# On the Dynamics of Political Discussions on Instagram: A Network Perspective

Carlos H. G. Ferreira  Fabricio Murai  Ana P. C. Silva  Jussara M. Almeida
Martino Trevisan  Luca Vassio  Marco Mellia  Idilio Drago  Universidade
Federal de Ouro Preto, Brazil  Universidade Federal de Minas Gerais, Brazil
Politecnico di Torino, Italy  University of Turin, Italy

###### Abstract

Instagram has been increasingly used as a source of information especially
among the youth. As a result, political figures now leverage the platform to
spread opinions and political agenda. We here analyze online discussions on
Instagram, notably in political topics, from a network perspective.
Specifically, we investigate the emergence of communities of co-commenters,
that is, groups of users who often interact by commenting on the same posts
and may be driving the ongoing online discussions. In particular, we are
interested in _salient co-interactions_ , i.e., interactions of co-commenters
that occur more often than expected by chance and under independent behavior.
Unlike casual and accidental co-interactions which normally happen in large
volumes, salient co-interactions are key elements driving the online
discussions and, ultimately, the information dissemination. We base our study
on the analysis of 10 weeks of data centered around major elections in Brazil
and Italy, following both politicians and other celebrities. We extract and
characterize the communities of co-commenters in terms of topological
structure, properties of the discussions carried out by community members, and
how some community properties, notably community membership and topics, evolve
over time. We show that communities discussing political topics tend to be
more engaged in the debate by writing longer comments, using more emojis,
hashtags and negative words than in other subjects. Also, communities built
around political discussions tend to be more dynamic, although top commenters
remain active and preserve community membership over time. Moreover, we
observe a great diversity in discussed topics over time: whereas some topics
attract attention only momentarily, others, centered around more fundamental
political discussions, remain consistently active over time.

###### keywords:

Political Discussions , Community Dynamics , Information Dissemination ,
Network Backbone Extraction , Instagram

##  1 Introduction

Social media applications are a major forum for people to express their
opinions and information. By interacting with such applications, users build
complex networks that favor the dissemination of information [1]. Indeed,
social media has become an important source of information for a large
fraction of the world population [2, 3, 4]. It has been shown to play an
important role in social mobilization and political engagement [5, 6], notably
during major political events [7].

Instagram has observed a surge in popularity in recent years [8], particularly
among the youth. The use of Instagram for consuming news has doubled since
2018, and the platform is set to overtake Twitter as a news source [9]. Not a
surprise, political personalities are increasingly leveraging Instagram to
reach the population at scale. Understanding how users interact with each
other is paramount to uncover how information is disseminated in the platform
and how the online debate impacts our society [10, 11, 7, 12, 5, 13, 14].
Prior studies of user behavior on Instagram mainly focused on user engagement
based on content type [15, 16, 17, 18, 19, 20], general characteristics of
comments associated with political messages [21, 22] and the impact of the
posted content on marketing contexts [16, 23, 24]. The literature lacks an
investigation of the networks that emerge from users’ interactions, in
particular around political contents, networks that play key roles in
information dissemination.

In Instagram jargon, a _profile_ is followed by a set of _followers_. A
profile with a large number of followers is called an _influencer_.
Influencers post content, i.e., _posts_ , containing a photo or a video.
Followers or any registered user in the case of public profiles can view the
profile’s posts and comment on them, becoming _commenters_. We here refer to
users who comment on the same post as _co-commenters_ , and to the
interactions that occur among multiple users (often more than two) when they
comment on the same post as co-interactions. Co-commenters may form
communities that arise either naturally (i.e., based on common interests on
specific topics) or driven by hidden efforts (e.g., ad-campaign or coordinated
behavior). By feeding the discussions, communities may favor the spread of
specific ideas or opinions while also contributing to increase the visibility
of particular influencers. Thus, revealing how such communities emerge and
evolve over time is key to understanding information dissemination on the
system.

Studying communities of co-commenters is however challenging. First, users may
become co-commenters incidentally because of the high popularity of some posts
and/or influencers. Equally, very active commenters naturally become co-
commenters of many other users as a side effect of their great frequency of
commenting activity. All these cases are expected to happen, especially given
the frequent heavy tail nature of content and user popularity in social media
[25]. Conversely, we are interested in finding the true group behavior, driven
by users’ interests or peer influence [26, 27, 28].

Moreover, often happening in large volumes, those incidental co-interactions
may lead to the formation of networks of co-interactions with lots of
sporadic, uninteresting or weak edges. Investigating the aforementioned
communities by looking at the entire networks may be quite misleading, as a
lot of sporadic and weak edges may mask the actual group behavior. In
contrast, we want to focus on the underlying strong topological structure
composed of edges representing salient co-interactions,111We use the terms
salient co-interactions and salient edges interchangeably. that is, co-
interactions that cannot be rooted in independent users’ behavior. We here
refer to such structure as the network backbone. Uncovering the network
backbone as well as the communities that compose it and investigating how they
evolve over time are thus important steps to understand the dynamics of the
online debate, ultimately shedding light on factors driving information
dissemination on Instagram.

In this paper, we face the aforementioned challenges to investigate the
structural and temporal dynamics of communities formed around salient co-
interactions of users on Instagram. Our ultimate goal is to understand the
important properties of these communities, with a focus on political content

  * •

__

  * •
  * •

. We model co-commenters’ activity as a network where nodes represent
commenters and edge weights indicate the number of posts on which both users
commented. To filter out uninteresting edges and reveal the underlying network
backbone, we employ a reference probabilistic network model in which edges are
built based on the assumption that commenters behave independently from each
other. Our model takes into account mainly two factors: the popularity of
posts, and commenters’ engagement towards each influencer. By contrasting the
network observed in real data with our reference model, we filter out edges
whose weights are within the expected range under the assumption of
independent users’ behavior, thus uncovering the network backbone __
representing the group behavior we are interested in. Next, we extract
communities using the Louvain algorithm [29], that we characterize in terms of
topological structure, textual properties of comments and discussions carried
out, highlighting how community membership and topics of discussion evolve
over time.

We build our study on a large dataset of Instagram comments, including
approximately $1.8$ $million$ unique commenters on $36\,824$ posts by $320$
influencers in two countries (Brazil and Italy). The dataset covers two months
surrounding major elections that took place in each country. For each country,
we selected popular political figures as well as top influencers in other
categories (e.g., athletes, celebrities, musicians), aiming to identify
differences that characterize the political discussions from other (general)
discussions. We track all influencers’ posts, recording all comments (and
commenters) associated with those posts. We study each week in isolation to
construct consecutive temporal snapshots of co-commenter networks and observe
how communities evolve over time.

In sum, in this paper, we tackle three research questions (RQs), which lead to
new contributions as follows:

  * RQ1: What are the characteristics of the network backbones emerging from _salient co-interactions_ on Instagram?

By extracting the network backbones, we show that the salient edges of the co-
commenters network build better-defined communities than those found in the
original (complete) networks, highlighting the need to uncover the network
backbone before studying such communities. More specifically, the communities
have proportionally more nodes, more edges and are more dense, indicating a
more correlated behavior among commenters of the same community.

  * •
  * RQ2: What are the distinguishing properties of the communities that compose such backbones, notably communities formed around political content?

We characterize the properties of the communities and find that, in politics,
multiple communities engage with the same influencer but are typically driven
by different topics.

  * •

Communities in politics tend to be more engaged in online discussions than
non-political counterparts. Comments in politics tend to be longer, richer in
emojis, hashtags and uppercase words (indicating assertive and emotional
content), and tend to carry a more negative tone than other categories.

  * •
  * RQ3: How do community properties evolve over time?

Aiming to shed light on how information propagates on Instagram through co-
commenters’ networks, we notice a heating up in political debate and large
variations on community membership in weeks preceding elections. Both are
reduced after the election day. Yet, top commenters remain consistently active
and preserve their community memberships over successive weeks.

  * •

Moreover, we observe a great diversity in discussed topics over time for
communities in politics. Whereas some topics attract attention only
momentarily (e.g., racism), others, centered around more fundamental political
subjects (e.g., rallies, particular candidates and political ideologies),
remain consistently active.

This study extends our preliminary work [30], where we discussed the emergence
of communities around political discussions on Instagram. We extend it by
providing a much broader characterization of the communities, covering not
only basic topological and temporal properties but also textual properties of
the content posted by communities, e.g., topics, sentiment and
psycholinguistic properties. As such, we offer a deep analysis of political
discussions on Instagram, which helps to understand content propagation during
electoral periods.

The remainder of this article is organized as follows: Section 2 summarizes
related work, while Section 3 presents our methodology to extract the network
backbone and analyze co-commenter communities. Section 4 describes our
dataset, and Sections 5-7 present our main results. Finally, Section 8
discusses our findings, offers conclusions and directions for future work.

##  2 Related work

We characterize political discussions on Instagram by analyzing user
interactions from a network perspective. Three bodies of work are related to
our effort: i) studies on online discussions in social media; ii) efforts to
model interactions among groups of users (i.e., co-interactions); and iii)
methods to extract network backbones.

###  2.1 Online discussions in social media applications

Several social media applications have been largely studied as platforms for
political debate. For example, Nguyen [31] presented a literature review of
the role of Twitter on politics, notably as a platform to help politicians win
elections and foster political polarization. Indeed, many studies have already
argued for the increasing polarization in political orientation [32, 33],
whereas others have explored the benefits that politicians can have from using
Twitter to reach their supporters [34].

Gorkovenko et al. [11] studied user behavior on Twitter during live political
debates, finding that people often use the platform to share their opinions,
make provocative statements, and inform others. Badawy et al. [35], in turn,
found evidence of the use of Twitter for political manipulation. In a
different direction, Caetano et al. [36] identified four groups of politically
engaged users on Twitter during the 2016 US presidential campaign, namely
advocates for both main candidates, bots and regular users, characterizing
properties of each group.

Online discussions have also been studied in the context of other platforms.
For example, Tanase et al. [12] studied the political debate around the Brexit
on Facebook, analyzing messages that generated higher engagement from users.
In [37], the authors developed a system to detect political ads on Facebook
and used it to present evidence of misuse during the Brazilian 2018 elections.
WhatsApp has also been analyzed as an important platform for political debate
and information dissemination, notably for the spread of fake news during
political elections [5, 38].

Considering Instagram, in particular, the literature on user behavior and
interactions is reasonably recent and somewhat restricted. Some authors have
analyzed user engagement [24, 23, 19, 39] and properties of the textual
content shared by Instagram users [40, 41], but with no particular focus on
political discussions. Closer to our present effort, Zarei et al. [22]
analyzed user engagement of twelve Instagram profiles, including profiles of
politicians, searching for _impersonators_ – i.e., users who simulate others’
behavior to perform specific activities, such as spreading fake news. Muñoz et
al. [6] studied image content posted by candidates during the US 2016 primary
elections, highlighting combined factors that attract user engagement, whereas
Trevisan et al. [21] performed a quantitative study of the political debate on
Instagram, highlighting that politicians’ profiles tend to have significantly
more interactions than others.

