# Analysing Twitter Semantic Networks:
the case of 2018 Italian Elections

Tommaso Radicioni
Scuola Normale Superiore
P.zza dei Cavalieri 7, 56126, Pisa (Italy) &Fabio Saracco
IMT School for Advanced Studies
P.zza S. Ponziano 6, 55100, Lucca (Italy)
&Elena Pavan
University of Trento
Via Verdi 26, 38122, Trento (Italy) &Tiziano Squartini
IMT School for Advanced Studies
P.zza S. Ponziano 6, 55100, Lucca (Italy) Corresponding author:
<EMAIL_ADDRESS>
###### Abstract

Social media play a key role in shaping citizens’ political opinion. According
to the Eurobarometer, the percentage of EU citizens employing online social
networks on a daily basis has increased from 18% in 2010 to 48% in 2019. The
entwinement between social media and the unfolding of political dynamics has
motivated the interest of researchers for the analysis of _users online
behavior_ \- with particular emphasis on _group polarization_ during debates
and _echo-chambers formation_. In this context, _semantic aspects_ have
remained largely under-explored. In this paper, we aim at filling this gap by
adopting a two-steps approach. First, we identify the _discursive communities_
animating the political debate in the run up of the 2018 Italian Elections as
groups of users with a significantly-similar retweeting behavior. Second, we
study the mechanisms that shape their internal discussions by monitoring, on a
daily basis, the structural evolution of the semantic networks they induce.
Above and beyond specifying the semantic peculiarities of the Italian
electoral competition, our approach innovates studies of online political
discussions in two main ways. On the one hand, it grounds semantic analysis
within users’ behaviors by implementing a method, rooted in statistical
theory, that guarantees that our inference of socio-semantic structures is not
biased by any unsupported assumption about missing information; on the other,
it is completely automated as it does not rest upon any manual labelling
(either based on the users’ features or on their sharing patterns). These
elements make our method applicable to any Twitter discussion regardless of
the language or the topic addressed.

## Introduction

In the last decade, social media platforms has brought fundamental changes to
the way information is produced, communicated, distributed and consumed.
According to Eurobarometer, the percentage of Europeans employing online
social networks on a daily basis has increased from 18% in 2010 to 48% in 2019
[1]. A similar report concerning the US showed that, as of August 2018, 68% of
American adults retrieve at least some of their news on social media [2]. As
social media facilitate rapid information sharing and large-scale information
cascades, what emerges is a shift from a _mediated_ , _top-down_ communication
model heavily ruled by legacy media to a _disintermediated_ , _horizontal_ one
in which citizens actively select, share and contribute to the production of
politically relevant news and information, in turn affecting the political
life of their countries [3]. In a context in which political dynamics unfold
with no solution of continuity within a hybrid media space, a multiplicity of
studies that cut across traditional disciplinary boundaries have multiplied
that uncover the many implications of users online behavior for political
participation and democratic processes.

The systematic investigation of online networks spurring from social media use
during relevant political events has been particularly helpful in this
respect. Endorsing a view of online political activism as complementary to -
and not as a substitution for - traditionally studied political participation
dynamics [4], detailed and data-intensive explorations of online systems of
interactions contributed to a more genuine and multilevel understanding of how
social media relate to political participation processes.

At the macro level, research has focused on mapping the structural and
processual features of online interaction systems to elaborate on the social
media potential for fostering democratic and inclusive political debates. In
this respect, specific attention has been paid to assessing grades of
polarization and closure [5, 6] of online discussions within echo-chambers [7]
with a view of connecting such features with the progressive polarization of
political dynamics [8, 9].

At the micro level, attention has gone towards disambiguating the different
roles that social media users may play - particularly, to identify influential
spreaders [10, 11, 12] responsible for triggering the pervasive diffusion of
certain types of information, but also to elaborate on the redefinition of
political leadership in comparison to more traditional offline dynamics [13].
More specifically, accounting for users behavior has helped characterizing the
different contributions that are delivered by actors who exploit to different
extents social media communication and networking potentials [14, 15, 16]. In
this way, concepts like "political relevance" and "leadership" get redefined
at the crossroads between actors’ attributes and their actual engagement
within online political discussions.

Additionally, increasing attention to online dynamics has entailed dealing
with non-human actors, such as platform algorithms [17] and bots [18, 19, 20,
21]. Consideration for non-human actors follows from extant social sciences
approaches such as the actor-network theory that invites to disanchor agency
from social actors, preferring a recognition for _actants_ , i.e. for any
agent capable of intervening within social dynamics [22]. Consistently, the
pervasive diffusion of social media in every domain of human action revamps
attention for both platform materiality (i.e. the modes in which specific
technological artifacts are constructed and function) and for actants,
starting from the premise that online dynamics are inherently sociotechnical
and, thus, technology features stand in a mutual and co-creative relationship
with their social understanding and uses [23]. Shrouded in invisibility,
platform algorithms and social bots actively filter and/or push specific types
of contents thus bending users behaviors and opinions - in some cases acting
as true agents of misinformation [24, 25].

In all its heterogeneity, this variety of studies shares a common feature,
insofar as it mostly grounds in the study of _networks of users_ and, thus,
approaches the study of online political dynamics by privileging the
investigation of direct relations amongst actors of different nature -
individuals, organizations, institutions and even bots. Conversely, less
attention has gone towards the _contents_ that circulate during online
political discussions and how these contribute to nurture collective political
identities which, in turn, drive political action and participation.

To be sure,studies that focus on social media content do exist and embrace a
multiplicity of political instances, from electoral campaigns to social
movements and protests. For example, looking at Twitter, research has compared
the content of tweets published by parties with the content of tweets sent by
candidates [26], analyzed the contents of the 2017 French presidential
electoral campaign [27], the online media coverage in the run up of the 2018
Italian Elections [28] and looked at the keywords and hashtags related to the
#MeToo movement [29]. Nonetheless, when the focus has been set on social media
contents, only rarely have these been investigated in connection with systems
of social relations established amongst users on social media platforms [30,
31]. Ultimately, the social and semantic aspects have hitherto been studied
independently and we are still missing empirical pathways to explore the nexus
between contents of online political conversations and the relational systems
amongst users sustaining them.

This paper aims at filling in this gap by proposing an innovative approach
that links the identification of communities of users that display a similar
communication behavior with a thorough investigation of the most prominent
contents they discuss. More specifically, by looking at the online
conversation that unfolded on Twitter in the run up of the 2018 Italian
Elections, our paper identifies _discursive communities_ as _groups of users
with a similar retweeting behavior_ and analyses the contents circulating
within these online political communities.

Several techniques of inferring the political alignment of Twitter users have
been already implemented looking specifically at electoral campaigns, such as
in the run-up to the 2010 U.S. midterm elections [32], the 2012 French
presidential elections [33] and the 2016 U.S. elections [34]. Inference
methods adopted in these works are based either on the construction of a
retweet network based on the manual labelling of (at least) a fraction of
Twitter users or on sharing patterns of web-links and/or hashtags. Moreover,
the final number of communities is often defined a-priori, as every link or
hashtag is assigned a specific political connotation linked to existing party
systems or the left-right ideological spectrum.

Against this background, the approach we adopt here to infer discursive
communities is innovative in two ways. First, it detects groups of Twitter
users without any manual labelling (either based on users’ features or on
content sharing patterns). Second, the political valence of online actions
such as retweeting is behavior-driven rather than ideologically determined as
it is based on the direct action, performed by unverified users, of expanding
the reach of verified users’ messages via retweets.

Having identified communities in this way, we turn towards the study of
contents they discuss by examining the semantic networks induced by the co-
occurrences of hashtags contained in the tweets sent by their members. Through
this procedure, it is possible to examine the semantic aspects of online
political debates while grounding them in users’ behaviors. Finally, we
implement several filtering algorithms [35] to detect the non-trivial content
of our semantic networks, identifying the most debated subjects. Filtering
ultimately allows us to identify the communication strategies adopted by the
different discursive communities and the backbone of the narratives developed
by the different groups.

The paper is organized as follows. Section Case Study and Data describes data-
acquisition and data-cleaning processes. In Section Methods, we discuss the
methods we employ to project our bipartite user-hashtag networks on the
hashtag layer and to derive our collection of semantic networks. We report and
discuss results of our analysis of the Italian case in the Sections Results
and Discussion. Finally, in Section Conclusions we further elaborate on the
potentialities and limits of our proposed approach.

## Case Study and Data

##### Case study.

The current study focuses on the Twitter discursive communities that emerged
during the weeks of the electoral campaign preceding the Italian Elections on
4 March 2018. The 2018 Italian Elections represented a crucial political event
that subverted the traditionally bipolar political competition characterizing
the so-called Italian Second Republic. A radically novel scenario, with three
poles of attraction did in fact emerge. The first pole was represented by the
centre-right coalition which eventually won the elections with 37% of the vote
share. Interestingly, the victory of the right-wing alliance was not led by
Silvio Berlusconi’s party, Forza Italia (FI), which obtained only a 14% of
preferences and thus gave way to the nationalist Lega led by Matteo Salvini
(17,4%). The second pole was represented by the center-left coalition led by
_Partito Democratico_ (PD) with 18.7% of the vote share - its worst result
ever - under the leadership of the secretary and Prime Minister candidate
Matteo Renzi. The third pole was represented by the populist party _Movimento
Cinque Stelle_ (M5S) which unexpectedly obtained 32.7% of preferences.

Ultimately, the 2018 elections constituted a true electoral earthquake
triggered by two elements. On the one hand, the extreme predominance of themes
such as immigration and criminality which eventually favored populist and
right-wing parties over more traditional actors such as Forza Italia and the
Partito Democratico. On the other hand, a significant contribution to the
shuffling of political balances was given also by the hybrid electoral
campaign [36] put in place by all leaders and candidates who combined
traditional and social media and managed to engage voters with pervasive and
low-cost communication strategies.

##### Social media platform and relations selection.

Twitter is hardly the only social media platform that hosted politically
relevant discussions during the observation period, as all social media
platforms play an increasingly relevant political role [37, 38]. Nonetheless,
extant studies show that Twitter is particularly prominent during electoral
dynamics [39] as it is the platform used by the vast majority of public
figures (e.g. political leaders, journalists, official media accounts, etc.)
to provide visibility to their statements. More specifically, in the Italian
context, Twitter is recognized to play an "agenda setting" effect on the
country’s mass media [40]. Hence, regardless of the fact that Twitter users
are not representative of the Italian population, allows for looking at the
discursive communities that emerge on this platform entails looking at a
pivotal - albeit non representative - portion of political discussions that
accompanied the electoral process.

