# Characterizing Nodes and Edges in Dynamic Attributed Networks: A Social-
based Approach

Thiago H. P. Silva, Alberto H. F. Laender, Pedro O. S. Vaz de Melo
<EMAIL_ADDRESS>Department of Computer Science
Universidade Federal de Minas Gerais31270-901 - Belo Horizonte - MG
Brazil

###### Abstract.

How to characterize nodes and edges in dynamic attributed networks based on
social aspects? We address this problem by exploring the strength of the ties
between actors and their associated attributes over time, thus capturing the
social roles of the actors and the meaning of their dynamic interactions in
different social network scenarios. For this, we apply social concepts to
promote a better understanding of the underlying complexity that involves
actors and their social motivations. More specifically, we explore the notion
of social capital given by the strategic positioning of a particular actor in
a social structure by means of the concepts of brokerage, the ability of
creating bridges with diversified patterns, and closure, the ability of
aggregating nodes with similar patterns. As a result, we unveil the
differences of social interactions in distinct academic coauthorship networks
and questions & answers communities. We also statistically validate our social
definitions considering the importance of the nodes and edges in a social
structure by means of network properties.

Social Networks, Node Classification, Edge Classification, Dynamic Attributed
Networks

##  1\. Introduction

The large amount of data available today from Internet services and
applications has allowed us to explore how entities relate to each other. As
such, we can map entities and their links as social networks in order to
provide new kinds of analysis, both structural and social (Easley and
Kleinberg, 2010), for instance, to characterize entities behaving like hubs
(Newman, 2004) or acting as bridges by connecting different parts of a network
(Granovetter, 1973). Indeed, the so-called social network analysis has
contributed to understand how highly connected complex networks work, ranging
from graph theory to property rights (Watts and Strogatz, 1998; Newman et al.,
2006; Silva, 2020). In this regard, based on how entities play structural
roles in networks, we contribute with a social-based perspective in order to
better analyze the behavior and the strength of the ties involving such
entities.

We recall that in general social networks are constructed considering the
existence of explicit relationships (e.g., social ties with relatives). In
this static structural scenario, one approach is to explore the notion of
social capital given by the position of the nodes in the social network
structure (Granovetter, 1973; Coleman, 1988; Burt, 1992). For instance,
Granovetter (Granovetter, 1973) defines the concept of weak ties as being
those important relationships that make a network more cohesive by means of
the creation of bridges between communities. As discussed by Aral (Aral,
2016), the most influential sociological theories explore bridging ties (e.g.,
connecting different parts of a network) and cohesive ones (e.g., building a
trust circle), which provide more advantage when accessing information passing
through a network.

However, as explicit relationships evolve to other kinds of interactions
(e.g., encounters, phone calls, exchanged messages, etc.), they become more
complex, thus bringing more information about these social interactions. In
this way, a more general approach is required to model these specificities by
using only edge or node attributes (Aggarwal et al., 2016; Rezaei et al.,
2017). By doing so, it is possible to promote more information about the
social motivation involving each interaction, since individuals tend to change
their attributes over time, whether in terms of location (a new job or
country), relationships with other people (childhood friends who no longer
participate in their network) or new skills acquired. This would enable us to
understand the evolution of social structures, in which the persistence of
attributes over time indicates the social value associated with each
interaction.

Additionally, several other works have investigated topological properties and
patterns of social networks in order to define the behavior of their actors
and measure the strength of their relationships (Newman, 2004; Barabási, 2009;
Huang et al., 2018; Leão et al., 2018; Levchuk et al., 2012). Exploring the
behavior and the dynamics of the actors in a social network is essential for a
better understanding of its social structure, which is usually characterized
by graphs that capture the social aspects involved (Medo et al., 2016; Silva
et al., 2015; Yang and Xie, 2016). Accordingly, Barabási (Barabási, 2009)
reinforces the importance of the network theory paradigm as fundamental for
understanding the complexity that involves actors and their relationships. For
example, Newman (Newman, 2004) measures the influence of the nodes in a
network based on their proximity and the number of shortest paths among them.

In a previous work (Silva et al., 2019, 2020), we analyzed how social aspects
impact knowledge transfer in a network. Our proposed model allows one to
represent the social dynamics of node-attribute relationships to capture the
influence generated by knowledge transfer. Here, we go a step forward and
focus on the strength of nodes and their dynamic relationships over time by
means of social capital.

More specifically, in this article, we propose to address together distinct
aspects: actors, interactions, time intervals, attributes and social concepts.
Our strategy to address theses issues consists in modeling nodes by
associating them with their attributes in order to extract persistent features
over time. Regarding its social perspective, our method is based on Burt’s
definition of social capital by considering two concepts: closure, the ability
of aggregating actors with similar patterns, and brokerage, the ability of
creating bridges with diversified patterns (Burt, 2005).

Figure 1. Visualization of a Computer Science academic coauthorship network
according to our proposed social classification. Blue edges emphasize the
closure concept (strong ties) and red ones the brokerage concept (weak ties).
Black edges correspond to those regarded as innocuous (i.e., edges that have
no important information passing through them). We have omitted multiple edges
connecting the nodes for a better visualization. Best viewed in color.

In a preliminary work (Silva et al., 2018), we presented two specific
contributions to this kind of analysis: (i) a node-attribute graph model that
captures the social tie of individuals and their associated attributes, thus
providing a dynamic attributed model that enables us to mine multiple
interactions over time; and (ii) a new method to classify nodes and their
relationships based on temporal node-attributes that considers the social role
of the nodes and the social meaning of the edges.