To the best of our knowledge, we are the first to analyze political
discussions on Instagram from a network perspective. As such, we complement
those previous efforts by providing an orthogonal and broader analysis of the
dynamics of communities of co-commenters who engage in and drive political
discussions. Our present effort builds on a preliminary work [30] where we
focused on identifying the structure emerging from the co-commenter network,
offering a novel methodology for backbone extraction in this kind of network.
We here greatly extend our prior effort by offering a much more thorough
characterization of the content and temporal properties of communities
extracted from the backbones.

###  2.2 Modeling interactions among groups of users

A plethora of phenomena related to in-person and online human interactions
have been analyzed using concepts of complex networks. Many of these
interactions occur among two or more entities simultaneously – referred here
as co-interactions. Co-interactions constitute an important substructure for
some complex systems, exhibiting a slew of properties relevant to the study of
the (often global) phenomenon of interest [43, 44].

Some recent studies have empirically analyzed co-interactions through the lens
of higher-order networks, including motif (or graphlet) representations,
multilayer networks, simplices and hypergraphs [44, 45, 47]. In their most
basic form, these structures are represented by different motifs (e.g.,
triangular motifs, star, structural hubs, etc) [48, 49]. Some studies focused
on characterizing many of these networks [51, 43], while others

analyzed the relationship between motifs and some specific phenomena of
interest on a particular network [52, 53]. Focusing on revealing communities
emerging from co-interactions, which is our present goal, some approaches are
concentrated at uncovering communities that are based on particular structural
patterns, specifically, on motifs [54, 55, 56, 57].

Conversely, we here aim at uncovering communities of co-commenters who may be
driving the online discussions. These communities are not necessarily specific
structural patterns, but rather tightly connected subgraphs with respect to
the rest of the network.

Hence, we focus on the densest and most uniform flavor of co-interaction,
where all individuals interact with each other in a motif known as clique
[59]. To do so, we model such co-interactions by projecting them into a
weighted and undirected graph, similar to other works present in the
literature. For example, Giglietto et al. [60] analyzed posts on Facebook
focusing on identifying inauthentic behavior by modeling the network of link
co-sharing, formed by entities (pages, groups, and verified public profiles)
which shared the same content frequently in a short period of time.
Cruickshank et al. [62] analyzed interactions among topics on Twitter by
modeling a sequence of networks from co-occurrences of hashtags used by
Tweeter users. Aiming to reveal coordinated behavior on Twitter, Pacheco et
al. [63] proposed a set of network models that capture different patterns of
co-interactions among users. Examples of patterns include using similar
hashtags, sharing the same images or chronological use of the platform. The
authors focus on the top 1% edges as being the most representative. Other
works adopt broader definitions of interaction, e.g., users co-retweeting,
using the same hashtags or URLs, mentioning the same accounts, or joining the
same conversation when reply chains with a common root tweet at the same time
[64, 65]. Yet, they still apply a fixed weight threshold across all edges.

Thus, as part of our proposal to model co-interactions that occur among
Instagram users as they comment on the same post, we must tackle the
challenges of using the projected network, notably the presence of a
potentially large number of weak and possibly irrelevant edges. Specifically,
we adopt an approach that reveals edges in the projected network that, in
fact, unveil how the discussion takes place on Instagram. In contrast to prior
work [60, 63, 66, 64, 65], we remove those co-interactions formed by chance,
due to the frequent heavy tail nature of the content and user popularity in
social media [25]. To address this challenge, we propose a generative model to
filter such noisy edges out of the network, thus retaining only salient edges
in the network backbone. In the next section, we review prior works focused on
this task, distinguishing our method from existing alternatives.

###  2.3 Network backbone extraction

Network backbone extraction consists of removing edges of a network to retain
a clearer image of fundamental structures governing the network [67]. As
several network models and algorithms assume that edges faithfully represent
the interactions under study, backbone extraction is a necessary step to avoid
that spurious, weak and sporadic edges blur and impair the investigation [68,
70].

Some of the simplest methods of backbone extraction explore topological
metrics and global properties of the graph. They typically propose to select
the most important edges for the study [72, 64, 63, 60, 66]. Examples include
the use of K-core searches for dense subgraphs [73, 74] and the removal of
edges based on a global threshold $\tau$, either applied directly to edge
weights [76, 77, 78] or to more sophisticated metrics such as the neighborhood
overlap of a pair of nodes [79, 81]. These methods are particularly adequate
when the concept of salient edge is well-defined by the problem context, e.g.,
large edge weight [76, 78]. However, threshold-based approaches may lead to
misleading interpretations and introduce bias in the analyzes, since setting
the $\tau$ threshold appropriately depends on the context and therefore can be
quite complex [82].

Other methods are based on local probability distributions, i.e.,
distributions specific to each edge or subset of edges. For instance, Serrano
et al. [87] propose the disparity filter method, based on the assumption that
an edge is salient if two nodes are connected with a disproportionately high
weight compared to the weights connecting them to their other neighbors. In
other words, salient edges are those that have weights that deviate
significantly from the null hypothesis that the weights of all edges incident
to a given node are uniformly distributed. Edge weights are compared to the
reference model and $p$-values are used to determine how much an edge differs
from it. Noise Corrected [67] is another local backbone extraction method,
based on the assumption that the salience of an edge results from
collaboration between the nodes. Unlike the disparity filter, this method is
able to preserve peripheral-peripheral connections by estimating the
expectation and variance of edge weights using a binomial distribution. It
considers the propensity of the origin node and the destination node to emit
and receive edges. To be regarded as salient, an edge must exceed its expected
weight considering the connection strength of its nodes.

Finally, other methods to extract the network backbone make use of a reference
model describing how the network should be built under certain assumptions –
e.g., interactions occur by chance, based on independent behavior [85] or
uniform weight distribution over edges incident to a node [68]. The general
idea is to keep only edges that deviate enough (in a probabilistic sense) from
these assumptions. For example, under the assumption of independent behavior,
the authors of [86] propose to filter out edges whose weights are below the
$95^{th}$ percentile of the edge weight distribution defined by the reference
model.

We here employ a generative model to extract the backbones from co-commenters
networks. This method was originally proposed in a preliminary version of this
work [81]. In contrast to the aforementioned methods, our model considers the
fundamental elements and structure of the target domain (influencers,
commenters and posts). Specifically, it takes into account post popularity and
user activity level as factors to model independent user behavior on a per-
edge basis, keeping only edges that deviate significantly from it. As such,
our method relies on a fine-grained local reference model to keep only salient
edges, thus revealing the network backbone.

##  3 Methodology

In this section we formally define the network of co-commenters on Instagram
and describe the probabilistic network model used as reference to uncover
salient interactions. We then describe how we extract communities from the
network backbone and present the techniques employed to characterize these
communities.

###  3.1 Network of co-commenters

We model the dynamics of interactions among users who comment on the same
Instagram post as a sequence of snapshots of fixed time window $w$, where each
snapshot aggregates posts of a selected set of influencers and their
associated comments. We here consider $w$ equal to one week as a reasonable
period to cover discussions around posts.

Given a time window $w$, we take the corresponding set of posts $P_{w}$, whose
creation times fall within $w$, to create a weighted and undirected graph
$G_{w}=(V_{w},E_{w})$. Vertices in set $V_{w}$ correspond to users who
commented in at least two posts in $P_{w}$. We choose to disregard commenters
whose activities were concentrated on a single post, and thus reflect sporadic
behavior.222Note that, by doing so, commenters who commented multiple times on
a single post, but did not comment on other posts, are removed. On Instagram,
commenters can also reply directly to another user’s comment. In our problem,
we are interested in finding users with similar behavior or interested in a
similar topic or influencer. As such, we build our network uniquely based on
the appearance of commenters in a post’s comments and neglect whether they are
answering to previous comments. This is also supported by our observation
that, in many cases, commenters engage in discussion on specific topics
without using the _reply to comment_ feature. Let $P_{w}(c)\subseteq P_{w}$ be
the set of posts on which user $c$ commented. An edge $e_{cd}=(c,d)$ is added
to set $E_{w}$ if $P_{w}(c)\cap P_{w}(d)\neq\emptyset$, i.e., commenters $c$
and $d$ commented at least once on the same post. Thus, edges link co-
commenters. The weight $\gamma({cd})$ of edge $e_{cd}$ is defined as the
number of posts on which $c$ and $d$ commented together, i.e.,
$\gamma({cd})=|P_{w}(c)\cap P_{w}(d)|\in\\{1,2,\ldots,|P_{w}|\\}$. Aiming at
characterizing similarities and differences in discussions across different
themes (political or not) and countries (Brazil and Italy), we build separate
networks $\mathcal{G}=\\{G_{1},G_{2}...G_{n}\\}$, where $n$ is the total
number of time windows $w$, for each scenario.

By definition, each post $p$ in $P_{w}$ generates a clique (i.e., a complete
subgraph) in the graph. Thus, the final network $G_{w}$ is the superposition
of all the cliques generated by the posts in $P_{w}$. As such, $G_{w}$ results
in a complex network with a large number of vertices and edges, many of which
may be the result of independent behavior of different commenters, i.e., not a
reflection of actual discussions. For example, a very popular post leads to a
large clique in the graph. Yet, many co-interactions captured by this clique
are likely a side effect of the popularity of the post, or of the influencer
who created it. Similarly, a user who is very active will likely co-occur as a
commenter with many others. That is, such co-interactions are to some extent
expected given users’ activity and post popularity. Thus, to analyze
interactions among co-commenters, we filter out such expected edges and focus
on those whose frequencies of occurrence are large enough to allow us reject,
with some confidence, the assumption of independent behavior. That is, we
focus on salient edges that most probably reflect real online discussions,
forming the underlying fundamental network backbone.

(a)

(b)

(c)

Figure 1: Illustration of the backbone extraction process in a simplistic
graph. The isolated vertices are removed from the final $B_{w}$ used in our
analysis.

###  3.2 Network backbone extraction

A fundamental question that arises when studying complex networks is how to
quantify the statistical significance of an observed network property [67,
70]. To that end, reference models are often used to determine whether
networks display certain features to a greater extent than expected under a
null hypothesis (e.g., independent behavior) [26, 27, 28]. A reference (or
null) model matches some of the features of a graph and satisfies a collection
of constraints, but is otherwise taken to be an unbiased random structure. It
is used as a baseline to verify whether the object in question displays some
non-trivial features (i.e., features that would not be observed as a
consequence of the constraints assumed). An appropriate reference model
behaves according to a reasonable null hypothesis for the behavior of the
system under investigation. One strategy to build a reference model is by
employing generative growing networks [88, 70].