Amongst all types of interaction modes featured by the platform, the current
study grounds on retweets, which we understand as a baseline online relational
mechanism that is particularly insightful when studying collective political
identities. Indeed, as pointed out in [4], while mentions and replies in
Twitter do sustain direct interaction and dialogue between users, retweets
suggest a will to re-transmit contents produced by others. This, in turn,
provides a more clear-cut indication of commonality and shared points of
reference. Moreover, extant research suggests that retweets proxy the actual
political alliances better than mentions and replies - as shown in [32], where
authors conclude that the use of retweets was more relevant than that of
mentions to grasp the bipartisan nature of online debates in the run up of the
2010 US midterm elections.

##### Data collection.

The extraction of Twitter data has been performed by selecting a set of
keywords linked to the Twitter discussion about 2018 Italian Elections. In
particular, each collected tweet contains at least one of the following
keywords: elezioni, elezioni2018, 4marzo, 4marzo2018 (literally, elections,
elections2018, 4march, 4march2018). Data collection has been realized by using
the Twitter Search API across a period of 51 days - from 28 January 2018 to 19
March 2018 - a time interval covering the entire period of the electoral
campaign and the two weeks after the Election Day.

##### Data cleaning.

The procedure described above led to a data set containing 1.2 millions of
tweets, posted by 123.210 users (uniquely identified via their user ID). As in
the Twitter environment hashtags play a central role, acting as _thematic
tags_ designated by the hash symbol # [41], we defined the nodes of our
semantic networks as the hashtags extracted from the text of tweets. Thus,
only tweets containing at least one hashtag have been retained. This procedure
left us with $\simeq 38\%$ of the original dataset. Notably, this result
indicates that only a small percentage of users employs at least one hashtag
while tweeting, as already reported elsewhere [42]. Hashtags were then
subjected to a merging procedure: any two hashtags have been considered as the
same if found "similar" and only the most frequent hashtag has been retained.
The similarity between hashtags has been quantified through the Levenshtein or
edit distance (see Supplementary Note 1 for more details), i.e. one of the
most common sequence-based similarity measures [43]. This procedure allows us
to get rid of hashtag duplicated deriving from typos or linguistic
variability. As shown by a check _a posteriori_ , our cleaning procedure
misidentifies less than $1\%$ of the final list of hashtags.

##### Data representation.

We then used the lists of user IDs and merged hashtags to define a bipartite
network for each day of our observation period (51 bipartite networks in
total). A bipartite network is defined by two distinct groups, or layers, of
nodes, $\top$ and $\bot$, and only nodes belonging to different layers are
allowed to be connected. The bipartite network corresponding to day $t$ can
be, thus, represented as a matrix $\mathbf{M}^{(t)}$ whose dimensions are
$N_{\top}\times N_{\bot}$, with $N_{\top}$ being the total number of users on
day $t$ and $N_{\bot}$ being the total number of hashtags (tweeted) during
that specific day: $m_{i\alpha}^{(t)}=1$ if the user $i$ has tweeted (at least
once) the hashtag $\alpha$ on day $t$ and 0 otherwise.

## Methods

The simplest way to obtain a monopartite projection out of a bipartite network
is that of linking any two nodes belonging to the layer of interest (for
example, $\alpha$ and $\beta$) if their number of common neighbors is
_positive_. Such a procedure yields an $N_{\bot}\times N_{\bot}$ adjacency
matrix $\mathbf{A}$ whose generic entry reads

$a_{\alpha\beta}=\Theta[V_{\alpha\beta}^{*}]$ (1)

where

$V_{\alpha\beta}^{*}=\sum_{j=1}^{N_{\top}}m_{\alpha j}m_{\beta j}$ (2)

counts the number of nodes both $\alpha$ and $\beta$ are linked to and
$\Theta$ represents the Heaviside step function. The condition
$a_{\alpha\beta}=\Theta[V_{\alpha\beta}^{*}]=1$ can be also rephrased by
saying that $\alpha$ and $\beta$ share _at least_ one common neighbor.

A more refined method to obtain a monopartite projection is that of linking
any two nodes if the number of common neighbors is found to be _statistically
significant_ according to an entropy-based framework [35]. More
quantitatively, this second algorithm prescribes to compare the empirical
value $V_{\alpha\beta}^{*}=\sum_{j=1}^{N_{\top}}m_{\alpha j}m_{\beta j}$ with
the outcome of a properly-defined benchmark model - here, generically
indicated with $f$ \- via the calculation of the p-value

$\text{p-value}(V_{\alpha\beta}^{*})=\sum_{V_{\alpha\beta}\geq
V_{\alpha\beta}^{*}}f(V_{\alpha\beta})$ (3)

and link $\alpha$ and $\beta$ only in case it "survives" a multiple hypotheses
test (see Supplementary Note 2 for more details). Such a procedure outputs an
$N_{\bot}\times N_{\bot}$ adjacency matrix $\mathbf{A}$ whose generic entry
reads $a_{\alpha\beta}=1$ if nodes $\alpha$ and $\beta$ are found to be linked
to the same neighbors a statistically significant number of times and
$a_{\alpha\beta}=0$ otherwise.

The null models used as filters for our analysis are the _Bipartite Random
Graph Model_ (BiRGM), the _Bipartite Partial Configuration Model_ (BiPCM) and
the _Bipartite Configuration Model_ (BiCM) [35] (see Supplementary Note 2 for
more details). In a nutshell, the BiRGM discounts the information provided by
the total number of retweets, the BiPCM discounts the information provided by
the total number of retweeted hashtags per user, and the BiCM discounts the
information provided by both the total number of retweeted hashtags per user
and the total number of retweeting users per hashtag.

For every bipartite network in our data set, we created two matrices following
the outlined procedure: first, a monopartite user by user network that we
employed to identify discursive communities; second, a monopartite hashtag by
hashtag network that we employed to study the contents discussed within the
identified discursive communities.

## Results

### User by user networks and discursive communities

Our first step to analyze the Twitter public discourse of the 2018 Italian
electoral campaign consists of identifying communities of online users with a
similar behavior. To this aim, we have divided users into two groups, by
distinguishing the accounts _verified_ by the platform from the _non-verified_
ones. It is worth noting that the account verification procedure can be
requested by any user to guarantee to other Twitter users that the account is
authentic: for this reason, the verified accounts are usually composed by
"entities" such as politicians, journalists, political parties or media. This
information can be easily retrieved by employing the Twitter APIs. A bipartite
network is, then, built as follows: a verified and a non-verified user are
linked if one of the two retweets the other one at least once during the
observation period - notably, the retweeting action is mainly performed by
non-verified users who share contents published by the verified ones. Then,
the procedure described in Section Methods has been employed to project the
bipartite network of retweets on the layer of verified users employing the
BiCM filter. Lastly, a traditional community detection algorithm has been run
to identify communities of verified users (see Supplementary Note 3 for more
details). These groups constitute discursive communities wherein the tweeting
activity of the verified users triggers a discussion between the non-verified
users sharing similar contents. Moreover, a handful of non-verified users are
"assigned" to the communities of the verified ones, via the computation of the
so-called _polarization_ (see Supplementary Note 4 and also [44, 45]).

Interestingly, identified discursive communities provide a faithful
representation of the alliances running at the 2018 Italian Elections and of
their supporters:

  * •

Movimento Cinque Stelle (M5S): a community composed by accounts of politicians
belonging to Movimento Cinque Stelle (e.g. DaniloToninelli, luigidimaio),
institutional accounts of the party (e.g. M5S_Camera, M5S_Senato) and users
engaging with all of them. The number of users belonging to this community is
11.151;

  * •

Center-right (CDX): a community of users composed by accounts of allied right-
wing political parties (e.g. forza_italia, LegaSalvini), center and right-wing
politicians (e.g. renatobrunetta, matteosalvinimi), their institutional
representative groups (e.g. GruppoFICamera), and users interacting with all of
these. The number of users belonging to this community is 5.842;

  * •

Center-left (CSX): a rather heterogeneous community of users composed by
accounts of political parties composing the center-left alliance (e.g.
pdnetwork, PD_ROMA), their politicians (e.g. giorgio_gori, matteorenzi), some
journalists (e.g. vittoriozucconi, jacopo_iacoboni), and users engaging with
them. The number of users belonging to this community is 12.065.

Figure 1: Volume of tweets characterizing the M5S, CDX and CSX communities
across the observation period: notice the peak of activity, evident for all
communities, registered in correspondence of the day _after_ elections (5
March 2018). The volume of tweets characterizing the M5S community is
systematically larger than the volume of tweets characterizing the other two
communities, across the entire period considered here - an element that
confirms the attitude of M5S supporters to use social media in political ways.

##### Activity level of discursive communities.

A first step in the analysis of these discursive communities consists of
examining their volume of activity. As fig. 1 shows, the evolution of the
Twitter activity of the three discursive communities is similar. Generally
speaking, a flat trend is followed by a steep rise few days before the
Election Day; then, a peak in the tweeting activity is registered the day
_after_ elections (5 March 2018). Afterwards, a rapid decrease of the number
of tweets can be observed: in comparison with values preceding the Election
Day, the volume of CDX tweets decreases by $\simeq 60\%$, the volume of M5S
tweets decreases by $\simeq 50\%$ and the volume of CSX tweets decreases by
$\simeq 20\%$. It is worth noting that the volume of tweets characterizing the
M5S community is systematically larger than the volume of tweets
characterizing both the CDX and the CSX community across the entire period
considered here, an element that confirms the renowned attitude of M5S
supporters towards the use of digital media for their organizational and
public communication activities.

### Hashtag by hashtag networks

Let us now move to the analysis of the monopartite projections on the layer of
hashtags which we label as _hashtag by hashtag_ or _semantic networks_. Below,
we discuss the results generated by non-filtered projections. In the next
section, we compare these results with those generated via filtered
projections.

##### Analyzing the topics prominence.

A closer inspection of semantic networks allows us to engage more
systematically with the contents discussed within discursive communities. A
first step in this direction can be made by exploring the number of _nodes_ ,
which proxies the number of topics discussed by users, and their _mean degree_
(i.e. the mean number of neighbors per node), which proxies the (average)
prominence of the topics that characterize the discussion. Results obtained in
this step are shown in fig. 2.

