# Center-Periphery Structure in Communities: Extracellular Vesicles

Eleanor Wedell EW and MP contributed equally to this manuscript Department of
Computer Science, University of Illinois Urbana-Champaign, Urbana, IL 61801
Minhyuk Park  Department of Computer Science, University of Illinois Urbana-
Champaign, Urbana, IL 61801  Dmitriy Korobskiy  NTT DATA, McLean, VA, 22102
Tandy Warnow<EMAIL_ADDRESS>Department of Computer Science, University of
Illinois Urbana-Champaign, Urbana, IL 61801  George Chacko
<EMAIL_ADDRESS>Department of Computer Science, University of Illinois
Urbana-Champaign, Urbana, IL 61801  Office of Research, Grainger College of
Engineering, University of Illinois Urbana-Champaign, Urbana, IL 61801

###### Abstract

Clustering and community detection in networks are of broad interest and have
been the subject of extensive research that spans several fields. We are
interested in the relatively narrow question of detecting communities of
scientific publications that are linked by citations. These publication
communities can be used to identify scientists with shared interests who form
communities of researchers. Building on the well-known k-core algorithm, we
have developed a modular pipeline to find publication communities. We compare
our approach to communities discovered by the widely used Leiden algorithm for
community finding. Using a quantitative and qualitative approach, we evaluate
community finding results on a citation network consisting of over 14 million
publications relevant to the field of extracellular vesicles.

##  1 Introduction

Community detection in networks is of broad interest and has been discussed in
comprehensive reviews (Fortunato and Castellano,, 2009; Fortunato,, 2010;
Javed et al.,, 2018). At a high level, the community detection problem amounts
to identifying groups within a complex network that share some common
properties. As observed by Coscia et al., (2011), this definition suffers from
some degree of imprecision given the diverse ways in which communities can be
defined and a richness of perspectives. For example, a community detection
approach may focus on vertex similarity or edge-density; disjoint, overlapping
or hierarchical community structure; and static versus dynamic networks.
Newman, (2006) had also noted distinctions between community discovery and
graph partitioning. Thus, the context of the question being asked and the
techniques being employed tend to determine the flavor of community detection
in a study.

From the perspective of scientometrics, detecting a research community can be
framed as a community finding problem in which communities of publications
defining areas of research are discovered in the scientific literature. First,
the scientific literature is modeled as a network with publications as nodes
and citations as directed edges (Boyack and Klavans,, 2019). From this
network, an area of research is defined by a community of publications–a
sufficiently citation-dense area in the network. Citation networks of
scientific literature can be constructed using different approaches. Direct
citations were used to build clusters of articles from a dataset of over 10
million publications (Waltman and van Eck,, 2012); this methodology was also
used in building citation maps from 19 and 43 million publications (Boyack and
Klavans,, 2014).

Direct citation, bibliographic coupling, and co-citation have been compared
for their relative value in identifying research fronts (Boyack and Klavans,,
2010), with a hybrid approach involving bibliographic coupling and textual
similarity performing the best. A subsequent study conducted at a larger scale
and with improved evaluation criteria suggested that direct citation was the
most promising (Klavans and Boyack,, 2017). We use direct citations in this
study.

Once constructed, citation networks can be analyzed using different community
finding or clustering approaches (Boyack and Klavans,, 2019; Ahlgren et al.,,
2020; Traag et al.,, 2019; Sciabolazza et al.,, 2017; Waltman and van Eck,,
2012; Šubelj et al.,, 2016). Of these approaches, a recent development is the
availability of the Leiden algorithm, which offers better partitioning and
performance (Traag et al.,, 2019) compared to a preceding approach, the
Louvain algorithm (Blondel et al.,, 2008), which seeks to optimize the
modularity quality function (Newman,, 2006).

We are interested in how research communities form and collaborate around
research questions (Kuhn,, 1970; Crane,, 1972). Collaboration within the
scientific community goes beyond co-authorship, and includes building upon
prior discovery by other researchers; citations between publications thus
indicate this more general form of collaboration, and the publication
communities detected in this process are evidence of such collaborations.
Further, the authors of the publications in the publication communities
represent communities of researchers working on related questions. Historical
studies have estimated the size of research communities to be in the order of
a few hundreds (Price and Beaver,, 1966; Crane,, 1972; Kuhn,, 1970; Mullins,,
1985). However, this question merits re-examination in the modern scientific
enterprise; expanded, globalized, and electronically connected.

Since researchers can work on more than one problem and be considered members
of more than one research community, to find author communities we begin by
finding communities of publications. Then, for each publication community, the
authors of the publications in the community constitute a researcher community
organized around the questions defined by the publication community.

We are interested in articles linked by citation as the products of a research
community rather than articles clustered by textual similarity, therefore, we
use direct citations to discover communities. In an earlier study
(Chandrasekharan et al.,, 2021), we explored this approach to detect
publication communities and subsequently their author communities in networks
of biology literature. We used an ensemble technique to find publication
communities coupled with limited qualitative analysis, where the publication
communities were significantly overlapping in clusters identified by the
Leiden algorithm and also the Markov Clustering (MCL) algorithm (Van Dongen,,
2008).

We were specifically interested in whether the author communities we found
exhibited substructure indicating the influence of a few individuals
associated with the majority of publications while exhibiting different
degrees of collaboration within and across subgroups (Price and Beaver,, 1966;
Crane,, 1972). While we did detect such center-periphery substructure
(Breiger,, 2014, p. 60) in both publication and author communities, our
findings were potentially limited by the clustering methods we used, Leiden
and MCL, since neither is designed to detect or require substructure when
identifying communities.

Here, we aim to investigate more carefully whether publication clusters
exhibiting center-periphery structure exist in citation networks of the
scientific literature. The central idea is that each community contains core
nodes representing the “center” of center-periphery organization and
additional nodes representing the “periphery”; our approach first finds the
core nodes and then augments the cluster to include peripheral nodes. Since
prior community detection methods are not explicitly designed to detect such
communities, we propose a new modular pipeline that specifically aims to find
such communities. To find the core node sub-community, we combine two
approaches represented in the clustering and community detection literature:
first, that valid communities should have positive modularity score (Fortunato
and Barthelemy,, 2007), and second that each community should be dense, which
is expressed by the ratio between the average node degree and the number of
nodes in the network.

Thus, our approach combines three ideas from the literature: the center-
periphery model of authorship communities extended here to a model for
publication communities, positive modularity for individual communities, and
sufficient citation density for individual communities. By distinguishing
between the core and non-core nodes, we can require that the positive
modularity and sufficient citation density requirements hold for the
subclusters of core nodes but not necessarily for the clusters that combine
both core and non-core nodes. This distinction potentially enables us to
better model real world community structure.

Our modular pipeline begins by finding clusters of core nodes, building on the
ideas of Giatsidis et al., (2011) who quantified the cohesiveness of a
community using the “k-core” concept from graph theory (Matula and Beck,,
1983). Although optimizing the total modularity in the clustering has
drawbacks (as demonstrated in Fortunato and Barthelemy, (2007)), we also
required that the clusters individually have modularity scores above $0$; this
is a relatively mild criterion that seeks internal cohesion, and has been
considered in the prior literature (e.g., Newman and Girvan, (2004); Fortunato
and Barthelemy, (2007) to be evidence of a valid community.

We tested our pipeline on a network of over 14 million publications that we
constructed by harvesting citing and cited articles from a seed set defined by
the keyword “exosome”. This keyword captures articles from the field of
extracellular vesicles, which may be important for intercellular communication
and development of some diseases, as well as having potential for therapy
(Edgar,, 2016; Kalluri and LeBleu,, 2020; Raposo et al.,, 2021). We chose
extracellular vesicles (Raposo et al.,, 2021) as the focus of this study for
two reasons: first, it is a large research area, and second, because it is
rapidly expanding–it has seen spectacular numbers of publications each year
since 2010, and therefore represents an excellent test case for community
finding methods in the modern scientific enterrprise.

Expecting that not all communities discovered in such a large network would be
directly relevant to exosomes, we use 1,218 cited references from 12 relevant
review articles as expert-identified markers for specificity in the
communities we discover. We report our findings in the following sections.

##  2 Materials and Methods

###  2.1 Data

A citation network consisting of 14,695,475 nodes and 99,663,372 edges was
generated using the Dimensions bibliography (Hook et al.,, 2018). Briefly, a
“seed” set, $S$, was obtained by performing a text search for the term
“exosome” with years of publication restricted to 2010 or earlier. This
constraint was applied to allow every element in the seed set to have
accumulated at least 10 years of citations. The search retrieved 11,156
publications of type article from Dimensions. To capture publications proximal
by citation to the seed set, a network was constructed using a protocol we
labelled SABPQ. First we start with the seed set $S$. Set $A$ is the set of
publications that cite at least one publication from set $S$. Similarly, set
$B$ is the set of publications that are cited by at least one publication from
set $S$. Once the sets $S$, $A$, and $B$ are identified, then we define set
$P$ as the set of publications that cite at least one publication from the set
$S\cup{}A\cup{}B$. Similarly, set $Q$ is the set of publications that are
cited by at least one publication from the set $S\cup{}A\cup{}B$. The network
contains directed edges defined by citations; if publication $x$ cited $y$
then we created an edge from $x$ to $y$. The SABPQ protocol was implemented
using Dimensions on BigQuery in Google Cloud Services. The data was then
exported to Google Cloud Storage Bucket and subsequently exported to a
PostgreSQL database for further analysis.