We here employ a reference generative model $\widehat{G}_{w}$ for each network
$G_{w}$ that is based on the hypothesis that commenters during $w$ behave
independently from each other [30]. That is, edge weights in $\widehat{G}_{w}$
are defined under a generative process in which commenters act independently
from each other, although their interactions with influencers’ posts (i.e.,
which post each user comments on) are not identically distributed. We can then
observe which edges of the real network $G_{w}$ do not behave in accordance
with the reference model $\widehat{G}_{w}$ – i.e., reflect interactions that
significantly deviate from an independent behavior. Such edges will compose
the network backbone. Intuitively, we want to highlight co-interactions that
occurred more often than what would be expected if commenters behaved
independently.

Our null model takes as input the popularity of each post (number of unique
commenters) and the engagement of commenters towards each influencer (number
of posts by the influencer each commenter writes on). Using these statistics,
comments are randomly assigned to commenters while preserving: i) the set of
influencers on which each commenter writes a comment; ii) the popularity of
each post, and iii) the engagement of each commenter towards each influencer.
The model assigns commenters to each post using independent and identically
distributed (i.i.d.) draws from a distribution where the probability is
proportional to the commenter’s engagement towards the target influencer. By
doing so, we prevent the backbone from being dominated by very active
commenters or by those engaged in highly popular posts.

More specifically, let $I_{w}$ be the set of all influencers who wrote posts
in $P_{w}$. Let $\mathcal{C}_{p}\subseteq V_{w}$ be the set of unique
commenters in post $p\in P_{w}$ and $\\{\mathcal{{P}}_{w}^{i}\\}_{i\in I_{w}}$
be a partitioning of $P_{w}$ based on the influencer $i\in I_{w}$ who created
the post. We define the engagement of commenter $c\in V_{w}$ towards
influencer $i$ (measured by the total number of posts in $\mathcal{P}_{w}^{i}$
commented by $c$) as

$x_{i}(c)=\sum_{p\in\mathcal{P}_{w}^{i}}\mathds{1}\\{c\in\mathcal{C}_{p}\\},$
(1)

where $\mathds{1}\\{.\\}$ is the identity function. We then define $c$’s
relative engagement towards $i$ w.r.t. other commenters as:

$f_{i}(c)=\frac{x_{i}(c)}{\sum_{d\in
V_{w}}x_{i}(d)}=\frac{x_{i}(c)}{\sum_{p\in\mathcal{P}_{w}^{i}}|\mathcal{C}_{p}|}.$
(2)

In this way, we can describe in details the three steps of the generative
process to build our reference model $\widehat{G}_{w}$:

  1. 1.

For each post $p\in P_{w}$, we consider a random assignment of each of the
$|\mathcal{C}_{p}|$ (unique) commenters to a commenter $c\in V_{w}$ with
probability $f_{i}(c)$, where $i$ is the author of $p$. Specifically, under
the assumption of independent behavior, we consider each such assignment as a
Bernoulli random variable with parameter $f_{i}(c)$. The probability that
commenter $c$ is not assigned to $p$ is thus a Binomial random variable, with
0 successes in $|C_{p}|$ experiments. Conversely, under the assumption of
independent behavior, the probability that $c$ has commented (at least once)
on a post $p\in\mathcal{P}_{i}$ is
$r_{p}(c)=1-(1-f_{i}(c))^{|\mathcal{C}_{p}|}$.

  2. 2.

For each pair of commenters $c$ and $d$, we denote by $r_{p}(c,d)$ the
probability that both get assigned to post $p$ and by $r_{p}(d|c)$ the
probability that $d$ gets assigned to $p$ given that $c$ is assigned to $p$.
The conditional probability $r_{p}(d|c)$ is necessary because, strictly
speaking, although we are drawing commenters independently, when $c$ is drawn,
it decreases the number of chances $d$ has for being drawn (since
$|\mathcal{C}_{p}|$ is fixed). Hence, $r_{p}(c,d)=r_{p}(c)\times r_{p}(d|c).$
We approximate $r_{p}(c,d)\approx r_{p}(c)\times r_{p}(d)$, for each $p\in P$.
Intuitively, this approximation works well when $|\mathcal{C}_{p}|$ is large
(as in the case of most influencers’ posts), because drawing $c$ decreases by
only one the number of draws that can be used to draw $d$. Then, for each post
$p\in P_{w}$, our model defines a distribution over the set of vertices
corresponding to $\mathcal{C}_{p}$, where the value of the random variable
$\widehat{\Gamma}_{p}{(c,d)}\in\\{0,1\\}$ indicates the existence of an edge
between commenters $c$ and $d$, and is given by a Bernoulli trial with
parameter $r_{p}(c,d)$, i.e.
$\widehat{\Gamma}_{p}{(c,d)}\sim\textrm{Bernoulli}(r_{p}(c,d))$.

  3. 3.

The reference model $\widehat{G}_{w}=(\widehat{V}_{w},\widehat{E}_{w})$ is
composed by the superposition of all the edges created for all $p\in P_{w}$.
Hence, an edge $\widehat{e}_{cd}\in\widehat{E}_{w}$ will have a weight
distribution described by a random variable
$\widehat{\Gamma}{(c,d)}=\sum_{p\in P_{w}}\widehat{\Gamma}_{p}{(c,d)}$.
Therefore, it will be a sum of Bernoulli random variables with distinct
probabilities [90], which follows a Poisson Binomial distribution with
parameters $r_{1}(c,d),r_{2}(c,d),\ldots,$ $r_{|P_{w}|}(c,d)$.

We can then compare the reference model $\widehat{G}_{w}$ with the observed
network ${G}_{w}$ to extract the backbone $B_{w}$ of the latter. We do so by
keeping in $B_{w}$ only edges of ${G}_{w}$ whose weights have values exceeding
the ones expected in $\widehat{G}_{w}$ by a large margin. Specifically, for
each edge $\widehat{e}_{cd}$ we compute the $(1-\alpha)^{th}$ percentile,
denoted by $\widehat{\gamma}_{1-\alpha}(c,d)$, of the distribution of edge
weight $\widehat{\Gamma}(c,d)$, and compare it with the observed edge weight
${\gamma}{(c,d)}$. We keep edge $e_{cd}$ if
${\gamma}{(c,d)}>\widehat{\gamma}_{1-\alpha}{(c,d)}$. Intuitively, we keep
only edges between co-commenters who interacted much more often than expected
under the assumption of independent behavior. That is, edges for which the
chance of such frequency of interactions being observed under the independence
assumption is below $\alpha$. We here set $\alpha$ = 5%, as done in prior
studies [87, 92]. Note that, after filtering out edges, isolated vertices are
also removed. At the end, we extract from the network $G_{w}$ its backbone
$B_{w}=(V^{b}_{w},E^{b}_{w})$ where $V^{b}_{w}\subseteq V_{w}$ and
$E^{b}_{w}\subseteq E_{w}$.

Note that the $(1-\alpha)^{\textrm{th}}$ percentile is computed separately for
each edge $e_{cd}\in E_{w}$ from random variable $\widehat{\Gamma}(c,d)$. For
such a Poisson binomial distribution, there is a closed form for computing a
given percentile [93], which, however, is expensive to compute. Instead, we
here use the Refined Normal Approximation (RNA) [93], a method that proved
very good performance with low computational complexity.

###  3.3 Backbone extraction exemplified

We illustrate how the backbone is extracted from a given input network $G_{w}$
by means of the toy example shown in Figure 1. Figure 1(a) shows a total of
five influencers, each with a different number of posts ($P1$, $P2$, etc), and
each post with associated commenters ($A$, $B$, etc). Posts have different
popularity, and commenters have different activity levels and engagement
towards each influencer. The projected graph $G_{w}$ is depicted in Figure
1(b), whereas the extracted backbone $B_{w}$ is shown in Figure 1(c). In both
networks, line thickness is proportional to the edge weight.

The question that arises is: why did we extract only the edges shown in Figure
1(c) to compose the network backbone? Recall that our model selects as salient
edges those that have weights large enough so that we can reject the
assumption of independent user behavior. Thus, for each edge in $G_{w}$, we
ask ourselves: is there enough evidence to reject the assumption of
independent behavior? If so, the edge is kept; otherwise, it is removed.

Let’s illustrate our decisions regarding four groups of edges, focusing first
on edges incident to commenters $A$, $B$, $C$. Note that all three commenters
commented on posts only by influencers $1$ and $5$ and they commented on all
posts by both influencers. These commenters are thus quite active, and the
popularity of these posts is actually high, considering the population of
users who commented on them. As such, it is possible that $A$, $B$ and $C$ are
driven by their individual interests on these two influencers, and, as such,
most probably would comment in most (if not all) posts by them. Thus, based on
the observed data, we cannot reject the assumption of independent user
behavior when considering co-interactions among $A$, $B$ and $C$ and the
corresponding edges are not kept as part of the network backbone in Figure
1(c). For example, the edge $e_{AB}$ has weight ${\gamma}{(A,B)}=9$ which is
below or equal to the $95^{th}$ percentile of the corresponding edge weight
distribution $\widehat{\gamma}_{0.95}{(A,B)}=9$. The same reasoning applies to
commenter $X$, who only commented on posts by influencer $1$. Thus, the co-
interactions of $X$ with $A$, $B$ and $C$ are not considered salient and the
corresponding edges are not kept.

Let’s consider now the edges incident to commenters $J$, $K$ and $L$. These
users co-comment with low frequency in posts by influencers $2$ ($P2$ and
$P3$), $3$ ($P3$) and $4$ ($P5$). These posts are the most popular posts by
such influencers, receiving comments from several other users as well. It is
therefore expected that commenters active on these posts will have several co-
commenters, as we can observe in Figure 1(b). However, when it comes to $J$,
$K$ and $L$, the weights of these edges are small, as the co-interactions are
somewhat sporadic. Moreover, note that the posts on which these users
commented are among the most popular ones by the corresponding influencers,
attracting most of their commenters. For example, $P2$ by influencer $2$
received comments by 9 out of all 10 users who commented on her posts. Co-
interactions built around such highly popular post are not considered salient
as one cannot tell whether commenters are truly interacting with each other or
simply reacting independently to a quite attractive content. From an
operational perspective, recall that, when building the reference model
$\widehat{G}_{w}$ we do need to assign commenters to comments associated with
each post. In the case of such very popular posts, most if not all potential
commenters are assigned, thus raising the chance of the edge being added to
$\widehat{G}_{w}$, and thus of the edge being considered expected under the
assumption of independent behavior.