The number of nodes shows a rising trend up to the day _after_ elections,
followed by a decreasing one. This indicates that the number of topics debated
by users increases as 4 March 2018 approaches. Again, the M5S seems to be the
most active community with the largest number of debated topics throughout our
observation period. The trend characterizing the M5S community is closely
followed by that of the right-wing alliance up to the end of February, when an
inversion takes place and a rise in the number of topics debated by the
supporters of the center-left alliance becomes clearly visible.

The trend of the mean degree is, overall, much less regular: it is, in fact,
characterized by several ‘bumps of activity’ throughout the entire period.
Peaks in the daily use of hashtags correspond to so-called mediated events,
i.e., events of social relevance broadcast by mass media and, in particular,
by national television channels. The importance of media events is suggested
by the prominence of hashtags such as #dallavostraparte, #tagadala7, etc.
which all refer to Italian political talk shows. To confirm this intuition, we
explored qualitatively the tweets contributing to activity bumps and indeed
found a systematic link between contents tweeted by users and mainstream media
contents, particularly, television shows featuring prominent politicians. We
further cross-referenced the contents of these tweets particularly with
printed and online news to verify the actual presence of political leaders and
figures during talk shows mentioned by users in their tweet. After this
qualitative validation, we concluded that users tend to become particularly
active during political debates signalling and/or commenting on the presence
of certain candidates in television. Such a behavior is particularly evident
for the CDX community, whose mean degree is characterized by a larger number
of peaks. More specifically, the peaks are observed in correspondence of the
following TV shows:

Figure 2: Temporal evolution of the number of nodes (top panels) and of the
mean degree (bottom panels) for each community-specific semantic network.
Peaks in the daily use of hashtags correspond to _mediated events_ , i.e.
events of social relevance broadcast by media. This behavior is particularly
evident for the CDX community whose activity increases in correspondence with
TV shows where politicians from the right-wing alliance are hosted.

  * •

09 February: interview of Silvio Berlusconi at TG La7 (hashtags:
#silvioberlusconi, #tgla7);

  * •

11 February: Silvio Berlusconi and Matteo Salvini are interviewed at Mezz’Ora
In Più (hashtags: #il4marzovotaefaivotareforzaitalia, #mezzorainpiù);

  * •

13 February: Nicola Porro, an italian journalist, announces via a Facebook
video, the topics that will be discussed on his TV show Matrix, broadcast by
Canale 5, a TV channel owned by the Berlusconi family (hashtags: #nicolaporro,
#matrix);

  * •

18 February: interview of Silvio Berlusconi in the TV show Che Tempo Che Fa
(hashtags: #chetempochefa, #silvioberlusconi);

  * •

19 February: interview of Silvio Berlusconi in the TV show Dalla Vostra Parte
(hashtags: #dallavostraparte, #silvioberlusconi);

  * •

22 February: Matteo Salvini and Anna Maria Bernini (from the Forza Italia
party) are hosted in the TV show Quinta Colonna broadcast on Rete 4, another
TV channel owned by the Berlusconi family (hashtags:
#forzaitaliaberlusconipresidente, #quintacolonna);

  * •

26 February: Guido Crosetto and Maurizio Gasparri (both from the right-wing
alliance) are hosted in the TV show L’Aria Che Tira (hashtag:
#lariachetirala7);

  * •

16 March: interview of Michaela Biancofiore (from Forza Italia) in the TV show
Tagadà (hashtags: #tagada, #tagadala7).

Beside confirming that Twitter discussions can be _influenced_ by external
events, our results point out that Twitter discussions can be also _triggered_
by external events. This is especially true for the CDX community whose
Twitter discussions do not emerge "spontaneously" but are driven by the
aforementioned mediated events [46], seemingly indicating that CDX users still
conceive of television as the main information tool when it comes to political
processes.

$H_{t}$ |  M5S |  CDX |  CSX
---|---|---|---
100% |  dimaio, lega, renzi, berlusconi, m5s, pd, italia |  salvini, m5s, centrodestra, pd, lega |  renzi, salvini, dimaio, m5s, pd
98% |  forzaitalia, salvini |  berlusconi, italia, renzi |
96% |  roma, ottoemezzo |  forzaitalia |  berlusconi, italia, lega
94% |  centrodestra, ricercapubblica |  |  russia
92% |  boschi, politica |  dimaio |  europa, politica, roma
90% |  fi, governo |  fi, governo |
88% |  casapound |  roma |
86% |  meloni |  |
84% |  fakenews, lavoro, liberieuguali |  casapound, politica |  forzaitalia, lavoro, usa
82% |  8800precari, gentiloni, migranti, senato, voto |  governo, lombardia |  centrodestra, leu, liberieuguali
80% |  bonino, campagnaelettorale, casini, leu, rosatellum |  cdx, flattax, sinistra |  milano, partitodemocratico, ue
78% |  avanti, iovotom5s, movimento5stelle, precari, sinistra |  lavoro, ue |  campagnaelettorale, fakenews, governo
Table 1: Hashtag persistence for each discursive community across the entire temporal period covered by our data set (51 days in total). The first column shows the percentage of days each hashtag is present in the set of tweets of each community. Notice that the hashtags that are always present are those carrying the name of political parties and political leaders, while other relevant themes for the political debate are absent from (at least) some of the discursive communities. These findings suggest that the online political debate is largely focused on single personalities/political entities (as particularly evident upon inspecting the CSX hashtags) and only to a much smaller extent on themes of public interest. $T_{t}$ |  M5S |  CDX |  CSX
---|---|---|---
31% |  (ricercapubblica, 8800precari, campagnaelettorale) |  |
27% |  |  |  (salvini, pd, m5s)
24% |  (pd, italia, m5s) |  |  (pd, lega, m5s); (pd, dimaio, m5s)
21% |  (cnr, campagnaelettorale, ricercapubblica); (precari, campagnaelettorale, ricercapubblica); (politica, pd, m5s); (dimaio, pd, m5s); (lega, pd, m5s) |  |  (m5s, dimaio, salvini); (liberieuguali, pd,m5s); (m5s, berlusconi, pd); (usa, europa, russia); (savona, accettolasfida, poterealpopolo)
20% |  (berlusconi, pd, m5s); (ottoemezzo, pd, m5s); (salvini, pd, m5s); (berlusconi, politica, m5s); (centrodestra, pd, m5s); (italia, stopinvasione, italiani); (italia, stopislam, italiani); (campagnaelettorale, piemonte, forzaitalia); (m5s, pd, m5salgoverno) |  (salvini, pd, m5s) |  (pd, m5s, renzi); (pd, italia, m5s); (salvini, lega, m5s); (forzaitalia, pd, m5s); (fattinonparole, partitodemocratico, avanti); (berlusconi, salvini, pd); (salvini, m5s, berlusconi)
| Dates
|  02 Mar 2018 |  20 Feb 2018 |  02 Mar 2018
|  20 Feb 2018 |  27 Feb 2018 |  06 Mar 2018
|  21 Feb 2018 |  02 Mar 2018 |  23 Feb 2018
|  07 Mar 2018 |  01 Mar 2018 |  04 Mar 2018
|  16 Feb 2018 |  22 Feb 2018 |  21 Feb 2018
Table 2: Persistence of triadic closures for each discursive community across
the entire temporal period covered by our data set (51 days in total), on non-
filtered projections. This analysis is particularly insightful to distinguish
the behavior of the three communities: while the CSX and CDX communities are
characterized by triads exclusively about political leaders, parties and
electoral slogans, the triads observed within the M5S community focus more on
themes of public interest. Notice that the largest $T_{t}$ value, i.e. the
largest percentage of days a specific triadic closure is present in our data
set, is sensibly less than the number of days covered by our data set (i.e.
51). Dates refer to the days with the largest number of triadic closures.

##### Identifying persistent topics.

A second step towards a closer understanding of the contents discussed within
discursive communities consists of quantifying the _interest towards a topic_
throughout the entire period covered by our data set. To this aim, we analyzed
_hashtag persistence_ , $H_{t}$, i.e. the percentage of days an hashtag is
present in our data set. Results are reported in table 1. As it shows, the
most persistent hashtags (in fact, the ones that are always present) are those
concerning the name of political parties (i.e. #lega, #m5s, #pd) and political
leaders (i.e. #berlusconi, #dimaio, #renzi, #salvini). Moreover, more
persistent hashtags in all discursive communities refer almost in all cases to
political actors and figures, more often than not of an opposing alliance.
When it comes to substantive electoral themes, instead, the three communities
seem to hold a common interest for work-related matters but also concentrate
on peculiar interests: migration flows for the M5S, taxation for the CDX and
the role of Europe for the CSX. This finding has been observed for all
discursive communities and it highlights the fact that the online political
debate largely focuses on single personalities/political entities and, albeit
to a lesser extent, on themes of public interest.

##### Identifying central topics.

In order to identify topics that, regardless of their prominence and
persistence, are more pivotal to the unfolding of the discussion, we computed
_hashtag betweenness centrality_ , a measure quantifying the percentage of
shortest paths passing through each hashtag, i.e.

$b_{\gamma}=\sum_{\beta(\neq\alpha)}\sum_{\alpha}\frac{\sigma^{\alpha\beta}_{\gamma}}{\sigma^{\alpha\beta}}$
(4)

(where $\sigma^{\alpha\beta}_{\gamma}$ is the number of shortest paths between
hashtags $\alpha$ and $\beta$ passing through hashtag $\gamma$ and
$\sigma^{\alpha\beta}$ is the total number of shortest paths between hashtags
$\alpha$ and $\beta$). In this sense, hashtag betweenness centrality provides
an entry point to identify strategic topics that "coordinate" the discussion,
as they bridge other topics that users do not directly connect within their
tweets. Interestingly, the basket of the most strategic hashtags (i.e. #pd,
#m5s, #renzi, #salvini, #berlusconi, #italia, #dimaio, #lega, #centrodestra)
is basically the same for all communities. This result reveals how the overall
discussion is highly personalized as the main players of the 2018 Italian
Elections embody crucial concepts for the definition of the narratives shaping
the political debates of _all_ communities. Nonetheless, the specificities of
each community are maintained when it comes to economic and societal issues.

##### Analysis of triadic closures.

As discussions develop around communities of topics, increasingly complex
semantic structures are to be considered. To this aim, we analyzed the
presence and the persistence of _triadic closures_ , i.e. _triangles of
connected hashtags_ , which in our approach represent the core of (larger)
semantic networks. In other words, they are the "seeds" around which more
complex discussions grow - exactly as triangular motifs represent the simplest
(yet informative) example of communities [47].