_Marker Nodes and Specificity_ As marker nodes for our analysis, we used 1,218
articles cited in 12 recent reviews on extracellular vesicles and exosome
biology (van Niel et al.,, 2018; Kalluri and LeBleu,, 2020; Verdi et al.,,
2021; Ghoroghi et al.,, 2021; Lananna and Imai,, 2021; Busatto et al.,, 2021;
He et al.,, 2021; Schnatz et al.,, 2021; Le Lay et al.,, 2021; Leidal and
Debnath,, 2021; Clancy et al.,, 2021; Raposo et al.,, 2021). All 1,218 markers
are present in our constructed network with 14,695,475 nodes. Any community
containing at least one marker node was considered relevant. Marker nodes were
matched to clusters using identifiers in our network. For example, the marker
node with title “Tumour exosome integrins determine organotropic metastasis”
and DOI 10.1038/nature15756 is identified as node 4431204 in our network. The
complete list of marker nodes is available on our Github site (Park et al.,,
2021).

###  2.2 Clustering methods

##### Leiden

We used version 1.1.0 of the Java implementation for the Leiden algorithm
(Traag et al.,, 2019) provided by the Centre for Science and Technology
Studies and available in Github (Traag,, 2021). We ran Leiden in default mode,
which means that the quality function being optimized was the Constant Potts
Model rather than modularity. Leiden includes a parameter for the resolution
value, which we vary in our experiments from 0.05 to 0.95.

##### New clustering methods

Here we describe at a high level the clustering and community-finding methods
we developed in our study. The methods we developed and use in this study are
freely available in Github, and the locations of these software and exact
commands we used are provided in the supplementary materials. We also provide
software version numbers and commands for the existing codes that we use in
the supplementary materials. We note here that the codes we developed rely on
NetworKit (Staudt et al.,, 2016), which is an open-source Python module
designed for scalable network analysis.

In our approach, the objective was to produce a set of clusters each of which
has core nodes and peripheral nodes, consistent with the “center-periphery”
structure described earlier. These clusters are considered to be “publication
communities”, with two types of members: core members that are densely
connected to each other and peripheral (non-core) members connected to the
core members but with fewer edges within a cluster.

Our approach requires values for $k$ and $p$, where $k$ specifies a minimum
connectivity between the core nodes, and $p$ indicates a minimum connectivity
between each non-core (“periphery”) node and the core nodes. These parameter
values for $k$ and $p$ are provided by the user, and different choices for
these parameters will produce different clusterings.

The required minimum connectivity $k$ between core nodes is related to the
$k$-core concept in graph theory, which we now describe. A $k$-core of a
network $N$ is a largest connected subnetwork $A$ of $N$ such that every node
in $A$ is adjacent to at least $k$ other nodes in $A$ (Seidman,, 1983; Matula
and Beck,, 1983; Pittel et al.,, 1996). The $k$-cores can be calculated in
polynomial time (Matula and Beck,, 1983), and our new clustering methods build
on these algorithms.

We are also interested in the modularity scores of the clusters that are
produced by each method, as given in Definition 1:

######  Definition 1.

The modularity of a single cluster $s$ within a network $N$, denoted by
mod(s), is given by

$mod(s)=\frac{l_{s}}{L}-\left(\frac{d_{s}}{2L}\right)^{2}$

where $l_{s}$ is the number of internal edges in cluster $s$, $d_{s}$ is the
sum of the degrees of the nodes inside $s$, and $L$ is the number of total
edges in the network $N$ (Fortunato and Barthelemy,, 2007). The total
modularity of a clustering is the sum of the modularity scores of its
clusters.

Rather than aiming to maximize the total modularity of the clustering, we will
only require that each cluster have positive modularity; as noted in Fortunato
and Barthelemy, (2007), this approach aims to detect valid communities. We now
define some additional terms that we will use in designing new clustering
methods:

######  Definition 2.

Given a network $N$, a clustering $\mathcal{C}$, and a cluster $C$ drawn from
$\mathcal{C}$ where $C$ is partitioned into core nodes and non-core nodes, we
will say:

  * •

$C$ is $k$-valid if and only if each core node in $C$ is adjacent to at least
$k$ other core nodes in $C$

  * •

$C$ is $m$-valid if and only if the sub-cluster induced by the core nodes is
connected and has a positive modularity score

  * •

$C$ is $p$-valid if and only if each non-core node is adjacent to at least $p$
core nodes in $C$

  * •

$C$ is $kmp$-valid if and only if it is $k$-valid, $m$-valid, and $p$-valid

  * •

The clustering $\mathcal{C}$ is $kmp$-valid if and only if every cluster
$C\in\mathcal{C}$ is $kmp$-valid

Note that if a cluster does not contain non-core nodes then it is vacuously
$p$-valid.

The clustering methods that we develop seek to produce $kmp$-valid clusters,
so that we can interpret these clusters as communities with center-periphery
structure. Moreover, we are interested in clusterings that produce a large
number of $kmp$-valid clusters, as well as those that include as many nodes as
possible in the $kmp$-valid clusters (which by definition must be non-
singleton when $k>1$). Hence we explore different techniques that seek to
optimize these two opposing criteria.

We also require positive modularity in the core node sub-clusters for each
cluster. This is a relatively mild requirement that avoids cases where the
core node sub-cluster may be k-valid and connected but might not reflect a
preference for itself over the outside. Consider the case where a 10-clique, a
complete graph on 10 nodes, is contained in a clique with 20 nodes. This
10-clique would satisfy k-validity for $k\leq 9$ and would be connected, but
would not have positive modularity. By enforcing positive modularity, we would
avoid returning such clusters. This example illustrates the advantage of
enforcing positive modularity even though the probability of it occurring in a
real world network is likely to be small. We also note that enforcing positive
modularity in the core node sub-cluster (or even in the final cluster that
contains both core and non-core nodes) is not the same as trying to maximize
the sum of the modularity scores of the individual clusters (total modularity
score). In other words, enforcing positive modularity does not have the same
vulnerability to the resolution limit that was established for the modularity
criterion, which seeks to maximize the total modularity score (Fortunato and
Barthelemy,, 2007).

####  2.2.1 Four-Stage $kmp$-Clustering

We designed a four-stage pipeline that is designed to enable the user to
explore different clustering options, while guaranteeing that the output is a
$kmp$-valid clustering. The input is a network $N$ and values for the
parameters $k$ and $p$. At a high level, the first stages aim to construct the
core member components. The second stage extracts valid sub-clusters from
those generated by the first stage. The third stage augments these clusters
with additional members, most likely non-core members, though some might
qualify as core members, and the fourth stage assigns core or non-core status
to the nodes, and retains only those clusters that are $kmp$-valid. We begin
with a description of the overall multi-stage structure of our new clustering
methods; note that stages 2 and 3 are optional.

  * •

Stage 1: Cluster the network $N$ into disjoint clusters (core members), so
that each non-singleton cluster is $k$-valid and $m$-valid.

  * •

Stage 2: Attempt to break each non-singleton cluster produced in Stage 1 into
a set of pairwise disjoint clusters, each of which is $k$-valid at minimum.

  * •

Stage 3: For each non-singleton cluster, add unclustered nodes, nodes that are
not in any non-singleton cluster, as non-core (peripheral) members, provided
that they are adjacent to at least $p$ core nodes in the selected cluster.
This is the augmentation stage, which adds non-core nodes to the clusters
produced in the earlier stage.

  * •

Stage 4: Process the clustering that is received so that each final cluster is
partitioned into core and non-core members, and so that the clustering is
$kmp$-valid.

Thus, Stages 1 and 2 together are directed at finding core members of
clusters, with Stage 1 directed at clusters with large numbers of core nodes
and Stage 2 aimed at extracting smaller clusters within these larger clusters.
At the end of Stage 1, all clusters will be $k$-valid and $m$-valid. If the
optional Stage 2 is applied, the clusters it produces will be $k$-valid and
connected, but may no longer have positive modularity. Neither of these stages
introduces any non-core nodes, and so the output of each stage is vacuously
$p$-valid. Stage 3 augments the clusters to include non-core nodes; by design
the clusters will be connected, $k$-valid, and $p$-valid, but depending on the
outcome of Stage 2, they may not have positive modularity and so may not be
$m$-valid. Stage 4 is designed to ensure that all final clusters are
$kmp$-valid, and so may modify or discard clusters found in the earlier
stages. However, after Stage 4 is run, the output clustering is guaranteed to
be $kmp$-valid. Furthermore, the clusters produced are parsed into core and
non-core nodes.

We now describe the techniques we have developed for each stage. For Stage 1,
we present iterative k-core (IKC) clustering, a method that is inspired by the
k-core concept in graph theory. For Stage 2, we also present two different
techniques: recursive Graclus (RG) and iterative Graclus (IG), both of which
are based on the Graclus (Dhillon et al.,, 2007) clustering method used in its
default setting and applied to split a graph into two parts. Stage 3 is
implemented using a straightforward algorithm that we describe below. In
contrast to the earlier stages, Stage 4 involves multiple steps, and is
described below. This multi-stage design provides a flexible framework by
allowing different techniques to be used at each stage.

####  2.2.2 Stage 1: Iterative k-core clustering (IKC)

To motivate the IKC algorithm, we first describe the technique that computes
$k$-cores and then describe the iterative method.

#####  $k$-core

For a network $N$ and specified positive integer value for $k$, a $k$-core of
a network $N$ is the largest connected subnetwork $A$ of $N$ such that every
node in $A$ is adjacent to at least $k$ other nodes in $A$. Note that for
every network that does not have any isolated vertices (i.e., nodes of degee
$0$), each connected component is a $1$-core of the network. The distribution
of $k$-core sizes also indicate how quickly a network shrinks as $k$ increases
(Leskovec and Horvitz,, 2008).

The identification of the $k$-core for a maximum achieved value of $k$ in a
network has been proposed as a quality measure for community finding that
measures cohesiveness and suggests collaboration (Giatsidis et al.,, 2011).
This idea is reiterated in Kong et al., (2019); Malliaros et al., (2019), who
discuss applications of the $k$-core in biology and real world networks.