Here, we extend our previous work by first redefining the classes assigned to
nodes and edges in order to reflect the social concepts behind the proposed
model. For this reason, both nodes and edges are now thoroughly classified
according to the concepts of closure and brokerage. We also contribute by
applying our new social classification strategy to different types of social
network, therefore providing a detailed discussion underlying social aspects
based on additional experiments.

In order to illustrate this, Figure 1 shows a Computer Science academic
coauthorship network, including more than 79 thousand nodes and 263 thousand
edges, built on data collected from DBLP (details presented in Section 4.1).
In this network, the edges classified according to the concept of closure are
shown in blue, those classified according to the concept of brokerage are
shown in red and those that express no social meaning (i.e., that are non-
relevant) are shown in black. Note that the edges based on the brokerage and
closure concepts dominate the center of the graph, while the extremities tend
to have a greater prominence of edges regarded as non-relevant. This means
that edges strongly related to social concepts tend to be better positioned in
a social structure (i.e., linked to central nodes), which provides early
access to information passing through the network. Our approach allows to
analyze networks in terms of their structural autonomy, which occurs when
people are tightly connected to one another with extensive bridge ties beyond
them, thus achieving high levels of innovation and productivity because there
are both trust and cooperation between individuals who connect different parts
of a network (Burt, 2005).

The rest of this article is organized as follows. Firstly, Section 2 reviews
related work, whereas Section 3 introduces our proposed model and describes
the methodology adopted for evaluating it. Then, Section 4 analyzes and
discusses the results of applying our classification method to different
social network scenarios, whereas Section 5 summarizes the results of our
experimental validation. Finally, Section 6 presents our conclusions and some
considerations for future work.

##  2\. Related Work

The study of the individuals’ dynamics enables us to understand the evolution
of social networks, thus providing models to characterize their behavior
(Silva, 2020; Iacobelli and Figueiredo, 2017; Medo et al., 2016; Silva et al.,
2015; Barabási et al., 2002). For instance, Barabási et al. (Barabási et al.,
2002) capture the social tie importance by observing the topology and the
nodes’ internal behavior in coauthorship networks, whereas Sun et al. (Sun et
al., 2013) propose a model to analyze the social dynamics of science in terms
of scientific disciplines. Yet, Iacobelli and Figueiredo (Iacobelli and
Figueiredo, 2017) explore random walks on dynamic networks to better
characterize and understand their structures. In another context, Silva et al.
(Silva et al., 2015) characterize the moving properties and the behavioral
profile of how researchers move around publication venues stratified in terms
of their quality, whereas Brandão et al. (Brandão et al., 2017) address how
the social roles of researchers change over time. Also, traditional network
metrics have been employed to identify the most important nodes within a
graph, such as done by Newman (Newman, 2004) that uses centrality metrics
based on shortest paths (e.g., closeness and betweenness) for determining the
best positioned nodes in academic social networks.

Several other studies analyze social networks based on particular social
concepts such as tie strength (Brandão et al., 2017; Brandão and Moro, 2015;
Gilbert and Karahalios, 2009; Vaz de Melo et al., 2015), the friendship
paradox (Adamic and Adar, 2003; Higham, 2019) and social influence (Jiang et
al., 2017), as well as on structures such as triadic closure and social
balance (Huang et al., 2018; Giscard et al., 2017). For instance, based on the
information shared between nodes, Adamic and Adar (Adamic and Adar, 2003)
measure the strength of relationships by analyzing the similarity between
messages exchanged between individuals. Yet, Gilbert and Karahalios (Gilbert
and Karahalios, 2009) also consider temporal aspects, but modelling tie
strength as a linear combination of different dimensions such as intensity by
means of the number of words exchanged, emotional support based on positive
words, social distance in terms of the political differences, among other
aspects. Finally, Levchuk et al. (Levchuk et al., 2012) propose an approach to
learn and detect network patterns such as repetitive groups of people involved
in coordinated activities.

Regarding social perspectives, several works have explored the notion of
social capital given by the strategic positioning of a particular actor in a
social structure (Granovetter, 1973; Feng et al., 2018; Burt, 2005). Based on
the premise that actors can make a network stronger by integrating different
parts, Granovetter (Granovetter, 1973) defines the concept of weak ties as
being those important relationships that make a network more cohesive by
creating bridges between communities. Likewise, Burt (Burt, 2005) describes a
structural hole as the gap formed by individuals who have complementary
knowledge, and then defines as brokers those nodes that hold certain
positional advantages due to their good location in the social structure.
Considering such results, Feng et al. (Feng et al., 2018), for instance, used
structural holes to identify the most central and bridging group of nodes in a
network.

In another context, Brandão et al. (Brandão et al., 2017) investigate the
strength of dynamic social relationships in academic social networks based on
topological metrics, thus revealing that such relationships tend to have more
weak and random ties than strong and bridges ones. Leão et al. (Leão et al.,
2018) analyze the role of random interactions in the structure of communities,
whereas Sanz-Cruzado and Castells (Sanz-Cruzado and Castells, 2018) analyze
the role played by strong ties (links within communities) and weak ties (links
between communities), thus showing that bridges work as enhancers of the
structural diversity in social networks.