As it has been noticed, this kind of structure provides deeper insights into
users’ tweeting behavior, by revealing which concepts appear _simultaneously_
in a discussion and measuring how often they do so [48]. This analysis is
particularly insightful to distinguish the behavior of the three communities:
as shown in table 2, while both the CDX and the CSX communities are
characterized by triads of concepts exclusively about political leaders,
parties and electoral slogans, the triads observed within the M5S community
reveal a greater concern of their members for themes of public interest (e.g.
the issues of precarious labour, migrants landing, public research).

Interestingly, we also notice that specific days exist in which an abundance
of triadic closures is registered. For instance, on the first day of the
electoral silence, i.e. 2 March 2018, users are particularly active in
building narratives around electoral slogans, while themes of public interest
constitute the topic of tweets at the end of the electoral campaign (i.e. the
last days of February). Finally, we notice that the abundance of hashtag
triads tends to rise in correspondence with mediated events, as observed for
the mean degree: this is the case for the days 27 February 2018 for the M5S
community (when Luigi Di Maio was interviewed at the political talk show
diMartedì), 20 February 2018 for the CDX community (when Silvio Berlusconi was
interviewed in a talk show called #Italia18 organized by the Italian newspaper
_Corriere della Sera_) and 23 February 2018 for the CSX community (when Laura
Boldrini was interviewed at the radio show Circo Massimo).

Figure 3: Analysis of the degree-degree correlations for two specific days,
i.e. 19 February and 05 March 2018. As the trend of $\kappa_{\alpha}^{nn}$
reveals, the daily semantic networks are disassortative for all communities,
i.e. nodes with small degree are (preferentially) connected to nodes with high
degree and vice versa. A close inspection of behaviors of the CDX and the CSX
communities shows groups of nodes with a (much) larger value of the ANND:
these clusters of hashtags constitute the core of the Twitter discussion in
the corresponding community which appear in correspondence of specific events
and disappear the day after.

##### Analysis of degree-degree correlations.

A closer inspection of correlations between hashtags degrees allows us to
elaborate more in depth on the ways prominent topics are connected to others,
shaping broader politically relevant narratives. To this aim, we consider the
average nearest-neighbors degree (ANND), defined, for the generic hashtag
$\alpha$, as the arithmetic mean of the degrees of the neighbors of a node,
i.e.

$\kappa_{\alpha}^{nn}=\frac{\sum_{\beta(\neq\alpha)}a_{\alpha\beta}\kappa_{\beta}}{\kappa_{\alpha}},\quad\forall\>\alpha$
(5)

with $\kappa_{\alpha}$ indicating the degree of the hashtag $\alpha$ in the
considered monopartite projection. The degree-degree correlation structure of
a network can be easily inspected by plotting the $\kappa_{\alpha}^{nn}$
values versus the $\kappa_{\alpha}$ values. A _decreasing trend_ would lead to
conclude that correlations between degrees are _negative_ \- that is, nodes
with a small degree would be "preferentially" connected to nodes with high
degree and vice versa. Conversely, an _increasing trend_ would signal that
correlations between nodes are _positive_ \- that is, nodes with a small
(large) degree would be "preferentially" connected to nodes with a small
(large) degree. Thus, decreasing and increasing trends offer us an entry point
to explore whether discussions in the three communities tend to anchor to some
key themes that work as conversational drivers.

The decreasing behavior of the ANND throughout our data set confirms the
presence of negative degree-degree correlations, i.e. the considered networks
are _disassortative_ (less prominent hashtags are connected with more
prominent hashtags and vice versa). Examples of these trends are reported in
fig. 3. The days considered here, i.e. 19 February 2018 and 5 March 2018, have
been chosen to highlight an interesting feature of our semantic networks: as
it is clearly visible upon inspecting the behavior of the CDX and the CSX
communities, groups of nodes with a (much) larger value of the ANND appear. As
it will become evident in what follows, these hashtags constitute the _core_
of the Twitter discussion in the corresponding community and are characterized
by a dynamics on a daily time-scale, i.e. they appear in correspondence of a
specific event (in the case of the CDX community, the interview of Silvio
Berlusconi in a TV show; in the case of the CSX community, Laura Boldrini’s
Twitter campaign) and disappear the day after.

As an additional analysis, we also considered the clustering coefficient,
defined as

$c_{\alpha}=\frac{\sum_{\gamma(\neq\alpha,\beta)}\sum_{\beta(\neq\alpha)}a_{\alpha\beta}a_{\beta\gamma}a_{\gamma\alpha}}{\kappa_{\alpha}(\kappa_{\alpha}-1)},\quad\forall\>\alpha$
(6)

and quantifying the percentage of neighbours of a given node $\alpha$ that are
also neighbours of each other (i.e. the percentage of triangles, having
$\alpha$ as a vertex, that are actually present). As shown in fig. 4,
decreasing trends are observed: poorly-connected hashtags are strongly inter-
connected and vice versa, thus suggesting the presence of several inter-
connected "small" discussions that are connected to a set of central topics. A
network with these features is also said to be _hierarchical_. Moreover, the
hashtags with a larger value of ANND are also those with a larger value of the
clustering coefficient - confirming the "coreness" of this group of topics.
Taken altogether, these results suggest that all discursive communities
revolve around a handful of few conversational drivers: overshadowed by the
predominance of these issues, a set of niche discussions tend nonetheless to
emerge, pointing out a variety of interests even within a single discursive
community.

Figure 4: Analysis of network hierarchical structure for two specific days,
i.e. 19 February 2018 and 5 March 2018. Plotting the clustering coefficient
$c_{\alpha}$ values versus the degree $\kappa_{\alpha}$ values for the three
communities reveals that our daily semantic networks are hierarchical, i.e.
poorly-connected hashtags are strongly interconnected and vice versa. Besides,
it also shows that the nodes with a larger value of the ANND are also the ones
characterized by a larger value of the clustering coefficient.

##### Semantic networks at the mesoscale: k-core decomposition.

Shifting perspective onto the mesoscale structure of semantic network helps us
to better clarify the power of conversational drivers we just identified. If
triadic closure allowed us to identify the seeds to thematic discussions
within communities, broadening the scope of the semantic analysis to the level
of clusters allows us to explore the main conversational lines within the
different communities.

In what follows, we focus our attention on 19 February 2018, but similar
considerations hold true for other daily semantic networks. We implement the
so-called _k-core decomposition_ , a technique which has been widely used to
find the structural properties of networks across a broad range of disciplines
including ecology, economics and social sciences [49]. The k-core
decomposition can be described as a sort of pruning process, where the nodes
that have degree less than $k$ are removed, in order to identify the largest
subgraph of a network whose nodes have _at least_ $k$ neighbors. This method
allows a "coreness" score to be assigned to each node of the network which
remains naturally divided into shells. Node coreness is equal to $k$ if the
node is present in the $k$-core of the network but not in the $(k+1)$-core.

Figures 5, 6, 7 show the the k-shell decomposition for the semantic networks
of our discursive communities, for the day 19 February 2018: five k-shells,
corresponding to five quantiles of the degree distribution, have been colored,
confirming the presence of a core of highly debated hashtags (the red one
collecting the most prominent and intertwined ones). To inspect the presence
of a substructure nested into the discussion core, we run the Louvain
algorithm on the innermost k-shell of the semantic networks of our discursive
communities. Their shell structure is indeed rich, as particularly evident
when considering the CSX and the M5S ones: indeed, several communities appear,
seemingly indicating that the discussions in which members of the two groups
are (more) engaged self-organize around sub-topics.

Figure 5: K-core decomposition of the semantic network for the non-filtered
projection of the CDX discursive community on 19 February 2018. In the left
plot, five k-shells are represented with different colors. In the right plot,
an expanded view of the innermost k-shell - basically overlapping with the
properly defined core individuated by the bimodular surprise - is represented.
The compact bulk is triggered by the interview of Silvio Berlusconi in the TV
show Dalla Vostra Parte. [Picture realized with Gephi software version 0.9.2.
For more information about Gephi [50]: https://gephi.org/]

For what concerns the CSX community, the hashtags sub-communities emerge as a
consequence of factors as the Twitter campaign born in support of the center-
left candidate Laura Boldrini (revealed by the presence of hashtags such as
#stoconlaura and #contasudime), the visit of Matteo Renzi in Bologna (revealed
by the presence of hashtags such as #bologna, #renzi, #errani, #casini,
hashtags that refer to Vasco Errani and Pier Ferdinando Casini, center-left
wing candidates for the Senate in Emilia-Romagna) and the presence of Massimo
D’Alema (another leader of the center-left alliance) in the radio show Circo
Massimo (revealed by the presence of hashtags such as #dalema).

On the other hand, the presence of multiple debates within the core of the M5S
semantic network relates to events like the electoral tour of Alessandro Di
Battista, a prominent figure of the party, who presented the M5S electoral
program in the southern Italy region named Basilicata (hashtags: #dibattista,
#ilfuturoinprogramma, #programmaindiretta, #basilicata), the presence of a
journalist of Il Fatto Quotidiano (a newspaper supporting the M5S) invited in
the TV show Otto e Mezzo (hashtags: #ilfattoquotidiano, #ottoemezzo) and the
presence of politicians supporting other coalitions in several TV shows such
as Porta A Porta, Mezz’Ora In Più and Dalla Vostra Parte.

However, these observations do not hold true when the CDX-induced semantic
network is considered. Its innermost shell is, in fact, a compact group of
topics that cannot be further partitioned.

As a second observation, we notice that - when present - the communities
partitioning the core are "held together" by the nodes with largest
betweenness centrality: as they coincide with the hashtags related to the name
of political parties/leaders, the latter ones can be imagined to act as
bridges connecting different discussions. Generally speaking, this indicates
that the concept of "most influential nodes" can be applied also within the
core of the networks of hashtags - a result that complements the one about the
influential spreaders individuated within the networks of users [51].

##### Semantic networks at the mesoscale: the core-periphery structure.

In order to complement the analysis above, we also implemented the method
proposed in [52] which prescribe to search for the network core-periphery
partition minimizing the quantity called _bimodular surprise_ , i.e.