We now turn our attention to the edges incident to two groups of commenters:
i) $D$, $E$, $F$ and $X$; and ii) $G$, $H$, $I$. In both cases, the commenters
co-interact on posts by influencers $2$, $3$ and $4$, and the co-interactions
occur very often on different posts by these influencers. However, unlike the
case of $A$, $B$ and $C$, discussed above, there are other users who also
commented on the same posts. Compared to these other commenters, $D$, $E$,
$F$, and $X$ (as well as $G$, $H$, $I$) clearly stand out as frequent co-
commenters. That is, taking the overall behavior of the commenters of these
posts, we find that the co-interactions among $D$, $E$, $F$, and $X$ (as well
as $G$, $H$, $I$) are more frequent than expected if these users were being
driven by independent behavior. For example, the weight of edge $e_{DE}$ is
${\gamma}{(D,E)}=12$ which is larger than the $95^{th}$ percentile of the
corresponding edge weight distribution $\widehat{\gamma}_{0.95}{(D,E)}=10$. We
consider this evidence strong enough to reject the assumption of independent
behavior. The same holds for the other aforementioned commenters. As
consequence, the corresponding edges are maintained in the backbone (see
Figure 1(c)).

Finally, we note that all isolated nodes are removed from the final network
backbone (see, for example, nodes $A$, $B$, $C$, $K$, $J$, and $L$, no longer
present in Figure 1(c)).

###  3.4 Community detection

Once extracted the backbone $B_{w}$, our next step consists of identifying
communities in $B_{w}$. Qualitatively, a community is defined as a subset of
vertices such that their connections are denser than connections to the rest
of the network. To extract communities from $B_{w}$, we adopt the widely used
Louvain algorithm [29, 94]. The goal of the Louvain algorithm is to maximize
the modularity of the communities. Given the backbone
$B_{w}=(V^{b}_{w},E^{b}_{w})$, the modularity is defined as:

$Q={\frac{1}{2M}}\sum\limits_{c,d\in
V^{b}_{w}}{\bigg{[}}\gamma({cd})-{\frac{k({c})k({d})}{2M}}{\bigg{]}}\delta(\ell({c}),\ell({d}))$

where $\gamma(c,d)$ is edge weight between vertices $c$ and $d$ ($e_{cd}\in
E^{b}_{w}$); $k(c)$ and $k(d)$ are the sums of the weights of the edges
attached to $c$ and $d$, respectively, in $B_{w}$; $M$ is the sum of all edge
weights in $B_{w}$ ; $\ell({c})$ and $\ell({d})$ are the communities assigned
to $c$ and $d$; and $\delta({\ell({c}),\ell({d})})=1$ if
$\ell({c})=\ell({d})$, $0$ otherwise.

Intuitively, the modularity captures how much densely connected the vertices
within a community are, compared to how connected they would be in a random
network with the same degree sequence. Modularity is defined in the range of
-0.5 to +1, and modularity scores of 0.5 or higher are considered strong
evidence of well-shaped communities. The Louvain method is a heuristic that
operates by finding first small communities optimizing modularity locally on
all vertices. Then, each small community is merged into one meta-vertex and
the first step is repeated. The final number of communities is the result of
an optimization procedure. We refer the reader to [29] for a detailed
description of the Louvain algorithm.

###  3.5 Community characterization

Once communities are extracted, we characterize them in terms of the textual
properties of the content shared by their members as well as their temporal
dynamics.

####  3.5.1 Content properties

We analyze the discussions carried out by each community by focusing on the
textual properties of the comments shared by its members. In particular, we
employ three complementary textual analysis approaches.

First, we perform sentiment analysis using
SentiStrength,333http://sentistrength.wlv.ac.uk/index.html a lexical
dictionary labeled by humans with multi-language support, including Portuguese
and Italian. Given a sentence, SentiStrength classifies its sentiment with a
score ranging from -4 (extremely negative) to +4 (extremely positive) [95].
SentiStrength has been widely applied to analyze the sentiment of social media
content, notably short texts (e.g., tweets), for which identifying sentiment
is usually harder [96, 97]. We noticed a high frequency of emojis in the
comments. To improve SentiStrenght’s ability to recognize them, we incorporate
its emoji dictionary with the labeled emoji dataset provided in [98]. We also
observed the presence of informal writing, slang abbreviations, and wrong work
variation could impact our conclusions. Then, we pre-process the comments
keeping only comment words with regular words in the country language. To this
end, we used Brazilian and Italian dictionaries in
Hunspell444https://github.com/hunspell/hunspell format and matched the words
found in the comment against them.

Second, we use _Term Frequency - Inverse Document Frequency_ (TF-IDF) [99] to
reveal terms that characterize each community. TF-IDF is traditionally used to
describe _documents_ in a collection with their most representative terms.
Given a particular term and a document, the TF-IDF is computed as the product
of the frequency of the term in the given document ($TF$) and the inverse of
the frequency at which the term appears in distinct documents ($IDF$). Whereas
$TF$ estimates how well the given term describes the document, $IDF$ captures
the term’s capacity to discriminate the document from others. To apply TF-IDF
in our context, we represent each community as a document consisting of all
comments of the community members. We pre-process the comments to remove
emojis, stopwords, hashtags, punctuation and mentions to other users, perform
stemming, as well as remove the overall top-1% most popular terms and rare
terms (less than 10 occurrences).555The former are words whose frequency is
extremely high and would not help to characterize the communities, while the
latter are mostly typing errors or grammar mistakes.

Each community is then represented by a vector $d$ with dimension equal to the
number of unique terms in the collection. The element $d[i]$ is the TF-IDF of
term $i$. We here use a modified version of $IDF$, called probabilistic
inverse document frequency [100], which is more appropriate when the number of
documents is small (as is our case). It is defined as
$IDF(i)=\log\frac{N-n_{i}}{n_{i}}$, where $N$ is the total number of
communities and $n_{i}$ is the number of communities using the term $i$. We
manually evaluate the terms with large TF-IDF of each community searching for
particular subjects of discussion.

Last, we delve deeper into community contents using LIWC [101], a lexicon
system that categorizes text into psycholinguistic properties. LIWC organizes
words of the target language as a hierarchy of categories and subcategories
that form the set of LIWC attributes. Examples of attributes include
linguistic properties (e.g., articles, nouns and verbs), affect words (e.g.,
anxiety, anger and sadness) and cognitive attributes (e.g., insight, certainty
and discrepancies). The hierarchy is customized for each language, with 64 and
83 attributes for Portuguese and Italian, respectively. We apply LIWC to each
comment of each community to quantify the fraction of words that falls into
each attribute. We search for statistical differences across communities based
on the average frequencies of their respective attributes. We first use
Kruskal’s non-parametric test to select only attributes for which there is a
significant difference across communities [102]. Then, we rank attributes with
significant differences to select the most discriminative ones using the Gini
Coefficient [103].

####  3.5.2 Community temporal dynamics

Finally, we analyze how communities evolve over time, in terms of their
memberships as well as main topics of discussion.

To analyze the dynamics of community membership we use two complementary
metrics: persistence and normalized mutual information. Persistence captures
the extent to which commenters remain in the backbone across consecutive time
windows. The persistence at window $w$+$1$ is given by the fraction of
commenters in $B_{w}$ who are present in $B_{w+1}$. If persistence is equal to
1, all commenters in $w$ are still present in $w$+$1$ (plus eventually
others). Yet, the membership of individual communities may have changed as
members may switch communities.

We also use the _Normalized Mutual Information_ (NMI) metric [104] to measure
changes in community membership from window $w$ to $w+1$. Given two sets of
partitions $X$ and $Y$ defining community assignments for vertices, the mutual
information of $X$ and $Y$ represents the informational overlap between $X$
and $Y$. Let $P(x)$ be the probability that a vertex picked at random is
assigned to community $x$ in $X$, and $P(x,y)$ the probability that a vertex
picked at random is assigned to both $x$ in $X$ and $y$ in $Y$. Let $H(X)$ be
the Shannon entropy for $X$ defined as $H(X)=-\sum_{x}P(x)\log P(x)$. The NMI
of $X$ and $Y$ is defined as:

$NMI(X,Y)=\frac{\sum_{x}\sum_{y}P(x,y)\log\frac{P(x,y)}{P(x)P(y)}}{\sqrt{H(X)H(Y)}}$
(3)

NMI ranges from 0 to 1 where 0 implies that all commenters changed their
communities and 1 implies that all commenters remained in the same community.
We compute NMI at each time window $w$+$1$ by taking the sets of communities
identified in windows $w$ and $w$+$1$, considering only members who persisted
from the backbone $B_{w}$ to the backbone $B_{w+1}$.

We also analyze how the topics of discussion of each community evolve over
time. To that end, we focus on the most representative terms used by each
community, as captured the the TF-IDF metric, to investigate to what extent
communities use the same lexicon over consecutive time windows. We start by
first generating, for each time window, the vector representation of each
identified community (as described in the previous section). Given the large
size of the vocabulary, we consider only the top-100 words with the highest
TF-IDF scores in each document, zero-ing other entries in the TF-IDF vectors.
Next, we need to match the communities found in week $w$+$1$ to the
communities found in week $w$ so as to be able to follow users commenting on
the same topics across windows. Rather than doing so by using the structural
information, we match them based on the topics or, more precisely, on the set
of terms they used in each window.

Specifically, we use the cosine similarity [100] of the TF-IDF vectors666The
similarity between communities $c_{j}$ and $c_{k}$ is defined as
$sim(c_{j},c_{k})=d_{j}\times d_{k}$, where $d_{j}$ and $d_{k}$ are the TF-IDF
vector representations of communities $c_{j}$ and $c_{k}$, respectively. Note
that $sim(c_{j},c_{k})$ ranges from $0$ (maximum dissimilarity) to $1$
(maximum similarity). to compute the pairwise similarity between all pairs of
communities in windows $w$ and $w$+$1$, matching each community $c^{w}_{j}$ in
window $w$ with the most similar one in window $w$+$1$, provided that this
similarity exceeds a given criterion of significance. The criterion we adopt
consists of comparing the similarity between two communities $c^{w}_{j}$ and
$c^{w+1}_{k}$ and the similarity between $c^{w}_{j}$ and an “average”
community in window $w$+$1$ Let $\mathbf{d}_{j}^{w}$ be the TF-IDF vector
representation of community $j$ in window $w$, we use all comments associated
with window $w$+$1$ to compute its TF-IDF vector $\mathbf{d}_{*}^{w+1}$ using
the term frequencies in the complete document (i.e., all comments) but the IDF
values previously computed considering individual communities in $w$+$1$. In
practice, the cosine similarity between the TF-IDF vectors
$\mathbf{d}_{j}^{w}$ and $\mathbf{d}_{*}^{w+1}$ gives us a significance
threshold for matching the communities, i.e., when
$\textrm{sim}(\mathbf{d}^{w}_{j},\mathbf{d}^{w+1}_{k})>\textrm{sim}(\mathbf{d}^{w}_{j},\mathbf{d}^{w+1}_{*})$,
the similarity between $c^{w}_{j}$ and $c_{k}^{w+1}$ is larger than the
similarity between $c^{w}_{j}$ and an “average community” in window $w+1$. In
case no community $c^{w+1}_{k}$ satisfies that condition, we deem that no
match was found for $c^{w}_{j}$. Instead, if we find a match, it means that we
have a significant mapping between two communities in different windows.