The $k$-cores can be calculated in polynomial time (Matula and Beck,, 1983),
as follows. First, we calculate the degree of every node in the network. Then,
every node of degree less than $k$ is deleted from the graph, and this process
repeats until every node has degree at least $k$ (i.e., every node is adjacent
to at least $k$ other nodes). Every connected component that remains is called
a $k$-core of the network. As an example, given a network that contains two
connected components: one is a clique of size $100$ and the other has a node
$x$ that is adjacent to 2000 other nodes, each of which is only adjacent to
$x$ (and so have degree $1$). Note that for all $k$ with $2\leq k\leq 99$, the
$k$-core of this network is the clique of size 100.

#####  $k$-core clustering

The simple $k$-core clustering method takes as input a network $N$ and a value
for $k$, and computes the $k$-cores of the network. The set of the $k$-cores
is returned as the clustering. By construction, the simple $k$-core clustering
method produces clusters that are $k$-valid and connected. However, it does
not constrain the clusters to have positive modularity.

##### Iterative k-core clustering

To improve on the simple k-core clustering technique for our purposes, we
developed an iterative k-core (IKC) algorithm. The input to the IKC algorithm
is a network $N$ and a positive integer $k$. IKC then operates as follows:

  * •

We will construct a bin $B$ of clusters that will be returned by the IKC
clustering. In this step, we initialize $B$ to be the empty set.

  * •

We run the k-core labelling algorithm, which labels every node in the network
with a non-negative integer. We let $L$ be the largest label found in this
labelling. If $L<k$, then IKC exits, and returns the clusters in the bin
$B$.Otherwise, the $L$-cores (i.e., the connected components that are labelled
by $L$) of the network are evaluated as potential clusters.

  * •

An $L$-core $A$ is added to the bin $B$ if and only if $A$ has positive
modularity.

  * •

The $L$-core is then deleted from the network, and the residual network is
recursively analyzed by IKC. The stopping condition is when all the nodes have
been deleted from the network.

This procedure produces a collection of clusters, each of which has the
following properties: (i) each cluster is connected and has positive
modularity, and hence each cluster is $m$-valid and (ii) each cluster is
$k$-valid, which means every node in the cluster is adjacent to at least $k$
other nodes in the cluster.

####  2.2.3 Stage 2: Finding clusters within clusters using Graclus

In Stage 2 we seek to discover $k$-valid clusters that exist within larger
$k$-valid clusters. For this, we use the Graclus clustering method (Dhillon et
al.,, 2007). Graclus has been previously used to cluster bibliometric data
(Dhillon et al.,, 2007; Devarakonda et al.,, 2020; Šubelj et al.,, 2016), but
here we use it to split a given cluster into two sub-clusters. We use Graclus
to optimize its default criterion, which is the normalized cut criterion. In
this setting, we seek a partition of a given cluster $C$ into two parts
$C_{1}$ and $C_{2}$ so as to minimize

${{links(C_{1},C_{2})}\over{links(C_{1},C)}}+{{links(C_{1},C_{2})}\over{links(C_{2},C)}},$

where $links(A,B)$ denotes the number of edges with one endpoint in $A$ and
the other endpoint in $B$.

As is the case in other optimization methods, local search in Graclus helps
the optimizer escape poor local minima; its default setting does no iterations
but this can be modified by specifying the number of iterations. In this study
we explore both the default mode, $l=0$ (no iterations) and $l=2000$
iterations. We implement our use of Graclus in two different ways: recursively
and iteratively. Thus, we use Graclus in four different ways.

##### Recursive Graclus

The input to this method is a clustering of the network $N$ and the value for
the parameter $k$. We create a bin $B$ of clusters (setting it initially to
the empty set). We take a cluster $C$ from the clustering and apply Graclus
recursively using either the default mode or the local search mode.

The result of this is a division of the cluster $C$ into two non-empty sets
$A_{1}$ and $A_{2}$. If $A_{1}$ has positive modularity and is $k$-valid, then
we add $A_{1}$ to $B$ (the bin we have created), and similarly for subset
$A_{2}$. If neither $A_{1}$ nor $A_{2}$ is added to $B$, add cluster $C$ to
$B$ and delete $C$ from the network, effectively removing it from further
consideration by Recursive Graclus.

The stopping condition for Recursive Graclus is that all nodes have been
deleted from the network. When the stopping condition is reached, the final
output of Recursive Graclus is the set of clusters in bin $B$. Though all
clusters that are produced by Recursive Graclus are guaranteed to be $k$-valid
and have positive modularity, they may not be $m$-valid since this requires
that the core node subsets be connected.

##### Iterative Graclus

To use Graclus iteratively, we follow a similar procedure as in Recursive
Graclus but with two key differences. The first is that the user provides a
parameter for the number of iterations, so that the procedure must stop after
that number of iterations, if it hasn’t already stopped. The second difference
is that, in contrast to Recursive Graclus, the procedure is guaranteed to
produce clusters that are $k$-valid and $m$-valid in each iteration, as we now
describe.

When we apply Graclus, in either default or local search mode, to split a
cluster into two sub-clusters, each of the created sub-clusters is parsed into
core and non-core nodes (using a variant of the algorithm described for Stage
4, see Section 2.2.6). If the core node set is empty, the sub-cluster will be
discarded. However, if the core is non-empty then the core node set is by
definition $k$-valid, and is then evaluated further. Each core node set is
divided into its connected components, and each connected component that has
positive modularity is passed to the next iteration. Any cluster that does not
end up producing a sub-cluster that is passed to the next iteration is added
to the bin $B$ as in Recursive Graclus and is then deleted from the network.
Iterative Graclus stops when one of two conditions occurs: the number of
allowed iterations has been completed, or all the nodes have been deleted from
the network. By design, the output of Iterative Graclus is a set of clusters
each of which is $k$-valid and $m$-valid (thus, every cluster is connected,
has positive modularity, and every node is adjacent to at least $k$ nodes in
its cluster).

####  2.2.4 Stage 3: Augmentation

The purpose of the augmentation step is to assemble the periphery of center-
periphery structures. The input to Stage 3 is a set of clusters, so that each
non-singleton cluster is $k$-valid and $m$-valid. Here we allow all nodes that
are not in any non-singleton cluster to be added to some cluster as long as it
is adjacent to at least $p$ core nodes in the (single) cluster to which it is
added. In this study, we set $p=2$ to ensure that we captured publications
that are linked by co-citation or bibliographic coupling to core nodes in a
community. If no such cluster exists such that a node can be added to it in a
$p$-valid manner, the node remains unclustered.

We add $x$ to the cluster $C$ that maximizes

$\frac{N_{C}(x)}{|C|}$

where $N_{C}(x)$ is the number of core node neighbors of node x in cluster $C$
and where $|C|$ denotes the number of nodes in cluster $C$. In other words, we
add node $x$ to the cluster where $x$ has proportionally the most core node
neighbors.

As an example, suppose $C_{1}$ and $C_{2}$ are clusters of core nodes and that
$x$ is not yet added as a non-core node to any cluster. Suppose $x$ has 5
neighbors in cluster $C_{1}$ and 10 nodes in cluster $C_{2}$, where
$|C_{1}|=1000$ and $|C_{2}|=20$. This procedure would add $x$ as a non-core
member to $C_{2}$ since 50% of the nodes in $C_{2}$ are neighbors of $x$ while
only $5/1000=0.5\%$ of the nodes in $C_{1}$ are neighbors of $x$.

####  2.2.5 Stage 4: Parsing clusterings to produce $kmp$-valid clusters

Although Stage 2 is guaranteed to produce $k$-valid clusters, it does not
always produce $m$-valid clusters. Furthermore, the impact of Stage 3 (the
augmentation step) is to add nodes to clusters that can participate as non-
core nodes, and it is possible for a node added to a cluster in Stage 3 to
have sufficient neighbors in its cluster to qualify for core membership.
Hence, the result of these three stages is a set of clusters that needs to be
“parsed” in order to know which nodes are core members, which nodes are non-
core members, and whether the clusters are $kmp$-valid (as defined in
Definition 2).

##### Parsing and modifying a single cluster

Here we describe how we perform this parsing on a given cluster $C$ (taken
from a clustering $\mathcal{C}$) and values for $k$ and $p$.

  * •

Step 1: We label every node in the cluster $C$ using the k-core labelling
algorithm, applied only to the subnetwork defined by $C$. We let $C^{\prime}$
denote the subset of nodes in $C$, each of whose labels is at least $k$, and
we put the remaining nodes into a bin $B(C)$.

  * •

Step 2: We compute the connected components of $C^{\prime}$, and delete the
components that do not have positive modularity; the retained components thus
have positive modularity, and are referred to as $C$-derived clusters (to
indicate their derivation from the original cluster $C$). The clusters
produced in this step will be the core node members in the final clusters we
produce at the end of Step 3.

  * •

Step 3: We augment the $C$-derived clusters using the bin $B(C)$ (i.e., we
find non-core members to add) as follows. We examine each node $x$ in bin
$B(C)$ to see if it has at least $p$ neighbors in at least one $C$-derived
cluster; if so, we select the best $C$-derived cluster $A$ (using the
algorithm from Stage 3) and add the node $x$ to $A_{nc}$ (where “nc” refers to
“non-core”). After all nodes are examined and processed, we let
$A^{\prime}=A\cup A_{nc}$ (for each $C$-derived cluster $A$) and output the
set of all such clusters $A^{\prime}$ as the “final clusters” derived from
cluster $C$. Note that this process indicates the parsing of each final
cluster $A^{\prime}$ into core ($A$) and non-core ($A_{nc}$) nodes.

  * •

Step 4: We return all the final clusters derived from $C$.

######  Theorem 1.

For any clustering $\mathcal{C}$ of a network $N$, and any positive integers
for $k$ and $p$ (with $p<k$), the output of $kmp$-processing is a clustering
that is $kmp$-valid. Therefore, the output of the four-stage clustering method
is $kmp$-valid for all networks $N$ and values for $k$ and $p$.

###### Proof.

Let $\mathcal{C}$ be an arbitrary clustering. Hence, some of its clusters may
not be $k$-valid, may not be connected, and may not have positive modularity.
We will prove that after the $kmp$-processing, all the clusters are
$kmp$-valid. Specifically, we will prove that the parsing produced in Step 3
into core and non-core satisfies $kmp$-validity.