$\mathscr{S}_{\parallel}=\sum_{i\geq l_{\bullet}^{*}}\sum_{j\geq
l_{\circ}^{*}}\frac{\binom{V_{\bullet}}{i}\binom{V_{\circ}}{j}\binom{V-(V_{\bullet}+V_{\circ})}{L-(i+j)}}{\binom{V}{L}}.$
(7)

The quantity above is the multinomial version of the _surprise_ , originally
proposed to carry out a _community detection_ exercise [52]. In our case, $L$
is the total number of links observed in our projections, while $V$ is the
total number of possible links, i.e. $V=\frac{N(N-1)}{2}$. The quantities
marked with $\bullet$ ($\circ$) refer to the corresponding core (periphery)
quantities: for example, $l_{\bullet}^{*}$ is the number of observed links
within the core, while $l_{\circ}^{*}$ is the number of observed links within
the periphery. The presence of three binomial coefficients allows three
different "species" of links to be accounted for: the binomial coefficient
$\binom{V_{\bullet}}{i}$ enumerates the number of ways $i$ links can
redistributed _within_ the core, the binomial coefficient
$\binom{V_{\circ}}{j}$ enumerates the number of ways $j$ links can
redistributed _within_ the periphery, and the binomial coefficient
$\binom{V-(V_{\bullet}+V_{\circ})}{L-(i+j)}$ enumerates the number of ways the
remaining $L-(i+j)$ links can be redistributed _between_ the two, i.e. over
the remaining $V-(V_{\bullet}+V_{\circ})$ node pairs (see Supplementary Note 3
for more details).

Figure 6: K-core decomposition of the semantic network for the non-filtered
projection of the CSX discursive community on 19 February 2018. In the left
plot, five k-shells are represented with different colors. In the right plot,
an expanded view of the innermost k-shell - basically overlapping with the
properly defined core identified by the bimodular surprise - is represented.
Notice the presence of communities, found through the Louvain algorithm and
emerging as a consequence of factors as diverse as the Twitter campaign born
in support of the center-left candidate Laura Boldrini, the visit of Matteo
Renzi in Bologna, the presence of Massimo D’Alema (another leader of the
center-left alliance) in the radio show Circo Massimo. [Picture realized with
Gephi software version 0.9.2. For more information about Gephi [50]:
https://gephi.org/]

The mesoscale structure characterizing all discursive communities consists of
a group of very well-connected vertices linked to a group of low-degree,
loosely inter-linked nodes, see figs. 5, 6, 7. Such a structure is known as
_core-periphery_ and is present in many social, economic and financial systems
[53]. Remarkably, nodes belonging to the innermost shell overlap with the core
ones computed with the multinomial version of the _surprise_ , as proved by
computing the _Jaccard index_ over two sets of nodes which is a measure of
similarity between two sets of elements and is defined as the size of the
intersection divided by the size of the union of the two sets:
$J(A,B)=\frac{|A\cap B|}{|A\cup B|}$.

Figure 7: K-core decomposition of the semantic network for the non-filtered
projection of the M5S discursive community on 19 February 2018. In the left
plot, five k-shells are represented with different colors. In the right plot,
an expanded view of the innermost k-shell - basically overlapping with the
properly defined core identified by the bimodular surprise - is represented.
Notice the presence of communities, found by running the Louvain algorithm.
These emerge as a consequence of events as the electoral tour of Alessandro Di
Battista (one of the M5S leaders), the presence of politicians in TV shows
such as Porta a Porta, Mezz’Ora In Più and Dalla Vostra Parte. [Picture
realized with Gephi software version 0.9.2. For more information about Gephi
[50]: https://gephi.org/]

As a last comment, let us explicitly show the evolution of the number of nodes
belonging to the core and to the periphery for each discursive community. As
fig. 8 shows, the core size is nearly constant throughout all the considered
period while the periphery size rises in correspondence of Election Day,
showing a peak in correspondence of the day after the elections (i.e. 5 March
2018). This behavior, common to all communities, seems to indicate that, as
the Election Day approaches, the number of topics discussed does increase.

### Filtering the projection

Let us now focus on the structural features of the filtered projections.
Before presenting the results of the analysis, we briefly recall how the
filtering procedure works.

Filtering lets the statistically significant overlaps of hashtags measured on
the real system emerge. More in detail, for any couple of hashtags, we count
how many users are employing them. Then, we consider as a benchmark a set of
networks that preserve on average some information of the user-hashtag
bipartite network, i.e. the total number of links (as in a bipartite Erdös-
Rényi, or Bipartite Random Graph, _BiRGM_), the degree sequence of the hashtag
layer (Bipartite Partial Configuration Model, _BiPCM_) or the degree sequence
of both layers (Bipartite Configuration Model, _BiCM_). Naturally, the
stricter the constraints (i.e. the properties preserved by the ensemble), the
more detailed the description of the ensemble, as compared to the real
network, and fewer edges are validated. In this sense, the number of validated
co-occurences are those non compatible with the expected structural features
of the different null models. In other words, the validation procedure retains
the non-trivial co-occurences of hashtags present in the initial bipartite
structure, namely those that are not explained by the constraints of the null
model used for filtering. Among the aforementioned null models, the BiRGM is
expected to retain the highest number of edges between hashtags while the BiCM
is the most restrictive among the filtering null models.

Such a procedure has been implemented in previous studies to detect the
backbone of the network structure, filtering the real system from random
noise, and to highlight non trivial behaviors in the original system [35, 54].
In the present case, the filtering procedure allows the detection not only of
_extremely popular hashtags_ but also of those hashtags connected only to a
single message retweeted by a significant number of users. The former, in
fact, are single hashtags tweeted by a huge amount of users and therefore
having a large number of co-occurences, a feature that is compatible with at
least one of the null models considered here and thus possibly filtered out by
this procedure. The latter, instead, are more likely to be groups of hashtags
whose non-trivial co-occurrence will survive the filtering procedure. As an
example, a set of hashtags used together only in one tweet can be considered:
if this particular tweet is retweeted a significantly high number of times,
the number of co-occurences of these hashtags appearing once is given by the
number of times the original message has been retweeted plus the contribution
of the original message. In this case, as the null model distribute the co-
occurence probability among all the other hashtags in the semantic network,
the probability for their co-occurence to be validated thus becomes larger.
Differently, a popular hashtag published by a large number of users has a
higher probability to co-occur with other hashtags and, at which point the
null model could explain its co-occurrence with these hashtags as induced by
the network properties. In other words, the filtering algorithm presented in
this work is more likely to discard co-occurences with popular hashtags than
with these hashtags appearing together in a single tweet shared a significant
number of times.

As mentioned above and as fig. 9, 10, 11 show, the overall effect of adopting
a filtering procedure - regardless of its peculiarities - is that of reducing
the total volume of the semantic networks. Differences exist, instead, when it
comes to the analysis of nodes’ mean degree. Particularly interesting in this
respect is the behavior of the semantic networks of the M5S discursive
community whose mean degree is affected to a much lesser extent by the BiRGM-
induced filtering than those of the CDX and the CSX communities. This, in
turn, implies that the information encoded into the total number of retweets
of the M5S bipartite user-hashtag network is able to account for the co-
occurrences between any two hashtags less effectively than for the CDX and the
CSX configurations. Similarly, it is possible to state that the information
encoded into the BiRGM (which is the simplest filter) recognizes the initial
structure of the M5S bipartite user-hashtag network as significant.

For what concerns topics persistence, the ranking observed above with
reference to the non-filtered projection basically coincides with the ranking
observed on the filtered ones. Regarding topics centrality, instead, we
observed that the filtering procedure with increasingly restrictive benchmarks
makes "emerge" previously screened hashtags (e.g. #sicurezza,
#fallimentocinquestelle and #precariato, respectively for the semantic
networks induced by the CDX, CSX and M5S discursive communities). Centrality
(e.g. the betweenness variant) is, in fact, a highly non-trivial feature that,
generally speaking, is not reproduced by the information encoded into the
degree sequence alone (not to mention the one encoded into the number of
links): in fact, as figs. 9, 10, 11 clearly show, only the hashtags belonging
to the innermost shells survive our filtering procedure.

Let us now move to discuss the mesoscale structure of the filtered projections
looking, as usual, at one specific day that shows the richest structure (again
19 February 2018). Filtering the projections by adopting an increasingly
restrictive benchmark make the projection sparser while letting less trivial
structures emerge. Interestingly, the core portion of the semantic network
corresponding to the M5S discursive community survives the most restrictive
filtering (i.e. the BiCM-induced one), signalling the presence of a non-
trivial group of keywords constituting the bulk of the communication in that
community (see fig. 9). Moreover, basically _all_ hashtags representing topics
of interest of the 2018 Italian electoral campaign persist. The same
conclusion holds true for the number of triadic closures observed in
correspondence of mediated events: their number is significantly larger with
respect to a network model accounting for the total number of tweets only.
This result is in line with what has been found for other socio-economic
systems (e.g. the World Trade Web [55]) whose abundance of triadic closures is
not reproduced by a benchmark model constraining the total number of links
only.

In the following we will describe with more details the main characteristics
of the filtered projections of the various semantic networks.

Figure 8: Evolution of the number of nodes belonging to the core and to the
periphery of each discursive community. The core size is nearly constant
throughout the observation period while the periphery size rises as the
Election Day approaches (the peak appears in correspondence of the day after,
i.e. the 5 March 2018). This behavior, common to all communities,reveals that,
as the Election Day approaches, the number of topics animating the discussion
increases. Figure 9: Mesoscale structure of (from bottom-right, clockwise) the
non-filtered projection of the semantic network corresponding to the CDX
discursive community on 19 February 2018 and of the projection of the same
network filtered according to the BiRGM, the BiCM and the BiPCM, respectively.
The BiCM lets only _few_ hashtags survive, reading #iussoli, #sicurezza,
#stopinvasione, #stopislam. [Picture realized with Gephi software version
0.9.2. For more information about Gephi [50]: https://gephi.org/]

##### The CDX discursive community.

Figure 9 depicts the semantic network of the center-right alliance on 19
February 2018.