In this article, we define social classes to better characterize social
networks. In this regard, Yang et al. (Yang et al., 2014) propose a metric for
expert identification in the StackOverflow Q&A site, which is based on the
quality of its users’ contribution. Specifically, they define two profiles:
sparrows, as being highly active users on the network that contribute to the
vast majority of its content, and owls, as being the most experienced users
that provide useful answers. Furtado et al. (Furtado et al., 2013) also
characterize users’ behavior in Q&A sites, but observing a dynamic
perspective. They define ten profiles based on motivation (e.g., activity
duration) and ability (e.g., how useful a comment is) metrics, thus
characterizing users as unskilled, expert, activist and hyperactivist. In
another context, Vaz de Melo et al. (Vaz de Melo et al., 2015) propose the
RECAST (Random rElationship ClASsifier sTrategy) algorithm that identifies
random and social interactions based on network properties. Specifically, such
algorithm explores topological and temporal aspects in order to measure the
strength of the nodes’ relations, which is derived from the neighborhood
overlap and the persistence of the relationships. Doing so, it is able to
classify the edges of a network by assigning them to one of the following
social classes: friend, acquaintant, bridge and random.

Our proposed method also relies on temporal aspects and on the regularity of
the relationships over time, but differs from those discussed above by mainly
exploring social concepts. In this regard, Alhazmi and Gokhale (Alhazmi and
Gokhale, 2016) measure the structural social capital of online social networks
by defining closure and brokerage as closed and open triads, respectively.
Alternatively, in a recent work (Silva et al., 2019), we classify nodes and
edges by inspecting how knowledge is transferred across a network. For this,
we depict a closure tie when two individuals are teaching to and learning from
each other, whereas a brokerage tie characterizes a knowledge transfer between
an expert and an inexpert user. Here, instead of describing an entire network
or exploring knowledge-transfer behaviors, we aim at characterizing nodes and
edges based on the strength of the social ties with their relevant attributes.
Thus, we explore strong ties between nodes and their relevant attributes as
representing the closure effect, and weak ties underlying the potential of the
knowledge acquired by the nodes in the network as depicting the brokerage
effect.

##  3\. Social-based Perspective

In this section, we first present an overview of our method for social-based
classification of multiple interactions in dynamic attributed networks (Silva,
2020; Silva et al., 2018). Then, we present and discuss our classification
scheme entirely based on social concepts. For this, we reinforced the notion
of social capital to capture the importance of the nodes based on their
positioning in the network structure and the social meaning of the
relationships involved.

###  3.1. Modeling Dynamic Interactions

In our previous work (Silva et al., 2018, 2020), we modeled attributed
networks by a dynamic multigraph $G=\bigcup_{1}^{t}\mathcal{G}_{i}$ that
represents a temporal aggregated graph within a time interval $[1,t]$. In
short, $G$ is the union of temporally disjoint graph instances
$\mathcal{G}_{k}=(\mathcal{V}_{k},\mathcal{E}_{k})$ constructed in time steps
of size $k$ (e.g., days) (Vaz de Melo et al., 2015). Likewise, in order to
consider the dynamic temporal attributes, we defined a heterogeneous dynamic
multigraph graph $H=\bigcup_{1}^{t}\mathcal{H}_{i}$, where
$\mathcal{H}_{k}=(\mathcal{V^{\prime}}_{k},\mathcal{E^{\prime}}_{k})$. This
graph consists of two types of node: actors (e.g., researchers) and attributes
(e.g., expertise). In other words, this strategy is an abstraction that
transforms the attributes of each edge into additional nodes, allowing an
original actor node to be directly connected to these new attribute nodes. In
this context, each actor is associated with a set of attributes that can
change overtime. We also assume that all attributes are related to some
knowledge, which can be seen as a skill acquired by the actors along the time.

###  3.2. Extracting Relevant Attributes

The next step in our approach is to determine the set of relevant attributes
for each node at each time interval. We define as relevant attributes those
that are closely connected to the nodes, i.e., persistent in their histories.
The idea is to identify, for each actor, all attributes and evaluate them in
terms of the set of attributes most strongly statistically associated with the
actor nodes (i.e., according to their stability along the time).

For this, we analyze the nodes’ interaction history in order to extract
knowledge from the node-attribute relationships. We apply the concept of
persistence of an edge along the time, which captures the importance of the
relationship between two nodes in terms of their associated attributes. The
persistence metric of an edge is defined as
$pers_{t}(u,a)=\frac{1}{t}\sum_{k=1}^{t}\mathds{1}_{\mathcal{E}^{{}^{\prime}}_{k}}((u,a))$,
where the indicator function is defined as

(1) $\mathds{1}_{\mathcal{E}^{{}^{\prime}}_{k}}((u,a))=\begin{cases}1,\text{if
}(u,a)\in\mathcal{E}^{{}^{\prime}}_{k},\\\ 0,\text{otherwise.}\\\ \end{cases}$

Note that this operation is performed on each attributed graph at discrete
intervals and not on the aggregated graph. In other words, it captures the
dynamics by observing the persistence in each temporal subgraph within the
time interval $[1,t]$.