##  4 Dataset

  * •

It is not clear how the authors identified influencers for the Brazilian
Instagram sphere: Didn’t we say that we used Hypeauditor for influencers? For
the politicians we made it manually like for Italy. We listed all congressmen,
senators, presidents, political parties and focus on the 80 most popular among
them. How does define popular here?

We now describe the dataset used in our study, which consists of over 39
million comments produced by over 1.8 million unique commenters, participating
in discussions triggered by 320 top influencers over two countries (Brazil and
Italy).

Table 1: Dataset Overview (weekly snapshots including election dates are shown in bold in the respective country). Weekly Snapshot | Politics |  | General
---|---|---|---
Brazil | Italy |  | Brazil | Italy
# Posts | # Commenters | # Posts | # Commenters |  | # Posts | # Commenters | # Posts | # Commenters
1 | 1 487 | 37 406 | 779 | 17 427 |  | 746 | 172 454 | 733 | 54 407
2 | 1 648 | 67 799 | 739 | 20 873 |  | 778 | 180 711 | 703 | 49 290
3 | 1 798 | 103 506 | 742 | 20 876 |  | 719 | 164 040 | 594 | 52 052
4 | 1 951 | 94 327 | 907 | 21 402 |  | 854 | 186 333 | 649 | 54 677
5 | 2 307 | 145 618 | 1 080 | 22 029 |  | 680 | 125 414 | 683 | 52 318
6 | 958 | 184 993 | 1 240 | 22 890 |  | 771 | 158 522 | 720 | 69 066
7 | 1 195 | 123 797 | 1 316 | 26 600 |  | 723 | 131 563 | 657 | 61 168
8 | 1 400 | 145 499 | 701 | 31 308 |  | 798 | 152 705 | 635 | 66 337
9 | 799 | 191 282 | 762 | 17 171 |  | 733 | 146 128 | 540 | 31 520
10 | 606 | 50 546 | 656 | 19 926 |  | 763 | 159 628 | 507 | 33 781

###  4.1 Dataset crawling

We collected data from Instagram profiles in Brazil and Italy. Our collection
targets electoral periods to capture the political debate taking place on the
social network. For Brazil, we focus on Instagram posts submitted during the
national general elections of October $7^{th}$ (first round) and October
$28^{th}$ (second round), 2018. Our dataset covers 10 weeks (from September
$2^{nd}$ until November $10^{th}$, 2018) which includes weeks before and after
the election dates. Similarly, for Italy we observed the European elections
held on May $26^{th}$, 2019, collecting data published from April $7^{th}$ to
June $15^{th}$ (also 10 weeks). We monitor posts shared by selected profiles
(see below), gathering all comments associated with those posts.

We use a custom web crawler to scrape data from Instagram that relies on the
Instaloader library777https://instaloader.github.io. We performed the crawling
in September 2019. Given a profile $i$, the crawler looks for posts $i$
created during the predefined period. For each post, the crawler downloads all
comments associated with it. As the interest in posts on Instagram tends to
decrease sharply with time [21], we expect that our dataset includes almost
all comments associated with posts created during the period of analysis. We
focus only on _public_ Instagram profiles and posts, collecting all visible
comments they received. We performed the crawling respecting Instagram rate
policies to avoid overloading the service. We did not collect any sensitive
information of commenters, such as display name, photos, or any other
metadata, even if public.

For each country, we monitor two groups of influencers:

  * •

_Politics_ : the most popular Brazilian and Italian politicians and official
political profiles. We manually enumerated political leaders (e.g.,
congressmen, senators, governors, ministers, president) of all political
parties and looked for their profiles on Instagram. We have kept only those
having a large number of followers (larger than 10 000 followers) and excluded
those with minimal activity. To perform our analysis we kept the top-80
profiles, ranked by number of followers. In total, the Brazilian politics
profiles created 14 149 posts and received more than 8 million comments by 575
612 unique commenters during the monitored period. Similarly, the Italian
profiles created 8 922 posts, which received more than 1.9 million comments by
94 158 distinct commenters.

  * •

_General_ : non-political influencers used as a control group. We rely on the
HypeAuditor888https://hypeauditor.com/ rank to obtain the list of most popular
profiles for the Sport, Music, Show, and Cooking categories in each country.
Similarly to the Politics group, we pick $80$ profiles for each country. The
Brazilian general profiles created 7 565 posts and received 15 million
comments by 295 753 distinct commenters during the monitored period.
Similarly, the Italian general profiles created 6 421 posts and received 14
million comments carried out by 897 421 commenters.

###  4.2 Data pre-processing

We consider only commenters who commented on more than one post when building
the network for a given period $w$. This step removes 70–85% of the
commenters. We observe that 95% of removed commenters commented less than
three times when considering the complete dataset. Results presented in the
following refer to the dataset after removing these occasional commenters.

To build the network of co-commenters, we aggregate posts by considering 7-day
intervals, always starting on Monday and ending on Sunday. We call each of
such snapshot a _week_ for simplicity. We separate our data by country (Brazil
and Italy) and category of influencers (general and politics). 999 We then use
comments observed on posts created in the given internal to build the co-
commenter network.

Notice that the periods covered by our data in Brazil and Italy are not
coincident – each case covers $10$ weeks in total around the respective
election days. In sum, our data pre-processing generates $40$ __ networks, one
for each of the $10$ weekly-snapshots of the 2 countries, for 2 distinct
categories of influencers.

###  4.3 Dataset overview

Table 1 presents an overview of our dataset, showing the numbers of posts and
distinct commenters per week. Election weeks are shown in bold. In Brazil,
elections were on Sunday of the $5^{th}$ and $8^{th}$ weeks ($1^{st}$ and
$2^{nd}$ rounds, respectively), whereas the election in Italy took place on
Sunday of the $7^{th}$ week. Focusing first on politics, we observe that the
number of posts tends to steadily increase in the weeks preceding elections,
reach a (local) maximum on the week(s) of the election, and drop sharply in
the following. Interestingly, the largest number of commenters appears on the
week immediately after the elections. Manual inspection reveals this is due to
celebrations by candidates and supporters. Regarding the general category, we
observe that the number of posts and commenters is rather stable, with a
slight decrease in the last two weeks for Italy due to the approaching of
summer holidays.

(a) Brazil.

(b) Italy.

Figure 2: Distributions of number of comments per post (notice the log scale
in $y$-axis).

We complement the overview with Figure 2, which shows the distributions of the
number of comments per post during each week. We use boxplots to ease
visualization. The black stroke represents the median. Boxes span from the 1st
to the 3rd quartiles, whiskers mark the 5th and the 95th percentiles. For
politics, the median is a few tens of comments per post, while general posts
receive 10 times as much (notice the log $y$-axes). Recall that the number of
distinct commenters is similar on both cases (see Table 1), thus commenters
are more active in the general profiles. Yet, posts of the main political
leaders attract thousands of comments, similar to famous singers or athletes
(holding for both countries). Considering time evolution, the number of
comments on politics increases by an order of magnitude close to elections,
with a sharper increase in Brazil.

##  5 Structural analysis

We describe the network structure emerging from our data. We first illustrate
characteristics of the original and network backbones. Then, we characterize
the communities and highlight insights emerging from the co-commenters
backbones.

###  5.1 The network backbones

We first show an example of network backbone, using the 1 week of the
Brazilian Politics scenario as case study.

(a) Probability distribution of edge weights $\gamma({cd})$ in the original
graph ${G}_{P}$.

(b) Actual edge weight $\gamma({cd})$ compared with null model edge weight
$\hat{\gamma}_{95}({cd})$.

(c) Fraction of edges included in the backbone ${B}_{P}$, separately for
different values of $\gamma$.

Figure 3: Network characteristics for posts of influencers for Brazil -
Politics (Week 1).

Figure 3(a) depicts the histogram of the edge weights in the original graph
${G}_{P}$. Notice that 82% of edges have weight equal to 1, i.e., the majority
of co-commenters co-comment in a single post. Higher weights are less frequent
(notice the log scale on the $y$-axis). Yet, some co-commenters interact on
more than 20 posts. In the following, we assess whether these weights are
expected – i.e., their weights agree with the assumption of independent user
behavior.

The scatter plot in Figure 3(b) compares the observed weight in ${G}_{P}$ and
the 95 percentile of weight estimated by our reference model $\hat{G}_{P}$.
Colors represent the number of edges, and lighter colors indicate larger
quantities. Most edges have very low value for both observed and estimated
weights – notice the lightest colors for weights 1 and 2 in the bottom left
corner. We are interested in the edges in which weights exceed the 95
percentile of the expected weight – i.e., those above the main diagonal. The
fraction of edges over the diagonal is higher for larger weight values. This
indicates that co-commenters interacting on many posts deviate from the
expectation.

Figure 3(c) digs into that by showing the percentage of edges that are
included in the network backbones separately by observed edge weight. If the
null model held true, 5% of the edges would be included (those exceeding the
95 percentile) – highlighted by the red dotted line. But in ${G}_{P}$, edges
weights do not always follow the null hypothesis of independent behavior,
especially for edges with large weights.

It is also important to remark that ${G}_{P}$ edge weights are integer
numbers, and our generative model provides discrete distributions. Therefore,
the computation of percentiles is critical since the same value can refer to a
_range_ of percentiles. This causes a rounding issue that is critical for low
values. Filtering weights _greater than_ or _greater or equal to_ particular
values results in significant differences for low weights. Figure 3c
illustrates it by reporting the fraction of edges that would be included in
the backbone in the two cases. Using _greater than_ corresponds to a
conservative choice since we include only edges for which the expected weight
is strictly higher than the 95 percentile (orange curve). Notice how the
number of edges in the backbone is reduced for low weights. Conversely,
_greater or equal to_ would preserve more edges, including those whose weight
possibly corresponds to a lower percentile (blue curve). We here maintain a
_conservative_ choice and keep edges whose actual weight is strictly greater
than the 95 percentile.

Table 2: Characteristics of the original network ${G}_{P}$ and network backbone ${B}_{P}$ for Brazil - Politics (Week 1). Network | # Nodes | # Edges | # Comm | Modularity
---|---|---|---|---
Original | 37 k | 74.09 M | 6 | 0.22
Backbone | 26 k (70.7%) | 1.06 M (1.4%) | 19 | 0.59

Table 2 describes the resulting network backbone ${B}_{P}$ after filtering,
comparing it with the original graph ${G}_{P}$. We focus on week 1 here, but
results are consistent for all weeks. Our approach discards 98.6 % of the
edges – i.e., the vast majority of them is not salient. We remove 29% of
nodes, which remain isolated in ${B}_{P}$. To highlight the benefits of the
approach, we include the number of communities and the modularity in the
original and backbone graphs. The Louvain algorithm identifies only 6
communities with very low modularity in the original graph. On the backbone,
it identifies more communities, and modularity increases from $0.22$ to
$0.59$.

