clustering techniques like _leading
eigenvector_ , but not _modularity_ maximization; these network-structural
communities are then compared to communities defined by socio-academic
similarities.

Figure 4: Size distribution for the 300 largest clusters (x-axis: cluster
size, y-axis: frequency)

We therefore proceed as follows: Applying local greedy agglomeration to
$G_{\mathbf{PA}}$ yields a clustering with 86761 clusters, achieving a
_modularity_ of 0.896896. The majority of clusters contain only a handful of
nodes, and likely correspond to the many tiny components of the graph, while
the dominant connected component is divided into several large clusters (see
Figure 4). With a clustering of the _authorship graph_ at hand, we attempt to
interpret such a _modularity_ -driven clustering in the context of
collaboration networks. The partition found by maximizing _modularity_ locally
identifies groups of authors who are densely connected through collaborative
ties. Our hypothesis is that we can infer a topical similarity from these
connections. More precisely, we conjecture that researchers form collaborative
ties around distinct areas of research, which is reflected in the clustering
structure of the graph. To put this hypothesis to the test, we compare the
_modularity clustering_ of $G_{\mathbf{PA}}$ to a ground-truth subdivision of
the author set based on conferences: Assuming that distinct areas of computer
science generally have dedicated conferences, we assign all authors who have
published at a particular conference to an author-cluster. (Unlike the
_modularity clustering_ , this does not yield a proper, complete and disjoint
partition of the author set, but is nonetheless informative.) Thereby we
arrive at _topical clusters_ of authors, which are suited as a ground-truth to
compare the _modularity clustering_ to.

| random | topical
---|---|---
$O$ | 0.04404 | 0.22832
$J$ | 0.00372 | 0.01390
TABLE III: Mean maximum overlap for modularity clustering and random vs
topical clustering

In order to evaluate the similarity between the two community structures, one
being the _modularity clustering_ , the other the _topical clustering_ defined
by conferences, we apply overlap measures to each pair of clusters: The
_Jaccard index_ $J(A,B):={{|A\cap B|}\over{|A\cup B|}}$ favors exact match of
the two sets; the _overlap coefficient_ $O(A,B):={{|A\cap
B|}\over{\min(|A|,|B|)}}$ treats containment of one set in the other set as a
strong match, which is more equitable when dealing with clusters of uneven
sizes. Applying these measures yields matrices of overlap values between
_modularity clusters_ and _topical clusters_. Additionally, we arrive at a
baseline for the overlap values by calculating the overlap matrix of
_modularity_ clustering and a random clustering. The random clustering is
constructed by copying the size distribution of the 250 largest modularity
clusters, but randomly assigning authors to the clusters.

In these overlap matrices, we are interested in the maximum entry for each
row, pointing to pairs of clusters that are most similar. Table III shows the
means of these maximum overlap values. It is evident that the maximum $J$ and
$O$ overlap is significantly better for _modularity clusters_ than for random
clusters. This shows that a more than coincidental relation between
_modularity clusters_ and _topical clusters_ exists. However, the values are
not close to 1.0 and indicate that the correspondence is not very strong.
Thus, factors in addition to joint conferences are influential in shaping the
community structure of the network. In the following section, we take an in-
depth look at one possible factor of this kind, namely participation in
research seminars.

##  IV Impact of Seminars on Network Evolution

After describing static aspects of the network in the previous section, this
section is concerned with its dynamics: We examine whether the Dagstuhl
Seminars, as academic and social events, leave a track in the structure of the
network, preferably in the form of increased collaboration between the
participants. In the authors’ subjective experience, the seminars present
valuable opportunities for networking. Our approach to this question can be
summarized as follows: Track groups of researchers (seminar participants and
others selected as reference groups) in the time-resolved graph
$\mathcal{G}_{\mathbf{PA}}^{1,1}$ and observe their publication output as well
as their collaborative links; take into account the date of a seminar in order
to observe immediate or long-term effects. The preparations necessary for this
approach are described in the following:

###  IV-A Preparations

#### Aligning Data Sets

Our data sets record a total of 11 625 seminar guests in the Dagstuhl database
and 852 250 authors in DBLP. All seminars took place in the 2000s. We align
the tests by author name, whereby some false (mis)matches cannot be avoided.
Still, a matching author in the publication database was found for 72 percent
of the seminar invitees.