Algorithm 1 Extracting Relevant Attributes

1:$H$, $t$

2:$\Gamma_{k}(u)$, $\forall u\in\bigcup_{k=0}^{t}V_{k}$

3:for all $u\in V_{t}$ do

4: $\mathcal{A}_{temp}\leftarrow\\{\\}$

5: for all $k\in[1,t]$ do

6: $\Gamma_{k}(u)\leftarrow\\{\\}$

7:
$\mathcal{A}_{temp}\leftarrow\mathcal{A}_{temp}\cup\\{a|(u,a)\in\mathcal{E}^{{}^{\prime}}_{k}\\}$

8: $vector\leftarrow\\{\\}$

9: for all $a\in\mathcal{A}_{temp}$ do

10: $vector.add(pers_{k}(u,a))$

11: $IQR\leftarrow percentile(vector,75)-percentile(vector,25)$

12: for all $a\in\mathcal{A}_{temp}$ do

13: if $pers_{k}(u,a)>percentile(vector,75)+IQR*1.5$ then

14: $\Gamma_{k}(u)\leftarrow\Gamma_{k}(u)\cup\\{a\\}$

More precisely, Algorithm 1 details the process of extracting relevant
attributes. It receives as input the aggregated graph
$H=\\{\mathcal{H}_{1},...,\mathcal{H}_{t}\\}$ and the final time interval $t$.
In summary, the algorithm inspects, for each actor, all attributes and
evaluates them according to their persistence along the time by means of
percentiles (function percentile on lines 9 and 11), thus identifying the set
of attributes most strongly statistically associated with the actor’s nodes.
The idea is to filter such attributes that are exaggeratedly linked to a node
in a specific period in comparison to the others, i.e., identifying the
abnormal presence of certain attributes at each time point. In order to choose
the appropriate statistical method to select the most significant attributes,
we first check whether the values of the edge persistence metric follows a
normal distribution. Then, we extract the relevant attributes based on the
definition of an outlier given by the interquartile range (IQR). Another
approach is to use the modified z-score for the same purpose (Iglewicz and
Hoaglin, 1993). Since the experimental results were similar for IQR and for
the modified z-score, we chose IQR due to the possibility of applying
different percentages by means of percentiles (i.e., adapting the constraints
according to specifics problems).

As a result, this strategy builds a set comprising all attributes
statistically relevant for each node $u\in G$ at a time interval $k$ (i.e.,
for each subgraph), which are referenced as $\Gamma_{k}(u)$. Note that the
sets $(\Gamma_{1}(u),\Gamma_{2}(u),...,\Gamma_{t}(u))$ are dynamically built
according to the degree of persistence, i.e., different instants $k$ may
contain completely distinct sets of attributes.

###  3.3. The Classifier

Our classification scheme reinforces the importance of social concepts as a
relevant factor for better understanding the complexity that involves actors
and their relationships in dynamic attributed networks. In summary, we
classify nodes and edges as follows:

  * •

Node classification. This classification captures the expertise of the nodes
by means of their relevant attributes. For example, in an academic social
network, a node that has a long-lasting association with attributes like
relational model, data definition and query language is likely to have an
authority over them. Thus, this node can be classified as having a strong tie
with the Databases domain.

  * •

Edge classification. This classification assigns a tie strength to the edges
in order to represent the kind of their interactions. For example, in a social
media network like Facebook, a strong edge may indicate a social tie between
relatives, whereas a weak one may represent a social tie with a co-worker.

Based on the social structure that models the dynamic interactions along the
time, the edge classification process assesses the degree of relevance of the
attributes associated with each node by considering its past interactions (see
Algorithm 1). For this, it determines the dynamic state of a node at each time
interval as representing a strong, weak or non-relevant association with a
specific attribute (knowledge). In this context, the strong state represents
the importance of a node in terms of its expertise within a closed group,
whereas the weak one captures its potential for connecting different parts of
a network. The next step consists in mapping these dynamic states in order to
determine the social classes of the edges. We propose three social classes for
edges111In our previous work (Silva et al., 2018), we defined seven classes
for the edges (very strong, strong, strong bridge, regular bridge, weak
bridge, ordinary and sporadic), but we report that they were not very
discriminatory. Thus, here we map the classes according to Burt’s social
theory (Burt, 2005), which provided more representative results.: closure,
brokerage and innocuous. In this way, such social classes emphasize the
strength of the relationships as strong ties (closure), weak ties (brokerage)
and non-relevant (innocuous), the latter when there is no relevant information
passing through the edge.