Table 3 summarizes the main characteristics of the network backbones obtained
on each week for Brazil, Politics. Focusing on the first four columns, notice
that we still include the majority of nodes, with percentages ranging from 68%
to 95%. Considering edges, the percentage is always low (0.6–2.6%). The fourth
column reports the fraction on edges in the backbone having weight larger than
1. Remind that, by design, a random behavior would lead to 5% of edges in the
backbone, while here we observe up to 19%, despite our conservative filtering
criteria. Results are rather stable and consistent over time.

###  5.2 Communities of commenters

We now study the communities obtained from the backbone graphs. The last two
columns of Table 3 show that we obtain from $19$ to $32$ communities,
depending on the week. Modularity values are high (always above $0.5$),
meaning that the community structure is strong.

Table 3: Breakdown of backbone and communities over different weeks for Brazil, Politics. In bold, the weeks of the elections. Week | % Nodes | % Edges |  % Edges ${\gamma}{(cd)}>1$ | # Comm | Mod.
---|---|---|---|---|---
1 | 70.69 | 1.40 | 11.43 | 19 | 0.59
2 | 93.36 | 2.11 | 12.19 | 27 | 0.64
3 | 73.81 | 1.01 | 4.75 | 20 | 0.52
4 | 93.63 | 2.23 | 15.10 | 32 | 0.69
5 | 94.30 | 2.65 | 19.36 | 17 | 0.61
6 | 91.49 | 2.36 | 19.37 | 31 | 0.66
7 | 94.05 | 1.87 | 15.45 | 31 | 0.66
8 | 95.40 | 2.13 | 15.29 | 27 | 0.64
9 | 68.01 | 0.62 | 4.06 | 24 | 0.59
10 | 71.33 | 1.11 | 7.21 | 29 | 0.61

We summarize results for the other scenarios in Table 4, reporting only
average values across the 10 weeks. First, focusing on Politics and comparing
Brazil and Italy (first two rows), we observe similar percentages of nodes in
the network backbones. For Italy a larger fraction of edges are retained,
potentially because of the smaller volume of profiles and comments (see
Section 4). For Brazil, we obtain a larger number of communities with higher
values of modularity than in Italy.

Table 4: Networks backbone and identified communities for Brazil (BR) and Italy (IT). We show average values over the 10 weeks. Scenario | % Nodes | % Edges |  % Edges ${\gamma}{(cd)}>1$ | # Comm | Mod.
---|---|---|---|---|---
BR Politics | 84.61 | 1.81 | 12.42 | 26 | 0.62
IT Politics | 87.33 | 3.39 | 21.79 | 11 | 0.44
BR General | 65.35 | 0.82 | 8.83 | 81 | 0.79
IT General | 60.03 | 2.23 | 12.57 | 48 | 0.72

Moving to the General scenarios (3 and 4 rows), we notice that fewer nodes and
edges are in the backbones compared to Politics. Interestingly, we identify
more and stronger communities. We root this phenomenon in the heterogeneity of
the General scenarios that include influencers with different focuses,
potentially attracting commenters with different interests. Manual inspection
confirms the intuition – i.e., we find some communities interested in sports,
others on music, etc. For politics, instead, we find a more tangled scenario.
Even if communities are rather strong, some of them include profiles
commenting on politicians of different parties and embracing different topics.
Next, we evaluate communities in the Politics scenario.

###  5.3 Analysis of political communities

We now focus on Politics and show how the activity of commenters spreads
across political profiles of different parties. Here we focus on the election
week for both countries to better capture the peak of the political debate on
Instagram.

We first focus on the main political leaders of the two countries and study
how the communities of co-commenters distribute their interests among their
posts. We consider six politicians in each country. Figure 4 shows how the
commenters of each community are spread among posts of each politician using a
heatmap. Columns represent politicians and rows represent communities. The
color of each cell reflects the fraction of the comments of the community
members that are published on the posts of the politician.

(a) Brazil (1st round)

(b) Italy

Figure 4: Distribution of comments among political leaders for each community
during the main election weeks.

(a) Brazil.

(b) Italy.

Figure 5: Dendogram of political influencers clustered according to commenter
communities. Influencers are colored according to their political coalition.

To gauge similarity of profiles, the top of the heatmaps report a dendrogram
that clusters politicians based on the communities of their commenters. We
define as similarity metric of politicians the Pearson correlation among the
activity of communities on their posts. In other words, we compare them by
computing the correlation between the corresponding columns of the heatmap.
Hence, two politicians that receive comments from the same communities have
high similarity.

Looking at the Brazilian case (Figure 4(a)), we notice that most communities
are interested in a single candidate - Jair Bolsonaro (jairmessiasbolsonaro),
with the large majority of comments focused on his posts. This behavior is
expected given his large number of followers and popularity. Indeed,
communities $1-9$ comment almost uniquely on Bolsonaro. Focusing on the
dendrogram on the top of the figure, Bolsonaro has the highest dissimilarity
from the others, i.e., he is the first candidate to be separated from others.
Other clusters reflect accurately the candidates’ political orientation. Left-
leaning candidates (Ciro Gomes, Fernando Hadaad and Luiz Inacio Lula999Haddad
replaced Lula, who was barred by the Brazilian Election Justice.) are close,
as well as the ones leaning towards the right-wing parties (Alvaro Dias, Cabo
Daciolo and Jair Bolsonaro).

Similar considerations hold for the Italian case (Figure 4(b)). Communities
$1-10$ focus on Matteo Salvini (matteosalviniofficial). He is the only one for
which we identify multiple and well-separated communities. The other right-
wing leaders have communities active almost exclusively on their posts, e.g.,
communities $13$ and $14$ for Silvio Berlusconi and Giorgia Meloni. Other
leaders (e.g., Matteo Renzi and Nicola Zingaretti for the Democratic Party and
Luigi Di Maio for the Five Star Movement) share a large fraction of commenters
in community $11$. This suggests these commenters are almost equally
interested in the three leaders. Indeed, looking at the dendrogram, these last
three profiles are close to each other. Matteo Salvini (leader of the most
popular party) has the maximum distance from others. Similar to the
Bolsonaro’s case, Salvini is a single leader who polarizes communities, thus
well-separated from others.

We now broaden the analysis to all politicians. We label each politician
according to his/her political coalition using available public
information.101010Differently from e.g., the US or UK, in both Brazil and
Italy the political system is fragmented into several parties that form
coalitions during and after elections [81]. For Brazil, we rely on the
Brazilian Superior Electoral
Court,111111http://divulgacandcontas.tse.jus.br/divulga/#/estados/2018/2022802018/BR/candidatos
while for Italy we use the official website of each party. Rather than
reporting the activity of each community on all politicians, we show only the
dendrograms that cluster them, following the same methodology used in Figure
4.

Figure 5 shows the results, where the party leaders/candidates shown in Figure
4 are marked in bold. Politicians of the same parties appear close, meaning
that their posts are commented by the same communities. For Brazil, the higher
splits of the dendrogram roughly create two clusters, for left and right-wing
parties. In Italy, we can identify three top clusters, reflecting the tri-
polar system. Less expected are the cases in which politicians from distant
political leanings attract the interest of the same communities and are close
in the dendrogram. For example, in Italy, we find the profile of Monica
Cirinnà (left-wing) very close to Angelo Ciocca (right-wing). Manual
inspection reveals a considerable number of disapproving comments to posts of
the first politician that are published by commenters supporting the second.
The same happens for Vladimir Luxuria, whose some supporters disapprove Marco
Bussetti’s posts (and vice-versa). The structure of the backbone graph
reflects the presence of profiles that bridge communities.

In sum, our methodology uncovers the structure of communities, which reflect
people’s engagement to politicians over the spectrum of political orientation.
Most communities are well-shaped around single profiles, but sub-communities
emerge too, possibly around particular topics, as we will check next. In some
cases, commenters cross the expected political divide, commenting on profiles
from different political orientations.

##  6 Textual properties of discussions

We now focus on how the communities differ in terms of textual, sentiment and
psychological properties of comments.

###  6.1 Political communities’ interests

We now look into how communities in politics are attracted by different posts.
Since communities differ in the number of members and in the number of
comments they post, we consider a relative _activity index_ of the community
in a post, given by the fraction of the community’s comments going to the
post. We use data from the week of the main elections in Brazil (week 5).

Figure 6a quantifies, for each post, the two most active communities. The
$x$-axis reports the index for the community with the highest activity on the
post, while the $y$-axis reports the index for the second most active
community in the post. We observe that, in all cases, the most active
community leaves less than 7% of its comments in a unique post (see the
$x$-axis). Given there are $2\,144$ posts in this snapshot, even a relative
activity of 1% could be considered highly concentrated attention, suggesting
that communities are built around specific posts. In $\approx 40$% of the
posts, the relative activity of the second most active community ($y$-axis) is
very low compared to the most active one. We quantify this in Figure 6b, which
reports the ratio between the relative activity of the first and the second
most active communities. We observe that, in the 55% of cases, the most active
community has at least 10 times higher index than the second one – notice the
x-axis log-scale. Hence, we have strong shreds of evidence that communities
are attracted by specific posts.

(a) Index of activity of the 1${}^{\textrm{st}}$ and $2^{\textrm{nd}}$ most
active communities. Each point represents a post.

(b) Ratio between the index of the 1${}^{\textrm{st}}$ and 2${}^{\textrm{nd}}$
most active community on posts.

Figure 6: Activity of communities on posts.

Figure 7 shows posts that attracted high interest from communities $3$ and
$7$, which we use as running examples along with communities $10$ and $11$.
Community $3$ comments mostly on posts related to public events Bolsonaro
promoted via Instagram (as in Figures 7a and Figures 7b), while community $7$
comments on posts where the candidate tries to show his proximity with black
people to debunk his associations with racism (Figures 7c and Figures 7d).

(a) Community 3 - Post about a rally in São Paulo.
www.instagram.com/p/BoXpvV6Hrkk

(b) Community 3 - Post about a rally in Vitória.
www.instagram.com/p/BoXMwvwn6xj

(c) Community 7 - Post discussing racism.
www.instagram.com/p/BomRItfH9p8

(d) Community 7 - Another post discussing racism.
www.instagram.com/p/Boe7fQcHfJB

Figure 7: Examples of posts by Jair Bolsonaro (jairmessiasbolsonaro) in which
two communities show high interest.