#### Area Launchers

In order to detect increased collaboration which can be clearly attributed to
the seminars, we first try to identify _area launchers_. These are seminars
intended to bring together a group of researchers who have not collaborated
much before. A stated goal of the Dagstuhl Seminars is that some of them are
intended to “launch” new areas of research by fostering collaboration between
previously unaffiliated researchers, thereby contributing to emerging fields.
_Area launchers_ are relevant to us due to the following argument: If
participants develop collaborative ties in the aftermath of an _area launcher_
seminar, it is possible to attribute this more clearly to the seminar rather
than existing relationships, developed, for instance, in the course of a
common conference.

We classify a set of seminars as _area launchers_ without special knowledge
about the intent or content of the seminar, but solely from participation
data: It is assumed that well-established areas of research generally spawn
their own dedicated conference, and that the participants of such a conference
represent the researchers active in this area. By this logic, a seminar
corresponds to an established area of research if the invitees have a strong
overlap with the participants of the respective conference. Furthermore, if
researchers attend the same conference, it is likely that they are already
familiar with each other as well as each other’s work. We therefore reason
that a seminar is an _area launcher_ if its invitees do not overlap strongly
and clearly with the participants of any particular conference. From this
calculated set of seminars, 10 seminars are selected by hand and classified as
_area launchers_.

#### Measures

We quantify the publication output and intensity of collaboration among
researchers using several measures which map sets of authors to real numbers.
For example, Figure 5 shows a small number of authors (light nodes) and their
publications (dark nodes) in the _authorship graph_. Authors belonging to $A$
are colored blue. Blue lines show existing (dashed line) and nonexisting
(dotted line) coauthorship relations between pairs of authors in $A$. This
illustrates the measure $\mathit{cad}(A)$, which is the fraction of actually
existing coauthorship relations within an author set.

Figure 5: Illustrating collaboration measure $\mathit{cad}$:
$\mathit{cad}(A)=2/3$

Before introducing all measures, it is helpful to define sets of
(co)publications, copublications internal to a group, and coauthors first:
Given a set of authors $A\subseteq\mathbf{A}$, the set of their publications
$P(A)$ is equal to

$P(A):=\bigcup_{a\in A}P(a)=\bigcup_{a\in A}\\{p\in\mathbf{P}:a\smile p\\}$

The set of _copublications_ for an author $a$ consists of publications which
were written as collaborations with another author:

$C\\!P(a):=\\{p\in P(a):\exists b\in\mathbf{A}:b\smile p\\}$

For an author set $A\subseteq\mathbf{A}$, the _aggregated copublications_ are

$C\\!P(A):=\bigcup_{a\in A}C\\!P(a)$

The set of _intra-copublications_ of a set of authors is defined as

$C\\!P_{\text{intra}}(A):=\left\\{p\in C\\!P(A):\exists{a,b}\in A:a\smile
p,b\smile p\right\\}$

The set of coauthors for a given author $a\in\mathbf{A}$ are those authors
with whom $a$ has authored a collaboration.

$C\\!A(a):=\\{b\in\mathbf{A}:b\frown a\\}$

This can be generalized for a set of authors $A$:

$C\\!A(A):=\bigcup_{a\in A}C\\!A(a)$

Based on these sets, we formulate five measures, listed and defined in Table
IV. These measures are intended to answer the following questions:

  * •

$\mathit{ap}(A)$: What is the general productivity of an average author from
the group?

  * •

$\mathit{acp}(A)$: What is the productivity of such an author in terms of
collaborations?

  * •

$\mathit{aca}(A)$: With how many other authors does an average author from the
group collaborate?

  * •

$\mathit{cpr}_{\text{intra}}(A)$: Do the authors collaborate more often within
the group or outside of the group?

  * •

$\mathit{cad}(A)$: How close is the group to a collaborative clique, i.e. a
group in which all authors have collaborated with each other?

measure | definition
---|---
$a\\!p(A)$ | $\frac{|P(A)|}{|A|}$
$acp(A)$ | $\frac{|C\\!P(A)|}{|A|}$
$\mathit{aca}(A)$ | $\frac{|C\\!A(A)|}{|A|}$
$cpr_{\text{intra}}(A)$ | $\frac{|C\\!P_{\text{intra}}(A)|}{|C\\!P(A)|}$
$cad(A)$ | $|\\{\\{a,b\\}\in\textstyle{A\choose 2}:a\frown b\\}|/|\textstyle{A\choose 2}|$
TABLE IV: Overview of collaboration measures and their definitions

#### Author Classes

The classes of author groups which we track are the seminar participants on
the one hand and several reference classes on the other:

  * •

_seminar attendees_ ($A\\!t_{s}$): For each seminar $s$, the set of
researchers who attended the seminar.