Algorithm 2 Classifying Edges

1:$G$, $t$, $\Phi$ e $\Gamma$

2:$\Delta((u,v)),\forall(u,v)\in{\bigcup_{k=1}^{t}\mathcal{E}_{k}}$

3:for all $k\in[1,t]$ do

4: for all $(u,v)\in\mathcal{E}_{k}$ do

5: if $|\Gamma_{k}(u)|\neq 0$ then

6: if $|\Gamma_{k}(u)\cap\Phi((u,v))|\neq 0$

7: then $u_{state}\leftarrow strong$

8: else $u_{state}\leftarrow weak$

9: else $u_{state}\leftarrow$ non-relevant

10: if $|\Gamma_{k}(v)|\neq 0$ then

11: if $|\Gamma_{k}(v)\cap\Phi((u,v))|\neq 0$ then

12: $v_{state}\leftarrow strong$

13: else $v_{state}\leftarrow weak$

14: else $v_{state}\leftarrow$ non-relevant

15: if $u_{state}=strong$ or $v_{state}=strong$ then

16: $\Delta((u,v))\leftarrow closure$

17: else if $u_{state}=weak$ or $v_{state}=weak$ then

18: $\Delta((u,v))\leftarrow brokerage$

19: else $\Delta((u,v))\leftarrow innocuous$

Formally, Algorithm 2 describes our process for classifying multiple edges.
Note that we express the set of attributes of the edge formed by the nodes $u$
and $v$ at time $k$ as the function $\Phi_{k}((u,v))$. In addition to function
$\Phi$, the algorithm receives as input the multigraph $G$, the final time $t$
and the function $\Gamma$ that defines all relevant attributes for each node
at each instant $k$ (Algorithm 1). First, the algorithm determines the nodes’
dynamic states. These states are assigned independently at each iteration of
the algorithm and considering each instant $k$ in which an edge is inspected.
A node is assigned a state strong when there is a strong temporal link with
its attributes at the exact moment of the interaction (lines 4 and 5, and 9
and 10). However, if these attributes do not apply to the inspected edge, then
the state weak is assigned to it (lines 6 and 11). If there are no relevant
attributes and the node is active in more than one time interval, then the
state non-relevant is assigned to it (lines 7 and 12). Once the dynamic states
have been assigned to nodes $u$ and $v$, the class of the corresponding edge
$e$ is assigned according to them (lines 13-17). More specifically, the
brokerage class can be seen as a social tie of nodes from distinct domains
(lines 13 and 14), whereas the closure one establishes a social role by
demonstrating a high tightness between a node and its attributes (line 15 and
16). Finally, an innocuous class means that there is no knowledge being
disseminated through the inspected relationship (line 17).

For classifying the nodes, the same classes are assigned to them, in which
case we mean by closure a node that has authority on certain attributes, by
brokerage a node that has a weak association with its attributes and by
innocuous a node that has an occasional presence in the network. The function
$\Omega$ for this node classification is given by

(2) $\Omega(u)=\left\\{\begin{array}[]{ll}closure,&\text{if
}|\Gamma_{t}(u)|\neq 0\\\ brokerage,&\text{else if
}\sum_{k=1}^{t}\mathds{1}_{\mathcal{V}_{k}}(u)>1\\\
innocuous,&\text{otherwise,}\end{array}\right.$

where the indicator function is defined as

(3) $\mathds{1}_{\mathcal{V}_{k}}(u)=\begin{cases}1,\text{if
}u\in\mathcal{V}_{k},\\\ 0,\text{otherwise.}\\\ \end{cases}$

In summary, the aforementioned social classes reinforce a sociological
perspective based on their positioning in a social structure (Granovetter,
1973; Burt, 2005; Guimera et al., 2005), i.e., by applying social concepts to
better understand the strength of the node-attribute relationships. More
precisely, we rely on Burt’s definition of social capital (Burt, 2005) by
considering the concept of closure as representing the importance of a node in
terms of its expertise within a closed group, whereas the concept of brokerage
captures its potential for knowledge transfer. In other words, by a closure
edge we mean a high tightness between a node and its attributes, whereas a
brokerage edge can be seen as a social tie of nodes with distinct relevant
attributes. Likewise, when classifying a node, the closure class is assigned
to it when there is a strong tie with some knowledge under its set of relevant
attributes and the brokerage class when it represents a potential to acquire
knowledge from attributes outside its own set of relevant attributes. Indeed,
strong ties with certain attributes show an authority on them, whereas weak
ties indicates a great potential to diffuse knowledge from its domain.
Finally, the innocuous class assigned to a node or edge represents no skill
acquired by an individual or a lack of relevant information passing through a
relationship, respectively.

##  4\. Characterization of Nodes and Edges

In this section, we characterize several social contexts based on our proposed
classification method. We begin by introducing the datasets considered. Then,
we analyze the overall results of our method when classifying the social
behavior of the nodes and the social meaning of their interactions.

###  4.1. Datasets

Table 1. Statistics of the social networks considered. Network | #snapshots | #nodes | #edges
---|---|---|---
24 SIG Academic Networks |  |  |
Average | 34.5 | 4.0K | 10.9K
Median | 35.0 | 2.6K | 7.1K
Standard Deviation | 9.8 | 2.9K | 9.2K
Full Academic Network | 55 | 79.7K | 263.1K
28 Q&A Communities |  |  |
Average | 2.7M | 4.8K | 20.9K
Median | 2.7M | 3.6K | 13.8K
Standard Deviation | 1.2M | 7.0K | 23.6K
Table 2. Social classification of nodes and edges for the coauthorship networks. Networks | Nodes | Edges
---|---|---
closure | brokerage | innocuous | closure | brokerage | innocuous
24 SIGs | Average | 27.0% | 15.2% | 57.8% | 29.4% | 35.3% | 35.2%
Median | 27.1% | 14.9% | 57.2% | 30.4% | 34.8% | 32.3%
Std. Dev. | 8.5% | 2.8% | 10.8% | 7.0% | 10.4% | 14.6%
Full Network | 18.8% | 12.2% | 69.0% | 31.5% | 37.1% | 31.4%

(a) Nodes

(b) Edges

Figure 2. Node and Edge classifications for the 24 ACM SIG communities and the
full network.

We consider two specific scenarios, academic social networks and Q&A
communities, whose datasets were built in our previous work (Silva et al.,
2018, 2019). Table 1 shows general statistics of the networks. Overall, they
present distinct characteristics that allow us to contrast the effect of our
classification method on each scenario.

In summary, the academic scenario consists of 24 co-authorship networks
derived from the ACM Special Interest Groups222ACM SIGs:
http://www.acm.org/sigs, as well as the full network comprising all groups
with more than 79 thousand nodes and 263 thousand multiple edges. In each
network, we modeled authors as nodes, coauthorships in each paper as
relationships, publications’ year as time intervals and tokens taken from the
publication titles as attributes (Silva et al., 2020). Note that such networks
are well-known in the Computer Science community, which enables us to carry
out a more accurate discussion of their behavioral dynamics.