###  6.2 Properties of communities’ comments

We now take all communities found in each week and extract properties of the
comments of their members, namely: i) Average comment length (in characters);
ii) Fraction of comments that include at least one mention; iii) Average
number of hashtags per comment; iv) Fraction of comments with at least one
uppercase word; v) Average number of comments per commenter; vi) Average
number of emojis per comment; and vii) Fraction of replies among comments.
Together these metrics capture important aspects of the communities’ behavior.
For example, the comment length, the number of emojis per comment and the use
of uppercase words (commonly associated with a high tone) can describe the way
the communities interact on Instagram. Mentions, the use of hashtags and
replies are strongly associated with engagement, information spreading and
direct interaction of commenters, respectively.

We study the communities by applying Principal Component Analysis (PCA) to
vectors that represent communities using the seven previously described
metrics. PCA is a well-known method for dimensionality reduction in
multivariate analysis. It projects the data along its principal components
(PCs), i.e., axes that capture most of the variance in the data [105]. Figure
8(a) shows the representation obtained for each community using the two
principal components, where the color represents the pair country-scenario.
The 2-D representations of communities for both politics scenarios are more
tightly clustered and overlapping than for the general scenario. This behavior
suggests that, when considering the given features, communities on politics
are more homogeneous than the communities on the general scenario.

To understand which metrics best distinguish the communities in Figure 8(a),
we study the _loading scores_ for the two principal components. The loading
score quantifies the contribution of each metric to a principal component. The
largest the score (in absolute value) the more the metric contributes to the
component (positively or negatively).

(a)

(b)

Figure 8: (a) 2-D representation of communities based on seven metrics using
PCA. (b) Description of the two principal components in terms of the original
metrics; the bar represents the loading scores for the components (positive or
negative).

In Figure 8(b) bars represent the magnitude of loading scores for each metric
for the PC 1 (left) and PC 2 (right). The PC 1 (left) can be associated with
lengthy comments, high usage of uppercase, emojis, replies and hashtags, and a
low number of comments per commenter. From Figure 8(a), we see that high
values for PC 1 is more common for communities in the politics scenarios.
Conversely, most communities of the general scenario have negative $x$
coordinates, thus pointing to the opposite behavior.

A less clear picture emerges for PC 2. Large values for PC 2 are associated
with high number of replies, mentions and comments per commenter (see Figure
8(b), right plot). For the politics scenario in Figure 8(a), communities are
concentrated in the $y\in[-2,3]$ range, with those for Italy being slightly
more positive than those from Brazil. In the general scenario, however, points
are spread out along the $y$ axis.

We conclude that commenters of politics influencers exhibit a more homogeneous
behavior than commenters of other influencers. Particularly, commenters on
politics leave larger comments and use higher tone. They also often rely on
typical online social mechanisms, such as replies, mentions and emojis.

###  6.3 Sentiment analysis

Although communities grow around particular posts and influencers, their
members do comment on posts from other influencers. Here, we analyze whether
there is a difference between the sentiment expressed in comments across
influencers. As explained in Section 6, we use SentiStrength to extract the
sentiment of each comment. SentiStrength provides an integer score ranging
from -4 (strongly negative) to +4 (strongly positive). Score 0 implies a
neutral sentiment. We here consider as _negative_ , _neutral_ and _positive_
comments with scores smaller than 0, equal to 0, and greater than 0,
respectively. We notice that many comments contain misspelled words and
informal writing that we want to remove to prevent bias in our analysis. To
this end, we use Brazilian and Italian dictionaries in Hunspell format and
match the words found in the comment against them. After filtering the non-
existent words, we also filter out 11% (4%) of the total comments for Brazil
(Italy) that we discard for this analysis.

Table 5 shows fraction of positive, neutral and negative comments. We notice
that positive comments are generally more common (between 49% and 65%),
followed by neutral comments (between 25% and 33%). Negative comments are the
minority in our data, but they are more prevalent in the politics scenarios
for both countries.

Table 5: Fraction of sentiment captured in comments using SentiStrenght. Scenario | Sentiment
---|---
Negative | Neutral | Positive
BR Politics | 0.12 | 0.26 | 0.62
IT Politics | 0.18 | 0.33 | 0.49
BR General | 0.07 | 0.32 | 0.61
IT General | 0.10 | 0.25 | 0.65

(a) Brazil (week 5)

(b) Italy (week 7)

Figure 9: Contrastive sentiment score (difference between fraction of positive
and negative comments) of communities towards political leaders during the
main election week.

We now analyze how the communities’ sentiment varies towards profiles of
different politicians. More specifically, we compute the breakdown of
positive, neutral and negative comments of each community on posts of each
influencer. To summarize differences, we report in Figure 9(a) and Figure 9(b)
a _contrastive score_ calculated as the difference between the fractions of
positive and negative comments for the particular community and influencer. We
ignore cases where a community has made less than 100 comments on a given
influencer’s posts to ensure that samples are representative. These cases are
marked as white cells in the heatmaps.[CH: 6]

Table 6: Example of words with the highest TF-IDF for some communities in the politics scenario in the main election week. Scenario | Comm. | Key Words | Context
---|---|---|---
BR | 3 |  | ‘Anapolis’, ‘Orla’, ‘Righteousness’, ‘Constant’,
---
‘Natal’, ‘Paulista’, ‘Spontaneous’,
‘JB17’, ‘Gesture’, ‘Avenue’
| It refers to several places
---
where pro-Bolsonaro rallies took
place during the election campaign.
BR | 7 |  | ‘Nazi’, ‘Jew’, ‘Hitler’,
---
‘Black People’, ‘Anonymity’, ‘Bozonazi’,
‘Distrust’, ‘Jerusalem’, ‘Homosexual’
| It refers to Bolsonaro’s posts about
---
specific social groups in an attempt to show
he has no prejudice against such groups.
BR | 10 |  | ‘Manuela’, ‘Haddad, ‘Scammer’,
---
‘Lulalivre’, ‘Birthday’, ‘Guilherme’,
‘Dilma’, ‘Gratefulness’, ‘Lula’
| It refers to left-wing names,
---
such as Fernando Haddad, his
deputy Manuela, Dilma Rousseff and Lula (ex-presidents).
BR | 11 |  | ‘Ciro’, ‘Experience’, ‘Political Activism’,
---
‘Polarization’, ‘Brazil’, ‘Second Round’,
‘Turn’, ‘Prepared’, ‘Project’
| It refers to the center-left candidate
---
Ciro Gomes who arrived close to
reach the second round of the elections.
IT | 3 |  | ‘Gooders’, ‘Big ciao”, ‘Captain’,
---
‘Crime’, ‘Good night’, ‘Polls’,
‘Never Give Up’, ‘Electorate’, ‘Lampedusa’, ‘Riace’
| General Salvini’s jargon,
---
as well as places related to
the arrival of immigrants in Europe (e.g., Lampedusa).
IT | 4 |  | ‘Monetary’, ‘Elite’, ‘Unity’, ‘Budget’,
---
‘Fiscal’, ‘Colonial’, ‘Equalize’,
‘Yellow Vests’, ‘Masonic’, ‘Store’, ‘IVA’,
| Generic taxes and monetary issues.
---
IT | 10 |  | ‘Consumption’, ‘Fuel’, ‘Insurance’, ‘Traffic’,
---
‘Helpless’, ‘Vehicular’, ‘Taxes’, ‘Redundancy’,
‘Veterinary’, ‘Animal rights’, ‘Cats’, ‘Abuse’, ‘Cruelty’, ‘Breeding’
| A combination of terms related
---
to taxes, vehicles and animals’ rights.
IT | 11 |  | ‘5S’, ‘Toninelli (ex-Transport Minister)’, ‘Corruption’,
---
‘Zingaretti (PD’s leader)’, ‘Calenda (ex-PD politician)’,
‘Honesty’, ‘Election list’, ‘Coalition’, ‘Budget’, ‘Growth’
| Debate on Five Stars Movement (a government
---
party at the time) and Democratic
Party (the main opposition party at the time)

In Figure 9(a) we consider the six political leaders already used for Figure
4. We focus on the week of the first election round in Brazil (week 5).
Predominantly, communities make positive comments on the profiles in which
they are more active, i.e., their “referring candidate”. More negative
comments are seen on “opposing candidates”. For instance, communities 1 to 9,
highly active on Jair Bolsonaro’s posts, display a more positive contrastive
score on them. Analogously, communities 10 to 12, mostly formed by commenters
very active on the profiles of left-wing influencers such as Ciro Gomes
(cirogomes) and Fernando Haddad (fernandohaddadoficial), tend to write
negative comments on their opponents, such as Jair Bolsonaro. This behavior
appears on all weeks and suggests that communities in politics tend to promote
their central influencers while trying to demote others.

Considering the Italian case, we observe similar results in Figure 9(b).
Communities exhibit positive contrastive scores towards candidates in general,
but with higher scores for the referring candidate.

###  6.4 Main topics of discussion

We now turn our attention to the analysis of the main topics around
discussions. As before, we focus on politics, during the election weeks. To
summarize the overall behavior of each community, we group together all their
respective comments in one document. As explained in Section 6, the documents
build a corpus on which we then use the TF-IDF metric to identify the most
representative words of each document (i.e., community), henceforth called
_top words_.

We show in Table 6 the top-10 words (translated to English) for communities
yielding the most interesting observations. We manually inspect the comments
and related posts, providing a reference context as the last column of the
table. The manual inspection suggests that these words give a good overview of
what the communities discuss.

Matching with Figure 7, communities 3 and 7 for Brazil are associated with
rallies in different locations in the country, and with debunking Bolsonaro’s
prejudice against ethnic and racial groups. The terms highlighted by TF-IDF
reflect quite accurately the respective topics, reporting locations of rallies
and words linked to racism and Nazism. Similarly, the top words for
communities 10 and 11 are focused on the names of the candidates whose
profiles they mostly comment on. For Italy, community 3 reflects the typical
jargon used by Salvini’s supporters. Community 4 debates on taxes and monetary
issues. Community 10’s comments refer to provoking posts that mix taxes, car
costs and animals’ rights. Last, community 11 seems to debate over the left-
wing party (the main opposition party at the time) and the 5-Stars movement
(the governing party at the time).

In a nutshell, the TF-IDF is instrumental to analyze what the communities are
discussing. The analysis demonstrates that communities are well-formed around
the topics they discuss, even if they have been built solely on the network of
commenters’ interactions.

###  6.5 Psycholinguist properties

In this section, we study the psycholinguistic properties of comments, aiming
at finding similarities and differences in the way commenters of communities
communicate. We rely on the Linguistic Inquiry and Word Count (LIWC) tool to
calculate the degree at which various categories of words (called attributes
in the LIWC terminology) are used in a text (see Section 6). For example,
attribute _Home_ includes the words “Kitchen” and “Landlord, and attribute
_Family_ “Daughter”, “Dad” and “Aunt”.