  * •

_seminar absentees_ ($A\\!b_{s}$): For each seminar $s$, the set of
researchers who were invited to the seminar but did not attend. (For some
seminars, the set was empty or very small, so these are only included if they
have a sufficient size.)

  * •

_random samples_ ($R\\!S_{i}$) Contains randomly assembled sets of authors
with the size of a typical seminar.

  * •

_connected samples_ ($C\\!S_{i}$) Contains sets of authors found by collecting
nodes from $G_{\mathbf{PA}}$ in a breadth-first search from a random initial
node until the typical size of a seminar is reached.

  * •

_all authors_ ($\mathbf{A}$) A single set containing all authors.

###  IV-B Evaluation and Results

We speculate that joint participation in a seminar leads to increased
collaboration between the participants. This would be measurable as higher
values for the collaboration measures ($\mathit{cad}$,
$\mathit{cpr}_{\text{intra}}$) on the respective subgraph. Additionally, we
measure whether seminar participation leads to a higher publication output for
the participants ($\mathit{ap}$, $\mathit{acp}$, $\mathit{aca}$). In order to
test this, seminar-related groups as well as reference groups are tracked
within the graph $\mathcal{G}^{1,1}_{\mathbf{PA}}$: For any author set $A$, a
subset $A^{\prime}\subseteq A$ has corresponding nodes $V_{A^{\prime}}$ in the
graph $G_{y}$. For all measures $M$, we evaluate $M(A^{\prime})$, yielding a
sequence of values for each group. The evaluation yields one value sequence
per author group, and thus several data points per year. All seminar-related
sequences are aligned according to the time of the seminar, in order to
compare values before and after seminar participation. We present these data
points in boxplot form (e.g. Figure 6), with the horizontal axis denoting time
relative to the seminar date and the vertical axis values of the respective
measure. By following the plotted median and quantiles along the time axis,
one can identify trends for the author class as a whole. The point in time
where a seminar occurs is marked by an arrow.

In the following section, we describe a selection of notable observations:

#### Average publication output remains rather constant

For the authors as a whole ($\mathbf{A}$), average publication output and
number of coauthors remain stable over time, even as the graph grows at an
increasing rate and author nodes accumulate.

#### Randomly grouped authors as a baseline for publication output

As a reference class, we evaluate the randomly compiled author groups $R\\!S$.
Both $\mathit{ap}$ and $\mathit{aca}$ are, on average, in the range of
0.6-0.8, showing that there are typically inactive authors in any given time
frame. As expected, there is no collaboration between authors in the random
samples.

#### Connected Sample Groups

Authors from the $C\\!S$ have a significantly higher productivity than
randomly selected authors, since breadth-first search finds high-degree nodes
with a higher probability. There is also an upward trend over time for all
measures. A possible explanation for this is that nodes gain connections over
time according to degree, if there is an underlying _preferential-attachment_
process at work (as suggested by the power-law degree distribution). Overall
$\mathit{cpr}_{\text{intra}}$ remains clearly below 0.5, showing that these
sample groups are just sections from greater collaborative clusters.

#### Attendees and absentees are equally productive

(a) $\mathit{aca}$: $A\\!t$

(b) $\mathit{aca}$: $A\\!b$

Figure 6: $\mathit{aca}$ (y-axis) for seminar attendees and absentees (x-axis:
time relative to seminar, arrow: seminar date)

The effect of seminar participation is best judged by contrasting attendees
with absentees. With respect to productivity, measured by the number of
coauthors and the number of publications, attendees and absentees are quite
similar, with some outliers among the absentees surpassing the attendees (see
Figure 6). For the productivity measures, an upward trend before the seminar
continues for a few years but then tends to reverse.

#### Attendees form a more cohesive group

(a) $\mathit{cpr}_{\text{intra}}$: $A\\!t$

(b) $\mathit{cpr}_{\text{intra}}$: $A\\!b$

Figure 7: $\mathit{cpr}_{\text{intra}}$ (y-axis) for seminar attendees and
absentees (x-axis: time relative to seminar, arrow: seminar date)

For seminar attendees, a larger fraction of their collaborations are internal
to the seminar group, both before and after the seminar (Figure 7). This
indicates that attendees already come from a more cohesive group. Values for
$\mathit{cad}$ agree with this interpretation: Clearly, those who choose to
attend the seminar form a denser subgraph in the collaboration network. There
seems to be no lasting increase in collaboration after the seminar, but a
downward trend for both attendees and absentees.