First, note that by construction the clusters (referred to as $C^{\prime}$)
that are produced in Step 1 have the property that every node in these
clusters is adjacent to at least $k$ other nodes in their cluster. Hence,
treating each cluster as only containing core nodes, these clusters are
$k$-valid. In Step 2, these clusters are divided into components and the
components are retained only if they have positive modularity; hence the
$C$-derived clusters that are produced are $k$-valid and $m$-valid, under the
interpretation that they contain only core nodes. In Step 3, the $C$-derived
clusters are augmented. This augmentation step maintains connectivity, and so
the final clusters are connected. It remains to establish that after parsing
any final cluster into core and non-core nodes, the final cluster would be
$k$-valid (i.e., every core node would be adjacent to at least $k$ other core
nodes), $p$-valid (i.e., every non-core node would be adjacent to at least $p$
core nodes), and the core node subcluster would have positive modularity, and
hence also be $m$-valid.

Let $A^{\prime}$ be some final cluster. By construction, it is formed by
taking a $C$-derived cluster $A$ produced in Step 2, and then augmenting it.
Thus, $A^{\prime}=A\cup A_{nc}$, where $A_{nc}$ is the set of nodes that are
added during the augmentation step. We will establish that applying Stage 4
$kmp$-parsing to this cluster $A^{\prime}$ will not change its decomposition
into core and non-core (i.e., $A$ will still be the core nodes and $A_{nc}$
will be the non-core nodes). Note that by construction, all the nodes in $A$
are adjacent to at least $k$ other nodes in $A$. Hence, when $A^{\prime}$ is
$kmp$-parsed, the nodes that are identified as core nodes will contain all the
nodes in $A$ and then possibly some nodes from $A_{nc}$. Independent of
whether there are new core nodes, $A^{\prime}$ will be $p$-valid. If there are
no new core nodes, therefore, then $A^{\prime}$ will be $kmp$-valid. Here we
show that in fact no node in $A_{nc}$ will be labelled as core, and so there
are no new core nodes.

Let $x\in A_{nc}$ with $A$ a $C$-derived cluster. Hence, $x$ is drawn from bin
$B(C)$. By Step 1, the label assigned to $x$ during Step 1 (when the nodes in
cluster $C$ were labelled) was a value $L_{1}$ that is strictly less than $k$.
Since $A$ is a $C$-derived cluster, $A^{\prime}\subseteq C$. Consider the
label $L_{2}$ assigned to $x$ by the k-core labelling of $A^{\prime}$. Since
$A^{\prime}\subseteq C$, it follows that $L_{2}\leq L_{1}$. Since $L_{1}<k$,
it follows that $L_{2}<k$. Hence, $x$ will not be placed in the core for
$A^{\prime}$, and the final clusters output in Step 4 are therefore
$kmp$-valid. ∎

####  2.2.6 Additional uses of $kmp$-parsing

The Stage 4 $kmp$-parsing routine is also used in modified forms in other
aspects of this study:

  * •

Strict $kmp$-parsing: This strict parsing routine evaluates each cluster in a
clustering for being kmp-valid: those clusters that are $kmp$-valid are
retained and all others are discarded. We use this strict parsing routine to
evaluate Leiden.

  * •

Using $kmp$-parsing to extract core node clusters: We also have a variant
where use the parsing to extract only the core nodes within each cluster, and
then return the components of the core node sub-clusters that have positive
modularity score; this variant is used within Iterative Graclus.

###  2.3 Multidimensional Scaling Analysis

We used Multidimensional Scaling analysis (MDS) to visualize clusters of
marker nodes. For the distance between marker nodes $x$ and $y$, we calculated
the number of clusterings in which $x$ and $y$ were not in the same cluster.
Using the matrix of pairwise distances, we produced a 2-dimensional
visualization using metric MDS. See supplementary materials for additional
details.

##  3 Results & Discussion

###  3.1 Properties of the citation network

Exosomes are an area of investigation within the larger field of extracellular
vesicles in biology (Raposo et al.,, 2021; Kalluri and LeBleu,, 2020). This
field has been exponentially expanding, as evidenced by a keyword search for
“exosome” in the Dimensions bibliography yielding a count of less than 100
publications in 1990 and earlier, 11,100 publications from 1991 through 2010,
and 115,300 publications from 2011-2021 (rounded). To find communities in this
research area, we constructed and analyzed a large citation network that
captured articles concerning exosomes and extracellular vesicles.

The citation network we built consisted of 14,695,475 publications in 13
components, of which the largest component accounts for 99.998% of the
network. The network was generated through amplifying a seed set of 11,156
articles (Materials and Methods). The degree distribution of the nodes in this
network is typical of citation networks with a few nodes of high degree and
many nodes of low degree (Figure 1). Roughly 68% of the nodes have degree at
most five and the 90th, 95th, and 99th percentiles of degree counts are 6113,
9186, and 24510. The highest degree is 256,836 and corresponds to an article
describing an assay for protein measurement.

The nodes in this dataset were roughly distributed by year of publication as
follows– 1990 or earlier (1.17 million), 1991-2010 (6.05 million), and
2011-2021 (6.99 million), suggesting not only a rapid growth of exosome
publications in the post-1990 period but also a substantial increase in
publications linked by citation to the seed articles.

Figure 1: Intra-network degree distribution of the 14,695,475 nodes in the
exosome citation network. _x-axis:_ log degree, _y-axis:_ log node count.
Figure 2: Cluster sizes using the simple $k$-core clustering algorithm. The
input exosome citation network (Materials and Methods) consists of 13
components summing to 14,695,475 nodes. Of these, a single component accounts
for 14,695,226 articles (99.998% of the network). The $k$-core clustering
algorithm was applied to the exosome citation network for multiple values of
$k$ _(x-axis)_. The size of the $k$-core is shown on the ordinate _(y-axis)_.
A single component is returned in each case, with the exception of $k$=1 and
$k$=2. Node coverage decreases as $k$ increases, and is approximately 36% and
21% when $k=5$ and $k=10$ respectively. The single cluster at $k$=56 has 3,630
nodes, amounting to node coverage of 0.02%. At $k$=57 or greater, the entire
network dissolves, thus the degeneracy of the network is 56. Clusters shown
have positive modularity (_mod +ve_) when $k=1$ or $k>=40$ and are colored
teal. By definition, the connected components of the network are the $1$-cores
so 13 clusters are returned for $k=1$. For $k=2$, only two clusters are
returned. Clusters of size 100 or less (0.001% of the network) are not
included in this plot and pertain only to $k$=1 or $k$=2. _Inset:_ $k$-core
sizes sampled at intervals of 5 are displayed using a linear scale.

###  3.2 Results of clustering methods

We now present results using different clustering methods, including the
$k$-core clustering method, Iterative $k$-core clustering, our four-stage
pipeline, and the Leiden algorithm. As noted earlier, we were explicitly
interested in discovering citation-dense regions with center-periphery
structure that reflected cohesiveness and collaboration (Giatsidis et al.,,
2011; Breiger,, 2014). In this case, collaboration refers to the recognition
of prior work by others in the community through citations. We were not
interested in communities that consisted of a single heavily cited article or
a single article that cited many references (Chandrasekharan et al.,, 2021, p.
193).

####  3.2.1 Results for the Leiden algorithm

We first used the Leiden algorithm, which guarantees connected communities
(Traag et al.,, 2019), as a benchmark for community finding. We consider
Leiden as a reference method in the scientometrics community, and have
previously used it (Chandrasekharan et al.,, 2021) in combination with Markov
Clustering (Van Dongen,, 2008) to detect communities in the immunology and
ecology literature. In the present study, we used the Leiden software (Traag,,
2021) with the Constant Potts Model as quality function, and with varying
resolution factors to cluster the exosome citation network. The resolution
factor is designed to modify the clustering, as it determines the required
minimum density within communities.

For this citation network, at most of the resolution values that were tested,
the Leiden algorithm generated a relatively large number of small clusters
(Table 1). At the smallest resolution factor value we examined (0.05), Leiden
produced 488,285 non-singleton clusters and 6,323,695 singletons and the
largest cluster comprised 960 nodes. Node coverage, defined as the ratio of
nodes in non-singleton clusters to the total number of nodes in the network
was 57% with resolution factor set to 0.05. As we increased the resolution
value, the number of singleton clusters increased, the sizes of non-singleton
clusters decreased, and we observed a progressive drop in node coverage (down
to 16% at resolution factor 0.25 and to 9% for resolution factor 0.50).

Resolution | Node Coverage | # Clusters | # Singletons | Min | Median | Max
---|---|---|---|---|---|---
0.05 | 57% | 488,285 | 6,323,695 | 2 | 17 | 960
0.25 | 16% | 481,780 | 12,408,446 | 2 | 4 | 192
0.50 | 9% | 434,973 | 13,412,183 | 2 | 2 | 97
0.75 | 8% | 489,937 | 13,496,111 | 2 | 2 | 39
0.95 | 8% | 497,757 | 13,499,132 | 2 | 2 | 16
Table 1: Cluster statistics for Leiden under different resolution values. Node
coverage, expressed as percentage, refers to the the ratio of nodes in non-
singleton clusters to the total number of nodes in the network. # of clusters
refers to the number of non-singleton clusters. The last three columns refer
to the sizes of non-singleton clusters. Results shown here are before
$kmp$-processing.

We also screened the clusters generated by Leiden for $kmp$-validity
(Materials and Methods, Definition 2) at $k$=5 or 10 and $p$ = 2, the values
that we use in when applying our pipeline. For the resolution value of 0.05,
the node coverage is 3.16% and 2.54% when $k$ is 5 or 10 respectively
(Supplementary Materials, Tables 3 and 4), a large drop from 57% for the
Leiden clustering before restriction to $kmp$-valid clusters. For larger
resolution values, restriction to $kmp$-valid clusters results in even smaller
node coverage. In addition, again using resolution value $0.05$, after
restriction to $kmp$-valid clusters, the number of clusters is much smaller:
only 4,076 for $k=5$ and 2,320 for $k=10$, a large drop from 488,285. Thus,
restriction to $kmp$-valid clusters greatly reduces the node coverage and
number of clusters compared to Leiden before restriction, and this holds for
all resolution values. Moreover, this analysis shows that only a small
fraction of the clusters produced by Leiden at any resolution value are
$kmp$-valid (e.g., less than 1% for resolution value 0.05).