For each community, we run LIWC on the comments and compute the average
frequency of the attributes. We then look for statistical differences between
communities based on the average values of the attributes. For Brazil, we
identify 62 attributes (from the 64 available in LIWC’s Portuguese dictionary)
for which differences across communities are statistically significant121212We
used the Kruskal non-parametric test to select attributes with a significant
difference between the distribution of community comments considering
$p-value=0.01$.. For Italy, we identify 77 (from 83 available in the LIWC
Italian dictionary). From those, we select the five attributes that exhibit
the largest variability across communities in terms of Gini index and use them
characterize the psycholinguistic of communities.

Figure 10 shows heatmaps for the top-five attributes found for the Brazilian
(top) and Italian (bottom) politics scenarios. The heatmap cells in a column
indicate the relative deviation of the given attribute for the given community
from the other communities. In other words, each column (attribute) is z-score
normalized – i.e., $z=(x-mean)/std$. Thus, each value gets subtracted the
average of the column, then divided by the standard deviation of the column.
The results show how communities are different in terms of the LIWC selected
attributes. For instance, for Brazil, Politics, communities 6, 10, 3 and 7
frequently use words regarding _death_ , but seldom words related to health.
Communities 2, 5 and 4 show positive scores on almost all attributes.
Community 13 focuses mostly on _health_. In Italy, community 6 is very focused
on _religion_ (commenters debated Salvini’s post that depicts a Rosary).
Communities 3, 4, 6, 7, 8 and 9 adopt attributes _we_ representing words and
verbs in the first person plural (e.g., we, our and us). This kind of word is
used used in phrases aiming at aggregating the community towards the same
goal. Community 12 and 13 exhibit some hate speech __.

In summary, LIWC is a useful tool to analyze the content of Instagram
comments, complementing the TF-IDF analysis with information on the topics
being debated. We find that communities debate on different topics and using
different lexicon. [CH: 6]

(a)

(b)

Figure 10:  Top 5 LIWC attributes and their relative difference between
communities.

##  7 Temporal analysis

In this section, we focus on the dynamics of communities during the 10 weeks
of observation. First, we analyze the community membership, studying to what
extent commenters persist in the network backbone and are found in the same
communities across weeks. Next, we characterize the dynamics of the content,
i.e., the topics that these communities are engaged in.

###  7.1 Community membership persistence

We start our analysis by studying the persistence of commenters inside the
network backbone and to what extent these commenters end up in the same
community week by week. We also want to check if the most engaged commenters
exhibit a different behavior – i.e., tend to persist more than those who are
less engaged. To this end, we perform a separate analysis selecting the top-1%
and top-5% commenters in terms of number of comments in week $w$ and $w+1$.
Then, we compute the persistence and NMI score (see Section 3.5.2),
restricting to these commenters and comparing the results with those obtained
with the full set of commenters.

(a)

(b)

(c)

(d)

Figure 11: Temporal evolution of commenters in communities. Blue: top 1%,
Orange: top 5%, Green: all commenters.

We report results in Figure 11 separately by country and for Politics and
General. Considering Politics (Figures 11a and 11b), we note that the
persistence in Brazil is moderately high, regardless the subset of commenters.
Around 50-60% of commenters remain in the backbone week after week until the
first round of elections (week 5). Since then, we observe a decrease (also due
to the drop of commenters in general) until the second round election (week
8), followed by a significant drop after. This trend shows that commenters
were very engaged in the election period, mostly in the first round when the
debate included more politicians, senators, congressmen and governors. In the
second round, fewer candidates faced – yet people were consistently engaged
before finally plumbing two weeks after elections. These results corroborate
the first intuition we observed in Table 1 – where the number of commenters
varied over time. Since persistence is similar for all subsets of commenters,
we can conclude that all commenters in the backbone are persistently engaged.
That is, the backbone members are quite stable.

Considering the membership of commenters within the same community, the NMI
shows that the top-1% and top-5% most active commenters (blue and orange
curves) are considerably more stable in their communities during the whole
time. When considering all commenters in the backbone, the NMI is
significantly lower. This is due to the birth and death of new communities,
centered around specific topics, where the debate heats up and cools down.
These dynamics attract new commenters that afterward disappear or change
community.

For Italy, Politics (Figure 11b) different considerations hold. The constant
persistence suggests a stable engagement of commenters in the backbone. We
just observe a sudden drop the week after the election, where the interest in
the online debate vanished. On the other hand, the NMI is rather low,
revealing more variability in community membership, even if we restrict our
attention to the most active commenters. Despite commenters in the backbone
tending to be the same (persistence is typically above 0.5), they mix among
different communities. Considering the low modularity of communities for this
scenario (see Table 4), we conclude that the community structure is weaker in
this case, indicating overlapping among communities that favor membership
changes. This result is also visible from the dendrogram in Figure 5, where we
observe that influencers receive comments from similar communities making the
latter also more clustered.

Moving to General (Figures 11c and 11d), we observe slightly lower persistence
than in Politics, but more stable over time. NMI instead often results higher
for General than Politics, reflecting better separation between communities,
which persist over time. More in detail, for Brazil (Figure 11c) we observe
that persistence and NMI are high and stable – especially for the most active
users. This suggests that the most engaged commenters have diverse, specific
and stable interests. Indeed, here there is no exogenous event that pushes a
temporal dynamic, like elections do for politics. Again, this result reflects
the high heterogeneity of posts and influencers in the General category.
Moving to Italy, Figure 11d shows that persistence is small and varies over
time. Here the lower popularity of Instagram in Italy than in Brazil may play
a role, coupled with the smaller number of comments (see Table 1). However,
NMI is high and stable. We conclude that although many users do not persist in
the backbone, the remaining are very loyal to their interests.

###  7.2 Topic persistence

(a)

(b)

Figure 12: Example of how communities’ comments change over time. We set weeks
5 and 7 as reference, being the election weeks in Brazil and Italy,
respectively.

We now discuss how the topics discussed by communities evolve over time. To
that end, we take as reference weeks 5 for Brazil and 7 for Italy in the
political scenario, being the weeks of elections in each country. We compute
the cosine similarity between the communities in the reference weeks
(illustrated in Table 6) and the communities extracted in all other weeks, for
each country. That is, for a given week, we identify whether there exists a
document/community that is significantly similar to those found in the
reference week, following the steps presented in Section 3.5.2.

Figures 12 show examples for both scenarios. In weeks 5 and 7 for Brazil and
Italy, respectively, the cosine similarity is 1 since the documents are
compared with themselves. Focusing on Brazil first, we observe a very distinct
behaviors among the picked-up examples. Remember that communities 3 and 7 are
focused, mainly, on Bolsonaro’s profile and comment on posts related to
rallies and racism, respectively. In both cases, we can observe that
discriminating terms for these communities are momentary and sporadic, with
some communities using terms about rallies that appear in some weeks, still
with a very similarity low. Conversely, the set of significant terms
representing community 10 and related to candidate Fernando Haddad. At last,
consider community 11, focused on Ciro Gomes. Again, we can observe that terms
used by his community in the election week were used in some communities
earlier, exhibiting high similarity. However, immediately after the first
round (week 5) when Ciro Gomes lost, the similarity drops significantly.
Indeed, Ciro Gomes was excluded from the run-off and the online debate (and
community) suddenly vanished. In Italy (Figure 12b) we observe a similar
behavior. Community 3, mostly consisting of Salvini’s supporters, use a very
specific jargon and are always present. Community 4 debates around taxes and
monetary issues, which already debated during week 3. The same considerations
hold for community 10, in which the fight between democrats and five stars
supporters heats more frequently.

In summary, people commenting in politics are more volatile than those
commenting on general topics, with debates suddenly growing and cooling down.
Some sets of terms remain “alive” throughout the observation period, while
other include communities born around short events such as rallies, which take
place on a specific date.

##  8 Discussion on main findings and conclusions

Our work contributes with a deep analysis of interactions on Instagram. Here,
we discuss the major findings of our analysis and put them in perspective of
the relevant literature in the field. Among key insights, we can mention:

  * •

We introduced a reference probabilistic network model to select salient
interactions of co-commenters on Instagram. We found that most users have at
least one interaction that deviates from the reference model, similarly to
previous work on user behavior on online social networks [26, 27, 28]. Our
model allows us to extract better quality information and thus better
understand how the political debate evolves on Instagram.

  * •

Commenters exhibiting salient interactions build strong communities, often co-
interacting on posts from different influencers. Hambrick et al. [106]
analyzed tweets about the 2012 London Summer Games, finding that communities
are born around viral posts. In politics, we reveal that multiple communities
emerge around different subsets of posts of the same influencer, and this
behavior seems to be guided by the discussed topics on Instagram as well.

  * •

Comments produced by political communities tend to be longer, richer in
emojis, hashtags and uppercase words

, indicating assertive and emotional content than communities around other
topics. Kim et al.[19] analyzed multiple categories of Influencers (outside
politics) finding that such textual features are not very discriminative
across the categories. We confirm their findings on our baseline of non-
politicians, however finding remarkable differences for Influencers on
politics.

  * •

We compared the use of hashtags and mentions across categories of influencers.
Previous works [21, 23, 24] associated these aspects to information spreading
strategies. We concluded that such strategies are even more prominent on
politics.

  * •

We show a predominance of positive sentiment, confirming findings of [40, 41].
We observe also larger percentages of negative comments on politics, a
phenomenon also studied by Kuvsen et al.[107] for dissemination of information
during the 2016 Austrian elections. However, here we also find that
communities built around a specific politician tend to leave negative comments
on profiles associates to opposite political spectra.

  * •

In weeks preceding elections, we noticed a heating up in political debate and
large variations on community membership, which is reduced after the election
day. Recurrent behaviors on Instagram had so far been evaluated only in other
context, such as cyberbullying [108, 109, 110].

  * •

We observe a large variety diversity in discussed topics over time for
communities in politics. Whereas some topics attract attention only
momentarily (e.g., racism), others, centered around more fundamental
fundamental political subjects (e.g., rallies, particular candidates and
political ideologies), remain consistently active over time. The rapid decline
of communities around specific topics has been observed on Twitter as well
[111].

Our analyses open up a number of potential avenues for further exploration.
One possibility is extending the study to other platforms, such as Facebook
and Twitter, with a similar network structure, which could reveal
distinguishing patterns. In particular, it would be interesting to compare the
dynamics of discussions around posts by the same person on different
platforms, to shed lights on the role of different social media platforms in
current society.

Another interesting future work is the evaluation of the role of commenters on
each community – e.g., considering topological and activity-related attributes
to determine commenters’ importance. Similarly, another interesting direction
is the investigation of the role of vertices in the backbone (and in
particular communities) as part of information dissemination campaigns,
notably misinformation campaigns.

## Acknowledgement

The research leading to these results has been funded by the SmartData@PoliTO
Center for Big Data technologies at Politecnico di Torino, Brazilian National
Council for Scientific (CNPQ), Technological Development and Brazilian
Coordination for the Improvement of Higher Education Personnel (CAPES) and
Minas Gerais State Foundation for Research Support (FAPEMIG).

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