In the BiCM projection, i.e. the strictest one, few links survive. In this
situation, it becomes almost inappropriate to talk about communities, since we
can find only links connecting two otherwise isolated nodes, or small cliques
and chains. Nevertheless, even these few hashtags carry important information
regarding the keywords used during the electoral campaign. It is the case of
the cluster including #stopislam, #stopinvasione (_stop the invasion_), #cdm
(the acronym for the Italian Council of Ministers) and #forzeordine (_law
enforcement agencies_), asking for stronger countermeasures to the immigration
flows from Northern Africa, perceived as dangerous for the security and for
Italian cultural identity. On a similar topic, there is a clique composed by
#roma, #labaro and #primaporta: the hashtags refer to neighborhoods in Rome,
in which, during the days of the data collection, some thefts in apartments
were reported. These hashtags were used to criticise the city administration
of Rome, run by Virginia Raggi of the M5S. Moreover, a pair of nodes which
represents insulting nicknames for the political opponents are connected
between themselves. Those hashtags, #pdioti (i.e., an hashtag mixing the
acronym of the _Partito Democratico_ and the word _idiots_) and #m5stellisti,
are present in a popular message displaying both hashtags, and, in particular,
it is the only message displaying #m5stellisti. There is also a clique formed
by #casapound (i.e., a neo-fascist party), #rai2 (i.e., the second channel of
the national TV public service) and #19febbraio. This clique is the result of
a viral tweet intended to advertise the presence of the leader of Casa Pound
in a public debate held on Rai2 on 19 February. Finally, the last clusters
present in the BiCM-induced projection are more institutional: the first
contains #torniamoagovernare (_let’s go back to govern_),
#elezioniregionali2018 (_2018 regional administrative election_) and #salvini,
while the other one is composed by #flattax, #programma (_program_) and
#veneto. The latter set of hashtags is related to an event where the flat
taxation government, as part of the electoral program, is presented.

The BiPCM projection displays a structure in which the various sub-groups
described above are reinforced (for instance, the chain #flattax, #programma
and #veneto is closed in a clique) and introduces new topics as #calenda (the
Minister of the industrial development at the time of the electoral campaign)
#ilva and #alitalia, respectively the greatest European steel factory which
had severe problems for its environmental, health and economic sustainability,
and the Italian national airline, which has been at default risk in the last
years. These hashtags are intended to criticize the action of the government
in charge at that time. Interestingly, another cluster consisting of the
hashtags #sullepalle, #fazio, #salvini is detected by the validated BiPCM
projection. These hashtags need a bit of context: during the electoral
campaign, the journalist Fabio Fazio invited politicians from all political
coalitions to his TV program Che Tempo Che Fa broadcast on the national
television service, to promote their campaign. Fazio has been accused by all
political forces of being too condescending with their opponents. Salvini
refused Fazio’s invitation, publicly with insulting language his aversion for
the journalist. These hashtags, together with others related to right-wing
campaign topics such as #vita and #famiglia (_life_ and _family_ , related to
the Italian anti-abortion movement) are associated with the communication
strategy of the most radical part of the center-right alliance.

In the BiRGM validated projection, the clusters found in the previous stricter
projections are merged together to form a network organised along two poles:
the first is more "institutional" with keywords related to the electoral
campaign of Forza Italia (the political party of Silvio Berlusconi), including
hashtags such as #campagnaelettorale (_electoral campaign_), #unitisivince
(_united we will win_), #votaforzaitalia (_vote Forza Italia_); the second is
linked to the other two right-wing parties with both the names of their
leaders (#salvini and #meloni), but also including their opponents, as #pd,
#renzi, #pdioti and #m5stellisti. Interestingly, both poles are organised with
a core and a periphery: the two cores are connected by the hashtag
#centrodestra (_center-right_), the peripheries by #casapound (i.e., the
aforementioned neo-fascist party).

##### The M5S discursive community.

Overall, the communication strategy of the M5S is peculiar since the users
tend to use a quite large number of hashtags and thus discuss a higher number
of topics. Hashtags are nearly the same across various tweets, since they were
copied and pasted from older messages on the same topics. In this sense,
Twitter users in the M5S community appear to be more coordinated and thus
manage to give their hashtags more visibility.

Considering the tweets and retweets published on 19 February, the M5S
validated semantic networks of fig. 10 displays a rich structure, even in the
BiCM projection, due to the tweeting behavior described above. In particular,
several clusters can be found, including the name of the opponents (#renzi,
#salvini, #gentiloni, #pd), or few nicknames assigned to them (as #prugnetta,
_little plum_ , for Brunetta, a member of Forza Italia; #renzusconi, a mix
between Renzi and Berlusconi, intending that there is few differences between
them) or other slogans teasing political opponents (#votiamolivia, _let’s vote
them away_ ; #nomarivotateli, _no, but vote them again_ , ironically targeting
PD supporters; #ocosìopd, _this way or PD’s way_ , advertising that the only
political alternative to Partito Democratico is the Movimento Cinque Stelle).
Few clusters represent some events in the electoral campaign. For instance, a
cluster following the electoral campaign tour of Di Battista, a member of the
Movimento Cinque Stelle, appears in this projection. Even a clique advertising
a live streaming on Facebook can be observed, discussing the management of the
public health system in the Lazio region (governed by the PD), with the
hashtags #lazio, #sanità (_public health system_), #sancesareo (the town were
the live streaming was set), #zingaretti (the president of the Lazio region).

The topic of bad governance of the political opponents represents a big part
of the semantic network of the M5S community: in addition to the cluster
mentioned above, another cluster focuses on the news about a journalist who
was attacked during a campaign event held by the center-left coalition in
Naples (#fanpage which is the online newspaper for which the journalist
worked; #inchiestanapoli, _Naples investigation_ ; #video). Moreover, the
hashtags #donatelialmicrocredito (_give them to the microcredit_) and
#rimborsopoli (_refund scandal_) refer to the scandal of a criminal
organisation in Rome bribing members of established political parties. The
Movimento Cinque Stelle expelled its representatives involved in this
investigation and proposed that other parties do the same and transfer the
amount of the bribe to the microcredit. There are also clusters targetting
harsh political debates, such as the case of #dibiase, referring to Letizia Di
Biase who is the wife of the Italian Minister of Cultural Heritage and
Activities. After being elected member of the council in the city of Rome, she
did not resign when elected as member of the council of the region of Lazio.
Di Biase was also criticised for criticizing the mayor of Rome Virginia Raggi
of the Movimento Cinque Stelle for filing for bankruptcy for the city agency
of public transportation while salvaging the regional one operated by the
regional administration of the Partito Democratico. Finally, there are traces
of the debate between the virologist Roberto Burioni and the Head of the
Italian Order of Biologists, Vincenzo D’Anna, concerning the presence of anti-
vaccine groups and Movimento Cinque Stelle supporters during a national
conference of the order of biologists. Other hashtags refer to Giorgia Meloni
(leader of Fratelli d’Italia) and the charges moved against her for leaning
close to neo-fascist parties and ideology.

The BiPCM projection increases the connections among the topics and few
hashtags appear to be related to names of places covered by the campaign tour
of Carlo Sibilia, another exponent of the M5S. Instead, the BiRGM projection
displays a strong core-periphery structure.

Figure 10: Mesoscale structure of (from bottom-right, clockwise) the non-
filtered projection of the semantic network corresponding to the M5S
discursive community on 19 February 2018 and of the projection of the same
network filtered according to the BiRGM, the BiCM and the BiPCM, respectively.
The core portion of this network survives the most restrictive filtering (i.e.
the BiCM-induced one), indicating that basically _all_ hashtags representing
topics of interest of the 2018 Italian electoral campaign persist. [Picture
realized with Gephi software version 0.9.2. For more information about Gephi
[50]: https://gephi.org/]

##### The CSX discursive community.

In the case of the CSX community, the number of hashtags used is relatively
small. With respect to other discursive communities, the semantic network of
the center-left group validated by the BiCM (see fig. 11) focuses more on
political subjects, as shown by the pair #diritti (_rights_) and #arcobaleno
(_rainbow_ ; both hashtags refer to the LGBTQIA+ civil rights; but also by the
coupling of #bimbi (_children_) and #rohingya (related to the subject of the
Rohingya exodus in Myanmar and the condition of young children). Other
clusters pivot around instructions for youngsters voting for the first time
(#primovoto, _first vote_ ; #comesivota, _how to vote_ ; #pernonsbagliare,
_how to avoid mistakes_) and call for fact checking during the electoral
campaign, with hashtags #factchecking and #checkpolitiche2018.

Interestingly, a clique linked to the particular virality of one specific
tweet, is formed by the hashtags #trivellopoli, #mafiacapitale and #consip,
i.e. three scandals in which the Partito Democratico was involved. This tweet
suggests that those scandals suspiciously appeared during the electoral
campaign in order to damage the name of the Partito Democratico thereby
limiting its performance at the general elections.

Another conversational line unfolds along the candidacy of Paolo Siani, a
physician particularly active in providing support, in collaboration with
local NGOs, to children of the poor neighborhoods of Naples at risk of being
recruited for organized criminal activities. More broadly, the public
presentation of the Partito Democratico candidates team constitutes a topic
widely debated within this discursive community as shown by the two hashtags
#renzi and #gentiloni, respectively the National Secretary of the Partito
Democratico and the candidate for the position of Prime Minister, in
connection with other hashtags. For instance, the clique #bologna, #avanti
(_let’s move forward_) and #sceglipd (_choose PD_) refers to an event led by
Paolo Gen- tiloni and Matteo Renzi in Bologna while the clique #lunedì
(_Monday_), #buongiorno (_good morning_) and #squadrapd (_PD team_) appeared
in a message promoting a massive electoral campaign.

In the BiPCM validated projection more connections appear, enriching topics
which had already emerged, as in the case of the candidacy of Paolo Siani
mentioned above: #babygang, #napoli (_Naples_), #infanzia (_childhood_) merge
with the previous hashtags #paolo and #siani. A new cluster containing the
name of the opponents (#dimaio, #salvini, #meloni, #fascismo) is also present.

In the BiRGM validated projection, the aforementioned structures gain new
links and new nodes and a richer structure becomes evident. In particular,
three main communities appear: one (in orange in fig. 11) pivoting around
political adversaries (including #salvini, #meloni, #dimaio, #grillini,
#berlusconi), one advertising political subjects and events of the electoral
campaign (including #sceglipd, _choose PD_ ; #squadrapd, _PD team_ ; #diritti,
_rights_ , and so on) and one related to the candidacy of Paolo Siani. A
peripheral clique advertising the event in Venice of _Liberi e Uguali_ , a
political party on the left of Partito Democratico, can also be found
(#antifa, #liberieuguali, #venezia, _Venice_).

##### Final remarks on the filtering procedure.

Summing up, in all naïve projections we observe a rich structure, with a
particularly evident core-periphery organisation. This structure is
progressively disintegrated through filtering and depending on the strictness
of the benchmark used. While this disintegration affects semantic structures
generated by all discursive communities, the various groups display a
different resilience to the filtering procedure: in particular, the one
revolving around M5S accounts are the one with the least trivial structure,
hence being affected the least. Quite relevantly, the different network
structures carry information about the strategy followed by the various
discursive communities during their political campaign.