In summary, while Leiden was able to efficiently cluster our network into a
large number of small communities that represented between 8% and 57% of the
network depending on the resolution factor employed, only a small fraction of
the communities exhibited $kmp$-validity. This is not surprising since the
Leiden algorithm and optimization criterion was not designed to produce
$kmp$-valid communities, and these trends indicated that Leiden had limited
utility for our purposes.

####  3.2.2 Results for $k$-core clustering

To identify citation-dense regions of the network, we ran the $k$-core
clustering method on our network for different values of $k\geq 1$ (Figure 2).
The largest value for $k$ for which a cluster is returned is $56$, indicating
that the degeneracy of the network is $56$. The network has no isolated
vertices and so $k=0$ and $k=1$ produce the same output, which is 13 clusters,
each corresponding to a connected component in the network. When $k=2$, two
clusters were returned. For each $3<k\leq 56$, only a single cluster was
returned, hence only $k=0,1,2$ produced more than one cluster, and in each of
these cases, a single cluster dominated in size.

An interesting trend in this analysis is how $k$ impacts the modularity scores
of the clusters. By definition, the components in the graph all have positive
modularity, and so when $k=1$ the clusters all have positive modularity. For
larger values of $k$, the modularity scores do not become positive until
$k=40$, and then all subsequent values of $k$ produce clusters with positive
modularity scores.

Cluster size decreased monotonically as $k$ increased to $56$, however we
observe a pattern of relatively stable core sizes at lower values of $k$
followed by a more rapid decrease as $k$ increases above 40. Leskovec and
Horvitz, (2008) reported similar findings about changes in core sizes on a
much larger network of instant messaging data that consisted of 180,000,000
nodes. These authors suggest that the rapid decrease in core size occurs once
nodes on the fringe of the network are removed. On our network, this more
rapid decrease of cores sizes also coincides with the appearance of positive
modularity of clusters; modularity was not reported in Leskovec and Horvitz,
(2008). Thus, we are mainly interested in the $k$-cores for large values of
$k$: they have positive modularity, small changes in $k$ result in large
changes to their sizes, and they have been identified in the prior literature
as what is left after the fringe of the network is removed.

While the simple $k$-core clustering method identifies citation-dense areas in
the network suggesting cohesiveness and collaboration, it has two limitations:
it does not ensure positive modularity for every cluster it produces, and, on
our data, for every $k\geq 3$ it produced only a single large cluster. We note
that for $k=0,1,2$, it produced two or more clusters, one of which was very
large. These limitations impact the ability to find multiple communities of
interest in the exosome literature, especially considering the possibility
that some of the communities of interest could be contained within larger
clusters with non-positive modularity.

####  3.2.3 Results for Iterative k-core (IKC)

We designed Iterative $k$-core (IKC) to improve on the $k$-core clustering
algorithm. The input to IKC is the network $N$ and the parameter $k$. The
first cluster that is found in the network is the $L$-core where $L$ is the
largest label assigned to any node. If $L\geq k$, then the $L$-core is
produced as a cluster and removed from the network, and otherwise the
algorithm stops. If the algorithm has not stopped, it is run recursively on
the reduced network. Therefore, IKC($k$) will contain all the clusters in
IKC($k^{\prime}$) for $k\leq k^{\prime}$.

We explored IKC varying $k$ between $5$ and $50$, and examined the
distribution of cluster sizes generated. We also recorded the minimum degree
in each cluster. Since IKC clusters satisfy $k$-validity, the nodes in the
clusters are all “core” members, and so this minimum degree is also the
Minimum Core Degree (MCD) of the cluster. As expected, increasing $k$ results
in decreases in cluster size and increases in the MCD value (Figure 3). In
order to include as much of the network as is reasonable and still have
sufficient density to define community structure, we selected $k=5$ and $k=10$
for IKC.

While IKC discovered $km$-valid communities that were trivially $p$-valid, it
too has limitations. It identifies only core nodes with modest node coverage
of 7.38% and 4.22% at $k$=5 and $k=10$, respectively. It also generates some
large clusters with lower MCD values that leave open the question of whether
denser $kmp$-valid communities exist within them.

Figure 3: Empirical statistics of the Iterative k-core (IKC) clustering
methods (varying $k$) on the Exosome network. The y-axis shows the cluster
sizes (logarithmic scale) and the x-axis shows the Minimum Core Degree (MCD)
values, where the MCD of a cluster is the minimum degree of any node in the
cluster. By design, IKC($k$) contains all the clusters of IKC($k^{\prime}$) if
$k\leq k^{\prime}$; thus, the panels showing IKC at lower values of $k$
contain greater numbers of clusters.

####  3.2.4 Results for the Four-Stage Clustering Pipeline

Figure 4: Our four-stage clustering pipeline takes as input a citation network
and produces clusters based on values selected for parameters $k$ and $p$.
Boxes adjacent to edges indicate stages in the pipeline; boxes with blue
borders indicate tests that are performed to determine which clusters are
passed to the next stage. In Stage 1, it runs the Iterative k-core (IKC)
algorithm for the selected value of $k$; clusters that are $km$-valid are then
passed to the next stage. Stage 2 (optional) breaks the clusters from the
first stage into smaller clusters, using either recursive Graclus or Iterative
Graclus (and in each case, using either the default version or a heuristic
search version). Clusters that pass the required validity check ($k$-validity
for Recursive Graclus and $km$-validity for Iterative Graclus) are then passed
to the next stage. These clusters are then enlarged with additional nodes in
Stage 3, the “Augmentation” step. All clusters produced are $p$-valid at this
point, and are passed to Stage 4, $kmp$-parsing, which produces a set of
$kmp$-valid clusters, each of which is parsed into their core subcluster and
non-core subcluster.

To address the limitations of IKC, we designed a four-stage pipeline (Figure
4). This four-stage pipeline is guaranteed to produce a $kmp$-valid clustering
of the network, for user-provided values of $k$ and $p$.

In Stage 1 we use IKC with $k=5$ and $k=10$. Stage 2 breaks the clusters found
in Stage 1 into smaller clusters; for this stage we apply either Recursive
Graclus or Iterative Graclus, and for each of these we use Graclus either in
default mode or in local search mode. Thus, for each setting of $k$ we have
four versions of the four-stage pipeline: Iterative and Recursive Graclus run
in either default or local search mode. In Stage 3, the clusters produced by
Stage 2 are augmented by the addition of nodes that satisfy $p$-validity for
$p=2$. In Stage 4, we parse the output of Stage 3 and retain only those
clusters that are $kmp$-valid.

Stage 2 | Stage 3 | Node Coverage | Clusters | Singletons | Min | Median | Max
---|---|---|---|---|---|---|---
|  |  | (number) | (number) |  |  |
$k=5$ |  |  |  |  |  |  |
No | No | 7.38% | 276 | 13,611,485 | 8 | 28.0 | 345,139
No | Yes | 36.63% | 276 | 9,312,583 | 15 | 265.5 | 856,623
IG(0) | Yes | 20.01% | 13,709 | 11,752,582 | 6 | 118.0 | 19,934
IG(2000) | Yes | 20.84% | 9,698 | 11,632,959 | 6 | 106.0 | 32,487
RG(0) | Yes | 26.27% | 2,261 | 10,835,596 | 10 | 145.0 | 579,720
RG(2000) | Yes | 26.09% | 3,417 | 10,861,670 | 11 | 105.0 | 578,265
$k=10$ |  |  |  |  |  |  |
No | No | 4.22% | 119 | 14,075,787 | 12 | 85.0 | 213,670
No | Yes | 33.69% | 119 | 9,744,368 | 62 | 1638.0 | 964,503
IG(0) | Yes | 18.51% | 4,185 | 11,975,796 | 33 | 427.0 | 27,007
IG(2000) | Yes | 20.00% | 3,044 | 11,757,196 | 31 | 488.5 | 60,189
RG(0) | Yes | 27.26% | 359 | 10,689,730 | 67 | 1014.0 | 679,922
RG(2000) | Yes | 27.61% | 473 | 10,637,388 | 55 | 761.0 | 620,491
Table 2: Cluster statistics for 12 variants of Four-Stage clustering. All
results include Stages 1 and 4, but some pipelines do not use Stages 2 or 3;
all clusterings are $kmp$-valid. Top: results for $k=5$, Bottom: results for
$k=10$. Stage 2 is performed either using Iterative Graclus (IG) or Recursive
Graclus (RG), which are each run with either $0$ or $2000$ local search
iterations. Node coverage refers to the percentage of network nodes contained
in non-singleton clusters and singletons refers to the number of nodes in
singleton clusters. All other statistics refer to non-singleton clusters, with
the last three columns refering to the sizes of non-singleton clusters.
Specific noteworthy trends include: (a) all clusterings that use Stage 3 have
node coverage above 18%, (b) all clusterings have at least one very large
cluster, (c) Stage 2 choice impacts maximum cluster size, and (d) setting
$k=5$ produces more clusters with a smaller median cluster size than setting
$k=10$.

We show results for the different versions of this four-stage pipeline in
Table 2, where the rows correspond to different ways of setting $k$ and
running Stages 2 and 3. Using IKC alone without Stages 2 and 3 resulted in 276
and 119 non-singleton clusters and had total node coverage of 7.38% and 4.22%,
with maximum cluster sizes of 345,139 and 213,670, for $k=5$ and $k=10$,
respectively. Skipping Stage 2 (breaking down clusters) but adding Stage 3
(augmentation) greatly increases the node coverage to at least 33% for both
settings of $k$ but also increases the maximum cluster size to 856,623 and
964,503 for $k=5$ and $k=10$, respectively. This approach also has large
median cluster sizes, especially for $k=10$ where the median is 1638. Thus,
using Stage 3 (augmentation) but not also Stage 2 produces high node coverage
and large cluster sizes.