Regarding the Q&A communities, we use the database built from the Stack
Exchange network (Silva et al., 2019). This dataset consists of 173 Q&A
communities divided into six categories (Technology, Culture/Recreation,
Life/Arts, Science, Professional and Business)333Stack Exchange:
https://stackexchange.com.. Specifically, nodes as representing community
members and edges as representing answers to questions, comments to questions
and comments to answers as described by Paranjape et al. (Paranjape et al.,
2017). In addition, each time interval has been configured to last one minute,
and tokens taken from the questions and answers as attributes. The extraction
process removes stop-words and reduces inflected words to their roots.

###  4.2. Academic Coauthorship Networks

(a) Nodes

(b) Edges

Figure 3. Node and Edge classifications for the 28 Q&A communities.

The Full Network shows a substantial drop from 27.0% to 18.8% in the number of
closure nodes when compared with the average of all 24 ACM SIG communities.
Despite that, the number of innocuous nodes considerably increased from 57.8%
to 69.0%. This was expected due to the fact that more active nodes
(researchers) tend to participate in more than one community. Thus, with more
subjects covered, the likelihood of having many relevant attributes decreases.
Even so, although there are fewer closure nodes, there is still relevant
information flowing through them (i.e., high figures for closure and brokerage
edges). In fact, such figures indicate that about 30% of all nodes have acted
structurally to make the network stronger by means of cohesion (i.e., closure)
and bridges (i.e., brokerage).

Note also that there are small variations between the means and medians for
the 24 ACM SIG communities, but with a marked standard deviation. This means
that there are different social behaviors according to the specificities of
each community. Specifically, Figure 2(a) presents the distribution of the
node classes for the 24 ACM SIG communities and the Full Network that includes
all these communities. Overall, the classification shows a significant
presence of nodes of the class innocuous (average of 57.8%). Indeed, an
academic coauthorship network usually has a strong presence of new nodes
(e.g., students or sporadic collaborators). Despite that, there is also a
strong presence of nodes of the class closure with percentages above 30% for
more established communities such as CIKM, KDD, SIGIR, SIGMOD, STOC,
SIGMETRICS, ISCA, PODC, POPL and MICRO. Particularly, most members from these
communities tend to be coherent in the research topics addressed throughout
their academic trajectories. In contrast, communities such as SAC, SIGUCCS,
SIGGRAPH and SIGDOC show percentages below 18% for the class closure, which
represents some lack of synergy among their members. Particularly, SIGUCCS
(University and College Computing Services) and SIGDOC (Design of
Communication) are two communities that address very specific topics. SIGGRAPH
(Computer Graphics), although a well established scientific community, covers
here only its editions up to 2003, since after that year their proceedings
were discontinued and replaced by special issues of the ACM Transactions on
Graphics.

Generally, such percentages can be seen as evidence of the characteristics of
each community. For instance, members of the STOC (Theory of Computing)
community have a tendency to show more competence in specific topics related
to computation theory, thus the higher number of nodes of the class closure
(41.3%). On the other hand, SAC (Applied Computing) is a community mainly
focused on applied issues, thus covering a wide range of topics, which
justifies the high number of innocuous nodes (69.9%).

Regarding the edge classification, Figure 2(b) presents the distribution of
the edge classes for the 24 ACM SIG networks and the Full Network, which
comprises the 24 SIG networks altogether. As we can see, most of these edge
classes carry some kind of information and have been characterized as closure
or brokerage (on average, they sum 64.7%), thus demonstrating a strong social
tie between the researchers and their relevant topics. On the other hand,
edges without any social meaning (i.e., innocuous) tend to be less present in
these networks. Again, specific communities show a singular behavior, such as
ISSAC (Symbolic and Algebraic Computation) and SIGIR (Research and Development
in Information Retrieval) with the highest presence of closure edges. SAC,
SIGUCCS and SIGDOC also stand out for having an expressive number of innocuous
edges (more than 50%), thus reinforcing the fact their members show no
regularity with their research topics.

###  4.3. Questions & Answers Communities

As we only consider frequent users in the Q&A communities (see Section 4.1),
by definition there are no innocuous nodes in these networks (Silva et al.,
2018). With respect to the node classes, Figure 3(a) shows few variations in
the percentages of closure and brokerage nodes across the communities (average
values of 79.8% and 20.2%, respectively). More specifically, the Vegetarianism
and Buddhism communities show the highest proportions for the closure class
(87.5% and 85.3%, respectively), whereas Anime & Manga stands for 72.8%.

In contrast, we notice that the full academic coauthorship network had 18.8%
of its nodes classified as closure, 12.2% as brokerage and 69.0% as innocuous
(see Table 2). Indeed, there are few closure nodes (e.g., research leaders) in
an academic network compared with the other ones (e.g., new students).
However, in the Q&A communities, users are in general experts and enthusiasts
about specific topics, which gives them some authority (Posnett et al., 2012;
Tang et al., 2012; Liao et al., 2017; Shah et al., 2016; Vasilescu et al.,
2014).

Considering the social classification of the edges in Figure 3(b), the
proportions by category and by community have significant oscillations, thus
reinforcing a distinct behavior of our classification method on several
topics. For example, the Buddhism community (85.3% of closure nodes) has 84.7%
of closure edges, whereas the AI community (81.4% of closure nodes) has a much
smaller proportion of edges (63.8%) belonging to that same class. There are
also notorious divergences between communities in the same category such as
Ask Patents and Quantitative Finance from the Business category, Aviation and
Freelancing from the Professional category, and Literature and Parenting from
the Life/Arts category. As we only selected frequent users, it justifies the
very low presence of innocuous edges.