The validation procedure proposed in [35] projects non-trivial co-occurrences
of links in the bipartite networks, i.e. those that are not explained by the
ingredients of the null-model used for filtering. In this sense, validated
nodes in the projection are not necessarily those with, for example, the
highest (bipartite) degree, but those grappling to other hashtags in the
semantic network to a larger extent than what expected by just looking at the
original bipartite network. With respect to the examined case study, the
validated projections show that the more the validated links, the more
hashtags are used to refer to a single subject, against the random
superposition of ubiquitous slogans. This seems to be the case particularly
for the M5S community while it is true to a much lesser extent for the CDX
discursive community where the amount of nodes in the BiCM validated
projection is extremely limited. The validation procedure allows us to focus
on the least trivial connections and thus to observe different conversational
lines that shape the political communication of the various discursive
communities. In this way, the validation procedure allows to uncover otherwise
invisible conversational lines that shape the Twitter activity of each
discursive community.

In the CDX, a clear thematic distance is present between the far right (formed
by parties led by Matteo Salvini and Giorgia Meloni) and center-right
politicians (Silvio Berlusconi and his party _Forza Italia_) in terms of
topics and electoral slogans. While the former insists on security issues
related to migration flows from Northern Africa, the latter tends to promote a
united center-right alliance. There is an evident semantic diversification
with completely different keywords used in the tweets: the far right uses more
aggressive statements and bad words, while the second is more reassuring and
institutional.

The M5S projected semantic networks are especially rich in structure, due to
the strong usage of hashtags in this community. Most of them are referring to
political opponents with nicknames and ironic slogans. A great part of the
filtered semantic network is devoted to highlight the deceitfulness of the M5S
opponents.

Validated semantic networks of the CSX community are poorer than those of M5S,
but richer than those of the CDX. Their major feature is to present mostly
events of the electoral campaign, their candidates at a national and regional
level and the weaknesses of their political opponents.

It is worth noticing that the peculiarities of the three discursive filtered
semantic networks are present in other days which are not explicitly commented
here. For instance, on 11 February, we can still observe two different poles
of the debates in the CDX community, one promoted by the supporters of _Forza
Italia_ and the other promoted by the supporters of far-right wing parties. As
observed for the 19 of February, the two poles use different vocabularies and
focus, respectively, on reforming taxation and labour or on the migration
issues. Analogously, the M5S displays a cluster of discussion against the use
of vaccines, few clusters against an alleged _quid pro quo_ between some PD
members and some businessmen as well as some other cluster teasing political
opponents. Finally, the CSX focus on the election candidates presentation and
few national problems (increasing inequality, poverty and the decreasing
birth-rate). In all three networks there are also mentions to the
demonstration involving nearly thirty-thousand persons against neo-fascism
held in Macerata on 10 February, albeit with different levels of attention.

Figure 11: Mesoscale structure of (from bottom-right, clockwise) the non-
filtered projection of the semantic network corresponding to the CSX
discursive community on 19 February 2018 and of the projection of the same
network filtered according to the BiRGM, the BiCM and the BiPCM, respectively.
The core portion of this network just partially survives the most restrictive
filtering (i.e. the BiCM-induced one), while it is present in the less strict
filtering (the BiPCM and the BiRGM induced), representing a structure in
between the stronge persistence of the M5S semantic network of fig. 10 and the
CDX one depicted in 9. [Picture realized with Gephi software version 0.9.2.
For more information about Gephi [50]: https://gephi.org/]

## Discussion

In this section, we would like to discuss more in details some relevant
features of our methodological approach and to summarize results about the
Italian case we examined throughout this work. Our study focused on the
activity on Twitter of three different discursive communities tied to the main
political topics competing during general elections in Italy in 2018. It
exploited approximately 1 million of tweets which we used to define networks
of statistically significant co-occurrences of hashtags at a daily time scale.
Compared to extant research, we argue that our proposed approach innovates
studies in this domain in two main ways. First, we propose a methodological
framework [11, 45] to investigate the semantic components of online political
discussions coupling attention for topics prominence and persistence with a
sound exploration of how they are organized and structured along
conversational lines. Second, we did not treat the semantic aspect in
isolation but, in fact, built a tight connection between contents discussed by
users and the type of interactions they performed via Twitter. Moreover, our
way of isolating discursive communities and related semantic networks does not
entail any manual intervention. Initial distinction between verified and non-
verified accounts is not defined by researchers but is, in fact, assigned by
the Twitter platform itself. Relevantly, as the categorization of accounts
according to these two categories is regularly provided through the Streaming
API by the platform itself, the solidity of the initial partition is ensured
platform-wise. Similarly, topics and conversational lines within semantic
networks are not biased by construction but, in fact, are a direct output of
the application of filtering procedures with maximally random benchmarks.

Against this background, we sought to offer a solid analysis of the public
discussion developed online during a crucial political event and to infer,
starting from semantic aspects, marking traits of the different political
identities that guide political courses of action in the Italian political
scenario. One of the main findings of this paper concerns the way the
topological structure of semantic networks "reacts" to the so-called mediated
events (i.e. TV debates, the media coverage of offline events, etc.) thus
revealing not only different sensibility towards the media sphere but, more
significantly, different identity traits that characterize each discursive
political community. The topology of the CDX community is strongly dependent
on these events (the mean degree of nodes increases in correspondence of
specific TV shows), meaning that this group of users is more involved in the
activity of retweeting during the appearance of political actors particularly
on television. Conversely, the activity of the M5S community appears to be
much more "distributed". In fact, although M5S supporters are sensitive to TV
shows as well, their retweeting activity is not exclusively driven by media
events but, rather, follows their preference for a generalized use of social
media for organizational and political communication activities. Finally, the
activity of the CSX community is characterized by a somewhat "intermediate"
behavior: even when mediated events affect the Twitter discussion, the
attention of the whole community is somehow "shared" among the various actors
constituting the center-left alliance.

Particularly insightful is the analysis of our semantic networks at the
mesoscale: what emerges is the presence of a core of topics, i.e. a densely-
connected bulk of hashtags surrounded by a periphery of loosely inter-
connected (sub-)topics. This indicates that daily semantic networks are
characterized by few relevant hashtags to which other, less relevant ones,
attach. This structure is maintained during the whole observation period and
differences emerge only with respect to the number of _peripheral_ themes
entering the discussion. The resilience of the core-periphery structure is not
the same for the various discursive communities. In the context of semantic
networks, the fact that the system is more or less resilient to the filtering
implies that the various political groups have developed differently their
political narrative, focusing their communications on few related terms per
subject or mentioning a set of omnipresent hashtags in all messages. Even in
the response to the filtering procedure, the M5S and the CDX communities
represent the two extremes, displaying respectively the most and the least
resilient semantic network.

These differences are the effect of various styles used in writing posts. When
targeting a specific theme, members of the M5S community use several hashtags
that are subsequently re-used by other users writing on the same argument in
order to make keywords and slogans more recognizable and visible. Conversely,
in the CDX community, the number of hashtags per message is more limited and
users tend to use particularly viral hashtags. Moreover, the CDX shows a
diversified communication strategy, hence a possible internal political
fracture, due to the different approaches of the various parties in the
alliance: right-wing politicians are more aggressive towards opponents, while
center-right ones tend to focus on unitive (for the coalition) keywords.
Somewhere in between, the CSX community balances a use of hashtags to
criticize its adversaries but also to amplify the reach of events and
initiatives of the electoral campaign.

## Conclusions

Social media platforms have dramatically changed patterns of news consumption
and, over the last years, they have become increasingly central during
political events, especially electoral campaigns. In this respect, Twitter has
been shown to play a major role, thus attracting the attention of scientists
from all disciplines. So far, however, researchers have mainly focused on
users’ activity, paying little attention to semantic aspects which are instead
particularly relevant to detect online debates, understand their evolution
and, ultimately, inferring the behavioral rules driving (online but also
offline) electoral campaigns.

As claimed in the Section Introduction, our goal in this paper is to advance a
comprehensive methodological framework to fill a persistent attention gap for
the semantic aspects of online political discussions. Accordingly, we did put
forward a scheme of analysis that couples attention for more evident aspects,
such as topic visibility, persistence and strategic uses in conversation, with
the systematic analysis of more invisible, and yet crucial aspects of content
production and circulation - particularly, the identification of
conversational cores and main lines of development. In doing so, we believe
that our proposed approach provides a solid starting point to understand the
symbolic aspects that flank and, in fact, nurture current dynamics of online
civic participation, political partisanship and polarization, which have so
far catalyzed attention within the research community.

More relevantly, our proposed approach did not bring prominence to semantic
aspects leaving the social side of online dynamics behind. The semantic
networks we analyzed in this paper follows from an identification of
discursive communities that leans on an entropy-based framework, which is a
methodological advancement per se [11, 45]. On the one hand, this technique
allowed us to filter the retweeting activity of users while singling out the
statistically-relevant information at the desired level of detail.
Consistently, the semantic structures induced from communities are indicative
of users’ political affiliation yet without passing through any manual
labelling of our media contents (e.g. as performed in [34, 32]). On the other
hand, we deduce the discussions taking place in each community by connecting
any two hashtags if used a significantly large number of times by the users of
that community, hence overcoming the limitations of other analyses [26, 29]
where online political conversations are studied in an unrelated fashion with
respect to the relational system amongst users sustaining them.

Our proposed approach allowed to reach several fine-grained insights about the
Italian case both at the macro level, grasping the semantic peculiarities of
broader conversations taking place within discursive communities, and, at the
micro level, narrowing down our exploration to single and meaningful points in
time during the electoral campaign period. Above and beyond the particular
case study we analysed, we believe that the same approach can be applied to
disentangle the intricacies of large-scale Twitter conversations in all
domains and regardless of the language in which they take place with the only
requirement of extracting the data set with a meaningful list of anchor
hashtags.