Using all four stages, and hence using Stage 2, reduces the node coverage to
values that range from 18.51% to 27.61% and also reduces the median and
maximum cluster sizes, but the choice of how Stage 2 is run has a significant
impact. Node coverage is higher when using Recursive Graclus rather than
Iterative Graclus. Using Recursive Graclus in default mode rather than local
search mode tends to produce a smaller number of non-singleton clusters that
are also somewhat larger; for example, when $k=10$, default usage of Graclus
that doesn’t employ the local search strategy produces a median cluster size
of 1,014 as opposed to 761 when using 2000 local search iterations.

The choice between $k=5$ and $k=10$ also impacts results, with $k=10$
producing a much smaller number of non-singleton clusters that are
substantially larger than the results for $k=5$. For example, using default
Recursive Graclus at $k=10$ produces 359 non-singleton clusters with median
size 1014 while the same setting for $k=5$ produces 2,261 non-singleton
clusters with median size 145.

####  3.2.5 Comparison between different clustering methods

We now compare the different clustering outputs with respect to node coverage,
number of non-singleton clusters, and the distribution of non-singleton
cluster sizes. As our discussion of the different variants of the four-stage
pipeline revealed, how Stages 2 and 3 are run and the value for $k$ impact
these statistics. If node coverage is the most important criterion, then
skipping Stage 2 but using Stage 3 is recommended. However, since these
approaches produce very large clusters, including Stage 2 is more likely to be
desirable. Among the techniques that use Stage 2, Iterative Graclus tends to
produce smaller clusters, but Recursive Graclus produces higher node coverage;
the choice between these should be made based on the specific question that is
being addressed. Similarly, how $k$ is set should depend on the features of
the citation network, and picking larger values of $k$ may be suitable under
some conditions.

A comparison to Leiden is also helpful: before restricting to the $kmp$-valid
clusters, Leiden has very high node coverage (57%) for resolution value
$0.05$, but after restricting to $kmp$-valid clusters, node coverage drops to
3.16% and 2.54% when k is 5 or 10, respectively. In contrast, the four-stage
pipeline has node coverage that varies from 18.51% to 27.61%, depending on $k$
and how Stage 2 is performed (Table 2).

Thus, a potential user of this approach is presented with options that can be
used to address contextual needs. For example, after considering features of
the source data and the purpose of community finding, a user may choose
Leiden, IKC, IKC with augmentation, or the complete pipeline with its
$kmp$-parsing requirements.

###  3.3 Marker Node Analysis

The network we constructed for this study has more than 14 million nodes. We
assumed that some of the communities discovered would represent areas of
investigation peripheral to exosomes and extracellular vesicles. Consequently,
we used a set of 1,218 independently selected articles from the extracellular
vesicle literature, all of which are present in the network, as marker nodes
(Materials and Methods) and used them to identify clusters of interest. Any
community containing at least one marker node was considered relevant;
however, we were particularly interested in communities with high numbers of
marker nodes.

For IKC clustering at either $k$=5 or $k$=10 (Figure 2), two clusters
contained 256 and 227 marker nodes respectively, and together accounted for
approximately 40% of the 1,218 markers. The first of these clusters, with 256
marker nodes, was the 56-core of the network, and comprised 3,630 nodes. The
second, with 227 marker nodes, exhibited an MCD (minimum core degree) value of
12 and consisted of 213,670 nodes. To visualize the distribution of the entire
set of marker nodes, we used a multidimensional scaling approach using the
frequency of co-occurrence in clusters across 12 different clustering methods
as the measure of similarity between publications. Each of these two sets of
marker nodes are found in dense and clearly defined clusters after
multidimensional scaling (Figure 5).

Figure 5: Multidimensional scaling (MDS) of 1,218 marker nodes based on the
frequency with which they are placed in the same cluster in 12 clustering
outputs. The circled beige cluster (bottom right) corresponds to the 256
markers found using either IKC(5) or IKC(10) in a single cluster of minimum
cluster degree (MCD) of 56, while the circled blue cluster (top) corresponds
to the 227 markers found in a different cluster with an MCD value of 12.

These two clusters were similar in having a large number of marker nodes but
were otherwise different from each other with respect to MCD and size;
therefore, we used the two sets of 256 and 227 markers as examples for further
study.

A second criterion considered was robustness to clustering method, which we
measure by the frequency with which marker nodes were found co-located in the
same cluster across the 12 clusterings we studied. We began this evaluation by
first determining which of these nodes are always placed in non-singleton
clusters for all 12 clustering methods. We found that 27 of 256 and 35 of 227
marker nodes respectively were always placed in non-singleton clusters, and
studied these two sets further.

The first set (A) consisting of 27 marker nodes contained 17 articles and 8
reviews that were published between 2006 and 2019 with 23 of these published
in 2010 or later. Based upon inspection of titles and journal, the contents of
articles in set A spanned basic cell biology, the role of exosomes in cancer,
and exosome isolation methods with some variation in terms of being
descriptive or mechanistic. The second set (B) of 35 markers contained 26
articles and 9 reviews published between 2013 and 2021, largely focused on a
basic and translational studies of exosomes in nervous tissue but also
including a few articles on exosomes in pregnancy and exosome isolation
methods.

We then examined the publications in sets A and B for co-occurrence in the
same cluster across all 12 clusterings. We found that 8 articles from set A
were always found in the same cluster and 4 articles from set B were always
found in the same cluster. While the numbers of markers in these sets are
small, they serve to identify a larger community, which can then be
characterized further by other techniques, such as detailed scholarly
examination or textual content analysis.

We identified the smallest cluster across the 12 clusterings that contained
the 8 articles from A; the selected cluster (Cluster 1) consisted of 73
articles and was focused on extracellular vesicles in cancer. We performed a
similar analysis for the 4 articles from B, and found a cluster (Cluster 2) of
145 articles that was focused on extracellular vesicles in the nervous system.
Thus, both these clusters were relatively homogenous with respect to article
content, one focused on extracellular vesicles in cancer and the other on
extracellular vesicles in the nervous system. Our use of a single label for
each cluster should be considered a subjective approximation; an alternate
view is that Cluster 2 also includes articles on cancer and has some focus on
astrocytes. Both clusters were derived from the IKC(5)-Iterative Graclus
branch of the pipeline.

We then extracted the authors of articles in these two clusters (Table 3).
Cluster 1 involved 356 authors of which 9 were authors of at least 5 articles
in the cluster and one person was an author of 17 articles in the cluster.
However, 301 authors (84.6%) had contributed to only one article in the
cluster. Cluster 2 involved 742 authors of which 4 were authors of at least 5
articles in the cluster. One author had contributed 7 articles and 650 authors
(87.6%) had contributed only one article each. Interestingly, the two
publication clusters share 14 authors. Thus, the two author communities
defined by two disjoint publication clusters overlap.

These trends are strikingly similar to the observations of Price and Beaver,
(1966) in that the authors segregate into a small number with large numbers of
papers in the cluster and many with only one paper in the cluster. Although we
only examined two clusters, both exhibited the center-periphery structure
described in Price and Beaver, (1966); our sample is too small to draw
conclusions beyond suggesting that the trends observed may be true for other
clusters, and this should be evaluated.

We also found discrete co-author groups within these clusters (Figure 6).
Cluster 1 featured 4 non-overlapping co-author groups where authors were
linked to each other if they had co-authored at least two articles in the
cluster. Cluster 2 featured 17 such discrete co-author groups suggesting,
despite its larger size, that influence within the group was more distributed
considering the larger number of co-author groups and the smaller number of
articles written by individual authors. These examples are provided to
illustrate the potential utility of the pipeline and the use of marker nodes.

| Articles | Core Nodes | Markers | Authors | Auth_$5$ | Max_Pubs
---|---|---|---|---|---|---
Cluster 1 | 73 | 47 | 16 | 356 | 9 | 17
Cluster 2 | 145 | 129 | 31 | 742 | 4 | 7
Table 3: Statistics on the two selected small clusters. Cluster 1 and Cluster
2 were selected based on marker nodes: the greatest number of marker nodes
that were found co-located in the same cluster across all 12 clustering
methods were used to define their common clusters, and the smallest of the
common clusters for each set was returned. Both clusters are $kmp$-valid for
$k=5$ and $p=2.$ Articles refers to the total number of nodes in the cluster,
core nodes refers to the number of these nodes that are core, and markers
refers to the number of nodes that are markers. Authors denotes the total
number of authors of articles in the cluster, Auth_$5$ refers to the number of
authors that have at least 5 publications in the cluster, and Max_Pubs refers
to the largest number of publications in the cluster by any single author.

(a) Cluster 1

(b) Cluster 2

Figure 6: Co-author clusters in two communities identified using marker nodes.
Two clusters were selected for analysis because they contained the greatest
number of marker nodes that were co-located across all 12 clustering methods,
and were the smallest of such clusters (see text). Discrete co-author groups
are found in both clusters when inclusion in a co-author groups requires at
least two instances of intra-cluster co-authorship between two authors. _(a)_
Cluster 1 consists of 73 articles contributed by 356 authors. This cluster
contains 4 non-overlapping co-author groups, with 5, 8, 11, and 28 authors.
_(b)_ Cluster 2 consists of 145 articles authored by 356 authors. This cluster
contains 17 non-overlapping groups, with four groups of 2 authors, three
groups of 3 authors, three groups of 4 authors, two groups of 5 authors, four
groups of 7 authors, and one group of 18 authors.