By comparing the Q&A distribution by community with the same figures from the
academic ones (see Table 2), we observed that the entire DBLP academic
coauthorship network had 38.5% of its edges classified as closure, 41.6% as
brokerage and 20.2% as innocuous. That is, we note that both scenarios reveal
very different proportions of assigned classes, particularly with a higher
proportion of the closure class in the Q&A scenarios, whereas in the academic
scenarios the most representative class tended to be the brokerage one.

##  5\. Evaluation of Nodes and Edges

(a) Clustering Coefficient

(b) Degree Centrality

(c) Closeness Centrality

(d) Betweenness Centrality

(e) PageRank

Figure 4. Distribution of network properties by node class. Outliers were
suppressed from graph (e) for better visualization.

Given the challenging task of analyzing social interactions in a social
network in order to better characterize the social role of its nodes and the
meaning of its edges, Newman (Newman, 2004) applies network properties to
evaluate the robustness of his proposed method. More specifically, he applied
centrality metrics to determine the best-placed nodes in a network.

As we are also dealing with non-labeled data, we evaluate our unsupervised
classification by means of the nodes and edges acting as structurally
important in a network. In others words, our methodology consists of
quantifying how well nodes and edges are positioned in a social structure. For
this, we explore network metrics as formally presented by Table 3, which their
social aspects are discussed as follows:

Table 3. Network Metrics. Metric | Formula
---|---
Degree centrality of a node $i$ | $\begin{aligned} d_{i}&=\frac{\sum_{j\in V}a_{ij}}{\operatorname*{arg\,max}\limits_{x\in V}~{}\sum_{y\in V}a_{xy}},\end{aligned}$
|  where $a_{ij}=\left\\{\begin{array}[]{ll}1,&\text{if }(i,j)\in V\\\
0,&\text{otherwise}\end{array}\right.$
Closeness centrality of a node $i$ | $\begin{aligned} cl_{i}&=\frac{|V|-1}{\sum_{j\in V}d(i,j)},\end{aligned}$
|  where $d(i,j)$ is the distance between
|  nodes $i$ and $j$
Betweenness centrality of an edge $e$ | $\begin{aligned} bc_{e}&=\sum_{s,t\in V:s\neq t}\frac{\sigma_{st}(e)}{\sigma_{st}}\end{aligned}$
|  where $\sigma_{st}(e)$ is the number of
|  shortest paths from node $s$ to node $t$
|  that pass through the edge $e$
Betweenness centrality of a node $i$ | $\begin{aligned} bc_{i}&=\sum_{s,t\in V:s\neq t}\frac{\sigma_{st}(i)}{\sigma_{st}},s\neq i,t\neq i\end{aligned}$
|  where $\sigma_{st}$ is the total number of
|  shortest paths from node $s$ to node $t$
|  and $\sigma_{st}(i)$ is the number of those
|  paths that pass through the node $i$
Clustering coefficient of a node $i$ | $\begin{aligned} cc_{i}&=\frac{e_{i}}{n_{i}(n_{i}-1)},\end{aligned}$
|  where $e_{i}$ is the number of edges
|  between neighbors of $i$ and $n_{i}$ is the
|  number of neighbors of node $i$

  * •

Degree Centrality. As shown by Srinivas and Velusamy (Srinivas and Velusamy,
2015), this metric indicates influential nodes as, for example, a node with an
immediate risk of catching a virus or getting some information. Thus, a node
with high connectivity is more likely to have early access to knowledge.

  * •

Closeness Centrality. Nodes with higher closeness are, by definition, closer
(on average) to the other nodes in the network. Then, we expect important
classes (closure and brokerage) to have high values for this metric, since
they have better access to knowledge from other nodes (e.g., making an opinion
to reach other nodes more quickly).

  * •

Betweenness Centrality. Following Newman (Newman, 2004), nodes with a high
degree of betweenness centrality are likely to be influential, since they act
as an intermediary for other nodes (e.g., in message-passing scenarios). Thus,
as nodes and edges with high betweenness centrality values play crucial roles
in the spread of knowledge in social networks (Mahyar et al., 2018), then we
expect high values for this metric for important nodes and edges assigned to
the closure and brokerage classes.

  * •

Clustering Coefficient. As this metric reveals the fraction of a node’s
neighbors that are connected to each other (i.e., how complete the
neighborhood of a node is) (Srinivas and Velusamy, 2015), we expect low
clustering coefficient values for the most important classes (closure and
brokerage), confirming the behavior of connecting different parts of a
network.

In addition, we also use the PageRank algorithm (Page et al., 1999) by
considering that more important nodes tend to make stronger endorsements due
to their connectivity and ties to other important nodes. That is, we also
expect closure and brokerage nodes to have high values for this metric.

###  5.1. Results

By means of the aforementioned social properties, we now assess the importance
of nodes and their dynamics relationships by contrasting the classes assigned
to them with the network properties444All experiments were performed with a
significance level of $\alpha=0.05$.. Considering the node classification,
Figure 4 shows the distribution of the network properties by node class. In
Figure 4(c), we can see that the lowest clustering coefficient values are for
nodes classified as closure, followed by those classified as brokerage. On the
other hand, nodes classified as innocuous tend to have worse positions in the
social structure. In this way, these results indicate that nodes classified as
innocuous are highly dependent on their neighborhood, while those classified
as closure and brokerage tend to diversify their relationships. In addition,
Figure 4(b) and 4(a) confirm that nodes classified as closure and brokerage
tend to have a better position in the social structure as, respectively,
having more connections in the network (high degree centrality) and being on
average closer to other nodes (high closeness centrality).