#### Area launchers are not exceptional

For the subset of seminars classified as _area launchers_ , we expect
comparatively less collaboration before the seminar, and a stronger increase
after. This effect would be most clearly captured by the measures
$\mathit{cpr}_{\text{intra}}$ (Figure 8) and $\mathit{cad}$. The plots in
Figure 8 support our reasoning about area launchers, namely that the authors
invited have a comparatively low probability of collaboration in the time
prior to the seminar: Values for $\mathit{cpr}_{\text{intra}}$ are generally
in the lower range compared to all seminars. Still, a visible change after the
time of the seminar is missing. The influence of an _area launcher_ seminar
does not seem to differ from the other seminars.

(a) $\mathit{cpr}_{\text{intra}}$: $A\\!t$

(b) $\mathit{cpr}_{\text{intra}}$: $A\\!b$

Figure 8: $\mathit{cpr}_{\text{intra}}$ (y-axis) for attendees and absentees
of _area launchers_ (x-axis: time relative to seminar, arrow: seminar date)

#### Subdivision by career stage

Suspecting that seminar participation affects researchers in early stages of
their career more strongly, we repeat a part of the evaluation with the
authors classified by career length ($\leq 5$, $\leq 15$, $>15$ years of
publication history). However, the results do not modify our conclusions: A
seminar effect for academic newcomers is no more observable than for all other
authors.

#### Summary and Interpretation

Seminar invitees are more productive and more collaborative than randomly
selected authors. Yet there is little difference between attendees and
absentees in terms of their productivity. Invited researchers are already
actively publishing, with an upward trend, prior to the time of the seminar.
For $\mathit{cpr}_{\text{intra}}$ and $\mathit{cad}$, attendees are
consistently better than absentees. This indicates that those who attend are
already a tightly connected collaborative group before the seminar, possibly
influencing their decision to participate. The general trend over time is an
increase up to the seminar and a slight decrease afterwards for both classes
of researchers. A possible explanation for the increase and decrease over time
is that invitations are biased towards researchers who are currently most
active: Invitations to seminars occur at a period of peak activity. There is,
however, no significant change of structure connected to seminars (either
significant short-term increase in collaboration directly after the seminar or
long-term increase). Most importantly, attendees and absentees do not differ
in this respect. While the focus on _area launcher_ seminars supports our
assumption that the invited researchers had collaborated less, a significant
structural change after the seminar is not visible. These results suggest that
a single event like a seminar is not influential enough to alter the network
structure of collaboration for the group of participants in ways observable
with our measures. Clearly, other factors have additional and apparently more
influence on the structure. Rather in the opposite direction, the network
structure might be employed to predict who will attend the seminar and who
will decline, since the participants evidently come from a more cohesive
group.

##  V Conclusion

This paper ties in with the existing work on scientific collaboration networks
and explores several new variations of network analysis methods. The
coauthorship graph in the field of computer science constitutes in many
respects a typical social network, as observed before in similar studies: We
encounter properties such as low average distances between researchers, a
_giant connected component_ , a power-law distribution with regard to
publications and coauthors (making it a _scale-free network_), and a regular
_$k$ -core_ structure. We detect dense communities of researchers through
_modularity_ maximization, and compare the resulting clustering to ground-
truth communities defined by conferences, from which topical similarity is
inferred. The overlap between the two partitions is clearly not coincidental,
although other factors seem to be at work in shaping the community structure.
In order to identify influential researchers by their network centrality, we
test a novel combination of bipartite author-paper graph and _eigenvector
centrality_. We are the first to incorporate data on participants of the
Schloss Dagstuhl research seminars and use it to evaluate the impact of such
seminars on the evolution of collaborative ties. Since the seminars are
designed to foster collaboration on cutting-edge research topics, and many
participants experience the seminars as a valuable opportunity for networking,
we investigate whether such effects can be observed as structural changes in
the collaboration network. Seminar invitees are more productive, more
collaborative and structurally prominent compared to the average researcher.
However, our methods suggest that seminar participation does not directly
affect the structure of the collaboration network. An interesting finding of
this analysis was that researchers who choose to attend the seminar form a
distinctly more cohesive subgraph than those who decline.

## Acknowledgment

We thank Ulrik Brandes for helpful discussions during the preparation of this
work. We also thank the Schloss Dagstuhl conference center for providing us
with the necessary data on their seminars.

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