##  4 Conclusions

Based on historical studies of research communities, we posed corresponding
properties for the graphical structure of communities in networks. We
developed an analytic pipeline to ask whether communities of publications with
center-periphery substructure exist in citation networks. In designing a four-
stage pipeline to find communities of this form, we were implicitly asking
whether the information encoded in the graphical structure of communities can
be used to make inferences on the social structure of these communities, for
example, discrete co-author groups. We examined these questions using a
citation network representative of exosomes and extracellular vesicles, a
field that has rapidly expanded in recent years.

In this citation network, our pipeline found many publication communities that
exhibit center-periphery structure. This finding supports our hypothesis that
communities of this type exist within the extracellular vesicles research
community, and shows that the pipeline we used can find such communities.
Whether such communities exist in other citation networks and whether our
pipeline is successful at finding such communities are important questions
that future work should address.

Our pipeline is designed to enable investigators to interrogate their data
with different options for each stage and different settings for $k$ and $p$.
As we observed in our study, changes to the settings for the parameters $k$
and $p$ as well as how each stage was performed produced clusterings that
differ from each other in terms of the the node coverage as well as the number
and sizes of non-singleton clusters, effectively providing different views of
the network. Thus, the specific question of interest and the properties of the
citation network are important in choosing how to set these parameters.
Alternatively, the pipeline can be used to generate many different
clusterings, and the investigator may assess community structure through an
integrative analysis that does not depend on a single clustering method.

We also saw significant differences between clusterings produced by our
pipeline and those produced by the Leiden software. While there is some
overlap in the range of cluster sizes generated, our pipeline tends to
generate much larger clusters than the Leiden software, and all of our
pipeline clusterings produced at least one very large cluster with more than
19,000 nodes and, in the case of Recursive Graclus, the largest cluster
contained more than 500,000 nodes. Given our focus on the small clusters
produced in our various pipelines, we did not explore large publication
clusters. It is not clear to us what insights can be gained from clusters that
have tens of thousands of nodes. We speculate that they may reflect the many
connections in a rapidly expanding field, and we also consider them as
tempting targets for future versions of Stage 2, which seeks to break up the
large clusters. Further work is clearly needed.

This study suggests several directions for future work. For method
development, our four-stage pipeline is designed to enable substitutions to
how each stage is performed; as noted above, breaking up large clusters might
be more successfully executed using new approaches rather than either
recursive or iterative Graclus. We also note that all the clustering methods
we developed produce disjoint clusters, yet publications may be expected to be
members of more than one research community. Some clustering methods have been
developed that can produce overlapping clusters (Rossetti,, 2020), and
exploring this approach in the context of large citation networks is likely to
provide additional insights. Methods that can combine information from
multiple clustering methods could lead to better insight into community
structure, and so principled development of ensemble methods (a standard
approach in machine learning) is another direction for future research.

One of the most intriguing directions for future research is the life cycle of
these research communities, both in terms of how ideas and questions being
focused on by the research community as a whole change over time and how
authors move between different communities over time. This is challenging to
study because the network evolves through growth each year and community
finding in dynamic graphs is a promising direction (Rossetti,, 2020).

Additional clusters could be examined for in-depth examination based, for
example, on specific authors, articles of particular importance, funding
sources, or clusters identified by marker node co-located in many but not all
12 clusterings. Other insights could be obtained by examining the relationship
between publication communities (e.g., citations between communities) in a
single clustering or comparisons of communities obtained using different
clustering methods; such investigations would help elucidate how the research
ideas and communities relate to each other, and the extent to which these
communities are hierarchically organized.

For extracellular vesicles, insight into community life cycles can be obtained
by studying, over time, communities containing key studies such as the ones on
transferrin recycling (Harding et al.,, 1983; Pan and Johnstone,, 1983), the
observation that B-lymphocytes secrete antigen-presenting vesicles (Raposo et
al.,, 1996), a report of exosome mediated transfer of mRNA and
microRNA(Ratajczak et al.,, 2006; Valadi et al.,, 2007), and the biological
effects of transferring exosomes between lean and obese mice (Ying et al.,,
2017). Our analysis was based on a single set of marker nodes; extending the
set of marker nodes and annotating each marker node with respect to content
would allow finer-grained evaluation.

Exploration of author communities associated to these publication communities
would shed additional insights into the social structure of the research
community, potentially identifying authors with high influence within a
particular emerging research area, and others that are highly influential
across several areas.

We close with comments about the high-level approach we took to understanding
community structure. Our approach relied entirely on the graphical structure
of the citation network. This restriction was used in order to provide a
scalable approach that did not rely on any other information or expert
knowledge; however, by design this limits which communities can be detected
(McCain,, 1986). Textual analysis, relationships between authors based on
institutions, other social interactions such as conference presentations and
sources of funding could be used to used to supplement citation data and would
likely lead to a different set of publication or author communities with
potentially different properties.

Understanding author role is also important, and again our reliance on
citations to identify influential researchers is biased towards well-cited and
well-funded authors. Perhaps one of the benefits, therefore, of our approach
to community detection is that we can use it to find small and thematically-
focused publication communities and hence identify those authors who are
influential within these small communities. Nevertheless, we propose that
while scalable methods for community detection may generally tend to rely on
purely graph-theoretic properties, mixed method approaches support more a more
nuanced understanding of social structures and dynamics within the scientific
enterprise.

## Competing Interests

The authors have no competing interests. Dimensions data were made available
by Digital Science through the free data access for scientometrics research
projects program. Digital Science personnel did not participate in
conceptualization, experimental design, review of results, or conclusions
presented. DK is an employee of NTT DATA, which had no role in this study.

## Funding Information

EW is a Siebel Scholar. TW receives funding from the Grainger Foundation.
Research reported in this manuscript was supported by the Google Cloud
Research Credits program through award GCP19980904 to GC.

## Data Availability

Access to the bibliographic data analyzed in this study requires access from
Digital Science. Code generated for this study is freely available from our
Github site (Park et al.,, 2021).

## Acknowledgments

We thank Valerie King from the University of Victoria for directing us to the
k-core literature. We thank Phil Stahl from Washington University in St. Louis
for helpful discussions and for drawing our attention to recent reviews of the
extracellular vesicle literature. We thank Digital Science, Google, the
Grainger Foundation, and the Thomas and Stacey Siebel Foundation.