Considering the importance of nodes in terms of the paths that pass through
them and how much endorsement they receive, Figures 4(d) and 4(e) respectively
show that nodes classified as closure and brokerage have more information
passing through them and are seen as topologically more relevant by their
peers. Note that all cases have a clear class distinction. Formally, all
distributions are statistically different by means of the Mann-Whitney-
Wilcoxon test (among all classes) and by the Kruskal-Wallis test (between each
pair) (Hollander et al., 2013).

(a) Our method

(b) RECAST

Figure 5. Distribution of betweenness centrality values by edge class.
Outliers were suppressed for better visualization.

As for the classification of the edges, Figure 5(a) shows the distribution of
the betweenness centrality metric with respect to our classification. We
clearly note that the brokerage and closure classes have more expressive
values for this metric. Note that the distributions of closure and brokerage
distinguish less than those reported for nodes, but now the brokerage class is
slightly superior to the closure one in contrast to the classification of the
nodes (Figures 4a-e). Nonetheless, they are still statistically different
according to the Kruskal-Wallis and Mann-Whitney-Wilcoxon tests. Moreover,
even though the innocuous class accounts for 31.4% of all edges, their
centrality values are very low.

For the sake of comparison, Figure 5(b) depicts the same distribution for the
RECAST classes. As discussed in Section 2, the RECAST algorithm assigns social
classes to edges in temporal networks. For this, it explores the regularity of
the relationships and the topological overlap existing among them over time.
By comparing such regularities with random temporal graphs, it classifies
social ties as friend, bridge, acquaintant and random. In this way, we expect
the important social classes (friend and bridge) to have better network
properties than those considered less important (acquaintant and random).

Similar to our classification, the most expressive values of centrality are
those assigned to the bridge class. On the other hand, RECAST classifies many
structural edges (i.e., those with high network properties) as random, as well
as several edges with low figures as friend. In conclusion, our method brings
a new perspective and provides a more accurate analysis to characterize such
relationships.

###  5.2. Sensitivity Analysis

Since we are dealing with temporal attributed networks, the relevant
attributes and time aspects must be properly analyzed regarding the
effectiveness of our classification method. Accordingly, we address these
issues next.

Discriminatory power of the attributes. In order to measure the strength of
social interactions, Algorithm 1 ensures the function $\Gamma$ containing the
sets of all statistically relevant attributes for each node. In fact, if an
attribute is associated with a node several times, then we can infer its
importance.

However, a specific statistical treatment can be added to this process in
order to exclude attributes that, even if randomly distributed, were
erroneously considered as relevant ones. This additional statistical step
consists in making the function $\Phi$, which associates each edge $e$ with a
specific set of attributes, a random association $\Phi^{\prime}$. Then, we get
$\Gamma$ from different $\Phi^{\prime}$ instances to measure the probability
that each attribute has been erroneously classified as being relevant.
Finally, we exclude such attributes that were considered as relevant with
probability significantly higher than the level of significance $\alpha$. In
other words, we filter from our input the attributes that can interfere in the
process of identifying the relevant ones. Even removing some of the data, we
expect the proposed method to be robust enough to properly classify nodes and
edges.

As a result, both configurations (without the exclusion step and with the step
of excluding attributes that are not statistically valid when randomly
distributed) are statistically equivalent by means of the distribution of
network properties by classes.

Existence time of the nodes. This sensitivity test consists in investigating
the robustness of our approach to differentiate nodes with similar existence
times. For this, we divided the nodes into the following annual time
intervals: $[1,5)$, $[5,10)$, $[10,15)$ e $[15,\infty)$. Our method was able
to distinguish the distributions of all network metrics by classes for all
time intervals in terms of the Kruskal-Wallis test. However, for the time
interval $[1,5)$, the Mann-Whitney-Wilcoxon test did not differentiate the
distributions between the classes closure and brokerage for the metrics
betweenness centrality and clustering coefficient.

##  6\. Conclusions and Future Work

In this article, we reinforce the importance of the network theory paradigm
for understanding the complexity that involves real world actors and their
relationships (Barabási, 2009). Based on the structural autonomy that captures
when people are tightly connected to one another with extensive bridge ties
beyond them (Burt, 2005), we emphasize the concept of closure as representing
the importance of a node in terms of its expertise according their associated
attributes (strong ties), whereas the brokerage one captures its potential for
transferring its attributes (weak ties). Then, we proposed a node-attribute
graph model that captures the social tie of individuals and their associated
attributes, thus exploring the importance of the persistence of node-attribute
relationships over time.

Overall, our classification method was able to reveal the social role of the
nodes and the strength of the social meaning of their multiple interactions in
different social contexts from academic coauthorship networks and Q&A
communities. For instance, there is a contrasting social behavior when
comparing the Theory of Computing and Applied Computing networks, as well as
when we compare the Buddhism and Islam communities. In addition, based on
Newman’s experimental methodology (Newman, 2004), we statistically validated
the assigned classes according to network properties, thus agreeing with their
expected social meaning.

As future work, we aim to apply our social-based characterization approach to
the problem of community detection (Leão et al., 2018; Dao et al., 2020). We
also intend to propose a new strategy to explore its propagation behavior,
mainly focusing on knowledge transfer aspects (i.e., characterizing how the
attributes pass through the network) (Silva et al., 2020). In addition, we
plan to investigate the persistence of the nodes with respect to their
neighborhood in order to identify the most influential ones.

## Acknowledgments

This work was supported by the authors’ individual grants from CAPES and CNPq.

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