## ORCID IDs

  * •

Eleanor Wedell 0000-0002-7911-9156

  * •

Minhyuk Park 0000-0002-8676-7565

  * •

Dmitriy Korobskiy 0000-0002-7909-0218

  * •

Tandy Warnow 0000-0001-7717-3514

  * •

George Chacko 0000-0002-2127-1892

## References

  * Ahlgren et al., (2020) Ahlgren, P., Chen, Y., Colliander, C., and van Eck, N. J. (2020).  Enhancing direct citations: A comparison of relatedness measures for community detection in a large set of PubMed publications.  Quantitative Science Studies, pages 1–16.
  * Blondel et al., (2008) Blondel, V. D., Guillaume, J.-L., Lambiotte, R., and Lefebvre, E. (2008).  Fast unfolding of communities in large networks.  Journal of Statistical Mechanics: Theory and Experiment, 2008(10):P10008.
  * Boyack and Klavans, (2010) Boyack, K. W. and Klavans, R. (2010).  Co-citation analysis, bibliographic coupling, and direct citation: Which citation approach represents the research front most accurately?  Journal of the American Society for Information Science and Technology, 61(12):2389–2404.
  * Boyack and Klavans, (2014) Boyack, K. W. and Klavans, R. (2014).  Including cited non-source items in a large-scale map of science: What difference does it make?  Journal of Informetrics, 8(3):569–580.
  * Boyack and Klavans, (2019) Boyack, K. W. and Klavans, R. (2019).  Creation and analysis of large-scale bibliometric networks.  In Glänzel, W., Moed, H. F., Schmoch, U., and Thelwall, M., editors, Springer Handbook of Science and Technology Indicators, pages 187–212. Springer International Publishing, Cham, Denmark.
  * Breiger, (2014) Breiger, R. (2014).  Explorations in Structural Analysis (RLE Social Theory): Dual and Multiple Networks of Social Interaction.  Routledge, New York.
  * Busatto et al., (2021) Busatto, S., Morad, G., Guo, P., and Moses, M. A. (2021).  The role of extracellular vesicles in the physiological and pathological regulation of the blood–brain barrier.  FASEB Bio Advances, 3(9):665–675.
  * Chandrasekharan et al., (2021) Chandrasekharan, S., Zaka, M., Gallo, S., Zhao, W., Korobskiy, D., Warnow, T., and Chacko, G. (2021).  Finding scientific communities in citation graphs: Articles and authors.  Quantitative Science Studies, 2(1):184–203.
  * Clancy et al., (2021) Clancy, J. W., Schmidtmann, M., and D’Souza-Schorey, C. (2021).  The ins and outs of microvesicles.  FASEB Bio Advances.  https://doi.org/10.1096/fba.2020-00127.
  * Coscia et al., (2011) Coscia, M., Giannotti, F., and Pedreschi, D. (2011).  A classification for community discovery methods in complex networks.  Statistical Analysis and Data Mining, 4(5):512–546.
  * Crane, (1972) Crane, D. (1972).  Invisible colleges; diffusion of knowledge in scientific communities.  University of Chicago Press, Chicago.
  * Devarakonda et al., (2020) Devarakonda, S., Korobskiy, D., Warnow, T., and Chacko, G. (2020).  Viewing computer science through citation analysis: Salton and Bergmark Redux.  Scientometrics, 125(1):271–287.
  * Dhillon et al., (2007) Dhillon, I., Guan, Y., and Kulis, B. (2007).  Weighted graph cuts without eigenvectors: A multilevel approach.  In IEEE Transactions on Pattern Analysis and Machine Intelligence (PAMI), volume 29:11, pages 1944–1957. ACM Press.
  * Edgar, (2016) Edgar, J. R. (2016).  Q & A: What are exosomes, exactly?  BMC Biology, 14(1).
  * Fortunato, (2010) Fortunato, S. (2010).  Community detection in graphs.  Physics Reports, 486(3-5):75–174.
  * Fortunato and Barthelemy, (2007) Fortunato, S. and Barthelemy, M. (2007).  Resolution limit in community detection.  Proceedings of the National Academy of Sciences, 104(1):36–41.
  * Fortunato and Castellano, (2009) Fortunato, S. and Castellano, C. (2009).  Community structure in graphs.  In Computational Complexity, pages 490–512. Springer New York.
  * Ghoroghi et al., (2021) Ghoroghi, S., Mary, B., Asokan, N., Goetz, J. G., and Hyenne, V. (2021).  Tumor extracellular vesicles drive metastasis (it's a long way from home).  FASEB Bio Advances.  https://doi.org/10.1096/fba.2021-00079.
  * Giatsidis et al., (2011) Giatsidis, C., Thilikos, D. M., and Vazirgiannis, M. (2011).  Evaluating cooperation in communities with the k-core structure.  In 2011 International Conference on Advances in Social Networks Analysis and Mining. IEEE.  https://doi.org/10.1109/asonam.2011.65.
  * Harding et al., (1983) Harding, C., Heuser, J., and Stahl, P. (1983).  Receptor-mediated endocytosis of transferrin and recycling of the transferrin receptor in rat reticulocytes.  Journal of Cell Biology, 97(2):329–339.
  * He et al., (2021) He, B., Hamby, R., and Jin, H. (2021).  Plant extracellular vesicles: Trojan horses of cross-kingdom warfare.  FASEB Bio Advances, 3(9):657–664.
  * Hook et al., (2018) Hook, D. W., Porter, S. J., and Herzog, C. (2018).  Dimensions: building context for search and evaluation.  Frontiers in Research Metrics and Analytics, 3:23.
  * Javed et al., (2018) Javed, M. A., Younis, M. S., Latif, S., Qadir, J., and Baig, A. (2018).  Community detection in networks: A multidisciplinary review.  Journal of Network and Computer Applications, 108:87–111.
  * Kalluri and LeBleu, (2020) Kalluri, R. and LeBleu, V. S. (2020).  The biology, function, and biomedical applications of exosomes.  Science, 367(6478).
  * Klavans and Boyack, (2017) Klavans, R. and Boyack, K. W. (2017).  Which type of citation analysis generates the most accurate taxonomy of scientific and technical knowledge?  Journal of the Association for Information Science and Technology, 68(4):984–998.
  * Kong et al., (2019) Kong, Y.-X., Shi, G.-Y., Wu, R.-J., and Zhang, Y.-C. (2019).  k-core: Theories and applications.  Physics Reports, 832:1–32.
  * Kuhn, (1970) Kuhn, T. (1970).  The structure of scientific revolutions.  University of Chicago Press, Chicago.
  * Lananna and Imai, (2021) Lananna, B. V. and Imai, S. (2021).  Friends and foes: Extracellular vesicles in aging and rejuvenation.  FASEB Bio Advances, 3(10):787–801.
  * Le Lay et al., (2021) Le Lay, S., Rome, S., Loyer, X., and Nieto, L. (2021).  Adipocyte-derived extracellular vesicles in health and diseases: Nano-packages with vast biological properties.  FASEB Bio Advances.  https://doi.org/10.1096/fba.2020-00147.
  * Leidal and Debnath, (2021) Leidal, A. M. and Debnath, J. (2021).  Emerging roles for the autophagy machinery in extracellular vesicle biogenesis and secretion.  FASEB Bio Advances, 3(5):377–386.
  * Leskovec and Horvitz, (2008) Leskovec, J. and Horvitz, E. (2008).  Planetary-scale views on a large instant-messaging network.  In Proceeding of the 17th international conference on World Wide Web - WWW '08. ACM Press.  doi:10.1145/1367497.1367620.
  * Malliaros et al., (2019) Malliaros, F. D., Giatsidis, C., Papadopoulos, A. N., and Vazirgiannis, M. (2019).  The core decomposition of networks: theory, algorithms and applications.  The VLDB Journal, 29(1):61–92.
  * Matula and Beck, (1983) Matula, D. W. and Beck, L. L. (1983).  Smallest-last ordering and clustering and graph coloring algorithms.  Journal of the Association for Computing Machinery (JACM), 30(3):417–427.
  * McCain, (1986) McCain, K. W. (1986).  The paper trails of scholarship: Mapping the literature of genetics.  The Library Quarterly, 56:258–271.
  * Mullins, (1985) Mullins, N. C. (1985).  Invisible colleges as science elites.  Scientometrics, 7:357–368.
  * Newman, (2006) Newman, M. E. J. (2006).  Modularity and community structure in networks.  Proceedings of the National Academy of Sciences, 103(23):8577–8582.
  * Newman and Girvan, (2004) Newman, M. E. J. and Girvan, M. (2004).  Finding and evaluating community structure in networks.  Physical Review E, 69(2).
  * Pan and Johnstone, (1983) Pan, B.-T. and Johnstone, R. M. (1983).  Fate of the transferrin receptor during maturation of sheep reticulocytes in vitro: Selective externalization of the receptor.  Cell, 33(3):967–978.
  * Park et al., (2021) Park, M., Wedell, E., Korobskiy, D., Warnow, T., and Chacko, G. (2021).  Community Finding and Clustering Project.  Github repository, University of Illinois Urbana-Champaign.  https://github.com/chackoge/ERNIE_Plus/tree/master/Illinois/clustering.
  * Pittel et al., (1996) Pittel, B., Spencer, J., and Worlmald, N. (1996).  Sudden emergence of a giant k-core in a random graph.  J. Combinatorial Theory Series B, 67:111–151.
  * Price and Beaver, (1966) Price, D. d. S. and Beaver, D. D. (1966).  Collaboration in an invisible college.  American Psychologist, 21(11):1011–1018.
  * Raposo et al., (2021) Raposo, G., Niel, G., and Stahl, P. D. (2021).  Extracellular vesicles and homeostasis—an emerging field in bioscience research.  FASEB BioAdvances, 3(6):456–458.
  * Raposo et al., (1996) Raposo, G., Nijman, H. W., Stoorvogel, W., Liejendekker, R., Harding, C. V., Melief, C. J., and Geuze, H. J. (1996).  B lymphocytes secrete antigen-presenting vesicles.  Journal of Experimental Medicine, 183(3):1161–1172.
  * Ratajczak et al., (2006) Ratajczak, J., Miekus, K., Kucia, M., Zhang, J., Reca, R., Dvorak, P., and Ratajczak, M. Z. (2006).  Embryonic stem cell-derived microvesicles reprogram hematopoietic progenitors: evidence for horizontal transfer of mRNA and protein delivery.  Leukemia, 20(5):847–856.
  * Rossetti, (2020) Rossetti, G. (2020).  ANGEL: efficient, and effective, node-centric community discovery in static and dynamic networks.  Network Science, 5(1).
  * Schnatz et al., (2021) Schnatz, A., Müller, C., Brahmer, A., and Krämer-Albers, E.-M. (2021).  Extracellular vesicles in neural cell interaction and CNS homeostasis.  FASEB Bio Advances, 3(8):577–592.
  * Sciabolazza et al., (2017) Sciabolazza, V. L., Vacca, R., Okraku, T. K., and McCarty, C. (2017).  Detecting and analyzing research communities in longitudinal scientific networks.  PLOS ONE, 12(8):e0182516.
  * Seidman, (1983) Seidman, S. B. (1983).  Network structure and minimum degree.  Social Networks, 5(3):269–287.
  * Staudt et al., (2016) Staudt, C. L., Sazonovs, A., and Meyerhenke, H. (2016).  Networkit: A tool suite for large-scale complex network analysis.  Network Science, 4(4):508–530.
  * Šubelj et al., (2016) Šubelj, L., van Eck, N. J., and Waltman, L. (2016).  Clustering scientific publications based on citation relations: A systematic comparison of different methods.  PLOS ONE, 11(4):e0154404.
  * Traag, (2021) Traag, V. (2021).  Network analysis, github page for the Leiden algorithm.  https://github.com/CWTSLeiden/networkanalysis, last accessed October 18, 2021.
  * Traag et al., (2019) Traag, V. A., Waltman, L., and van Eck, N. J. (2019).  From Louvain to Leiden: guaranteeing well-connected communities.  Scientific Reports, 9(1).
  * Valadi et al., (2007) Valadi, H., Ekström, K., Bossios, A., Sjöstrand, M., Lee, J. J., and Lötvall, J. O. (2007).  Exosome-mediated transfer of mRNAs and microRNAs is a novel mechanism of genetic exchange between cells.  Nature Cell Biology, 9(6):654–659.
  * Van Dongen, (2008) Van Dongen, S. (2008).  Graph clustering via a discrete uncoupling process.  SIAM Journal on Matrix Analysis and Applications, 30(1):121–141.
  * van Niel et al., (2018) van Niel, G., D'Angelo, G., and Raposo, G. (2018).  Shedding light on the cell biology of extracellular vesicles.  Nature Reviews Molecular Cell Biology, 19(4):213–228.
  * Verdi et al., (2021) Verdi, V., Bécot, A., Niel, G., and Verweij, F. J. (2021).  In vivo imaging of EVs in zebrafish: New perspectives from “the waterside”.  FASEB Bio Advances.  https://doi.org/10.1096/fba.2021-00081.
  * Waltman and van Eck, (2012) Waltman, L. and van Eck, N. J. (2012).  A new methodology for constructing a publication-level classification system of science.  Journal of the American Society for Information Science and Technology, 63(12):2378–2392.
  * Ying et al., (2017) Ying, W., Riopel, M., Bandyopadhyay, G., Dong, Y., Birmingham, A., Seo, J. B., Ofrecio, J. M., Wollam, J., Hernandez-Carretero, A., Fu, W., Li, P., and Olefsky, J. M. (2017).  Adipose tissue macrophage-derived exosomal miRNAs can modulate in vivo and in vitro insulin sensitivity.  Cell, 171(2):372–384.