Paralleling these advantages, our approach remains limited mainly in two
respects. First however detailed and multilevel, our semantic analysis remains
a partial investigation of the symbolic universe that is produced and
circulated online in conjunction with relevant political events and dynamics.
The semantic structures we investigate in this paper are formed in the space
created by a single platform and pivot around the use of a specific feature
for marking contents - i.e., hashtags. Ad-hoc publics that assemble around
topics, in fact, are not exhausted by communities that form on particular
social media platforms - let alone around specific hashtags [56]. Moreover,
looking at conversations forming around specific hashtags fails to include
those contributions that, albeit pertinent, are delivered without including
any specific content markers [57]. The very procedure to discount all those
messages that did not contain an hashtag from the initial corpus of tweets
containing election-related keywords well illustrates the need to account for
multiple communicative actions performed by users.

Second, albeit automatically inferred and not depending in any way from
aprioristic assumptions on users’ political orientation, our discursive
communities are neither representative of the Italian voting population nor an
exact indication of users’ political affiliation. On the one side, it is
widely recognized that Twitter users are not representative of broader
populations (in this case, of all Italian citizens) and that Twitter Search
API does not guarantee the representativeness of the data themselves [58]. On
the other, the identification of discursive communities starts from retweets
which, as mentioned above, simply express an explicit bestowal of attention.
The total lack of information about the actual political affiliation of users
does severely limit our capacity to predict, starting from semantic data,
relevant political outcomes such as voters turnout, election results, or the
construction of political alliances between parties.

Nonetheless, without any claim of exhaustivity, our mapping of the Twitter
discussion in occasion of national elections provides a useful entry point to
reason around the online construction of political collective identities. A
plethora of studies based on Twitter freely available data has shown that it
is indeed possible to infer the political orientation of users from tweets and
to analyze electoral debates and societal discussions [12, 44, 13, 32, 45, 59]
shedding light on the political implications of non-traditional political acts
such as expressing publicly on social media. Users employing in their tweets
election-related keywords and hashtags did in fact contribute to frame the
electoral campaign period along certain lines and they did so upon a platform
that was not only widely diffused in Italy in that specific moment (According
to Audiweb [60], 9 millions of Italian users were active on Twitter in 2018)
but that also plays a pivotal political communication role [40]. Moreover, the
strict filtering procedure we applied leads to the identification of networks
with only statistically-relevant hashtags information, as the projections that
we adopted guarantees that the analysis of induced semantic networks is sound
from both a methodological and interpretative point of view. Thus, albeit non
representative of and non generalizable to the overall Italian population,
both discursive communities and induced semantic networks that we examined on
can be thought as a solid starting ground to develop more fine-grained studies
of voters’ political opinion and behaviors.

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## Acknowledgements

F. S. and T.S. acknowledge support from the European Project SoBigData++ (GA.
871042). F.S. also acknowledges support from the Italian ‘Programma di
Attività Integrata’ (PAI) project ‘TOol for Fighting FakEs’ (TOFFE), funded by
IMT School for Advanced Studies Lucca. E.P. acknowledges support from the
project "I-Polhys - Investigating Polarization in Hybrid Media Systems" funded
by the Italian Ministry of University and Research within the PRIN 2017
framework (Research Projects of Relevant National Interest for the year 2017;
project code: 20175HFEB3).

## Author contributions statement

T.R., E.P, T.S. and F.S. contributed equally to outline the research,
interpret the results, write and review the manuscript. T.R., T.S. and F.S.
provided the analytical and numerical tools and T.R. performed the analysis.

## Additional information

The authors declare no competing interests. T.R. is responsible for submitting
on behalf of all authors of the paper.

## Appendix

### Supplementary Note 1: Defining a similarity measure

A sequence-based similarity quantifies the cost of transforming a string $x$
into a string $y$ when the two strings are viewed as sequences of characters.
String transformation is defined by three elementary operations: 1) deleting a
character, 2) inserting a character and 3) substituting one character with
another [61]. The edit distance function $d(x,y)$ aims at capturing the
mistakes of human editing, such as inserting extra characters or swapping any
two characters. To merge only strings that are either misspelled or different
by number (i.e. singular in place of plural and viceversa) we have set the
threshold for the maximum number of allowed differences between any two
strings to 2.

### Supplementary Note 2: Projecting and validating bipartite networks

As anticipated in the main text, the idea behind a filtered projection is that
of _linking any two nodes belonging to the same layer if found to be
sufficiently similar_. The steps to implement such a procedure are described
below.

##### Quantifying nodes similarity.

First, a measure quantifying the similarity between nodes is needed. Given any
two nodes (say, $\alpha$ and $\beta$) we follow [35] and count the total
number of common neighbors $V_{\alpha\beta}^{*}$, i.e.

$V_{\alpha\beta}^{*}=\sum_{j=1}^{N_{\top}}m_{\alpha j}m_{\beta
j}=\sum_{j=1}^{N_{\top}}V_{\alpha\beta}^{j}$ (8)

the value of $V_{\alpha\beta}^{j}$ being 1 if nodes $\alpha$ and $\beta$ share
the node $i$ as a common neighbor and 0 otherwise. Notice that the non-
filtered projection of a bipartite network corresponds to a monopartite
network (say, $\mathbf{A}$) whose generic entry reads
$a_{\alpha\beta}=\Theta[V_{\alpha\beta}^{*}]$ (i.e. it is an edge in
correspondence of any non-zero value of $V_{\alpha\beta}^{*}$).

##### Quantifying the statistical significance of nodes similarity.

The statistical significance of any two nodes similarity is quantified with
respect to a bunch of null models which will be now derived from first
principles. To this aim, let us consider the maximization of Shannon entropy

$S=-\sum_{\mathbf{G}\in\mathcal{G}}P(\mathbf{G})\ln P(\mathbf{G})$ (9)

over the set of all, possible, bipartite graphs with, respectively, $N_{\top}$
nodes on one layer (say, users) and $N_{\bot}$ nodes on the other (say,
hashtags). Since entropy-maximization will be carried out in a constrained
framework, let us discuss each set of constraints separately.

Bipartite Configuration Model. The Bipartite Configuration Model (BiCM)
represents the bipartite variant of the Configuration Model (CM). Upon
introducing the Lagrangian multipliers $\bm{\theta}$ and $\bm{\eta}$ to
enforce the proper constraints (i.e. the ensemble average of the degrees of
users and hashtags, respectively
$h_{i}^{*}=\sum_{\alpha}m_{i\alpha},\>\forall\>i$ and
$k_{\alpha}^{*}=\sum_{i}m_{i\alpha},\>\forall\>\alpha$) and $\psi$ to enforce
the normalization of the probability, the recipe prescribes to maximize the
function

$\mathcal{L}=S-\psi\left[1-\sum_{\mathbf{G}\in\mathcal{G}}P(\mathbf{G})\right]-\sum_{i=1}^{N_{\top}}\theta_{i}[h_{i}^{*}-\langle
h_{i}\rangle]-\sum_{\alpha=1}^{N_{\bot}}\eta_{\alpha}[k_{\alpha}^{*}-\langle
k_{\alpha}\rangle]$ (10)

(with respect to $P(\mathbf{G})$. This leads to

$P(\mathbf{G}|\bm{\theta},\bm{\eta})=\frac{e^{-H(\mathbf{G})}}{Z}=\prod_{i=1}^{N_{\top}}\prod_{\alpha=1}^{N_{\bot}}\left(\frac{x_{i}y_{\alpha}}{1+x_{i}y_{\alpha}}\right)^{m_{i\alpha}}\left(\frac{1}{1+x_{i}y_{\alpha}}\right)^{1-m_{i\alpha}}=\prod_{i=1}^{N_{\top}}\prod_{\alpha=1}^{N_{\bot}}p_{i\alpha}^{m_{i\alpha}}(1-p_{i\alpha})^{1-m_{i\alpha}}$
(11)

where $x_{i}\equiv e^{-\theta_{i}}$ and $y_{\alpha}\equiv e^{-\eta_{\alpha}}$.
The quantity $p_{i\alpha}=\frac{x_{i}y_{\alpha}}{1+x_{i}y_{\alpha}}$ can be
interpreted as the probability that a link connecting nodes $i$ and $\alpha$
is there; the matrix of probability coefficients $\\{p_{i\alpha}\\}$ induces
the expected values $\langle
h_{i}\rangle=\sum_{\alpha}p_{i\alpha},\>\forall\>i$ and $\langle
k_{\alpha}\rangle=\sum_{i}m_{i\alpha},\>\forall\>\alpha$ and can be
numerically determined by solving the set of $N_{\top}+N_{\bot}$ equations
$\langle h_{i}\rangle=h_{i}^{*},\>\forall\>i$ and $\langle
k_{\alpha}\rangle=k_{\alpha}^{*},\>\forall\>\alpha$.

According to the BiCM, the presence of each $V_{\alpha\beta}^{j}$ can be
described as the outcome of a Bernoulli trial:

$\displaystyle f_{\text{Ber}}(V_{\alpha\beta}^{j}=1)$ $\displaystyle=$
$\displaystyle p_{\alpha j}p_{\beta j},$ (12) $\displaystyle
f_{\text{Ber}}(V_{\alpha\beta}^{j}=0)$ $\displaystyle=$ $\displaystyle
1-p_{\alpha j}p_{\beta j}.$ (13)

The independence of links implies that each $V_{\alpha\beta}$ is the sum of
independent Bernoulli trials, each one characterized by a different
probability. The behavior of such a random variable is described by a
Probability Mass Function (PMF) called Poisson-Binomial.

Bipartite Partial Configuration Model. The BiCM constrains the degrees of both
the users and the hashtags. Such a model can be ‘relaxed’ by limiting
ourselves to constrain the degrees of the nodes belonging to the layer of
interest - in this case, the degrees of the hashtags. Upon ‘switching off’ the
user-specific constraints, one end up with a simplified version of the BiCM,
characterized by a generic probability coefficient reading
$p_{i\alpha}=\frac{h_{\alpha}^{*}}{N_{\top}}$, in turn leading to the
expression
$f_{\text{Ber}}(V_{\alpha\beta}^{j}=1)=\frac{h_{\alpha}^{*}h_{\beta}^{*}}{N_{\top}^{2}}$.
The evidence that the latter expression does not depend on $j$ simplifies the
description of the random variable $V_{\alpha\beta}$, now obeying a PMF called
Binomial, i.e.

$f_{\text{BiPCM}}(V_{\alpha\beta}=n)=\binom{N_{\top}}{n}\left(\frac{h_{\alpha}^{*}h_{\beta}^{*}}{N_{\top}^{2}}\right)^{n}\left(1-\frac{h_{\alpha}^{*}h_{\beta}^{*}}{N_{\top}^{2}}\right)^{N_{\top}-n}.$
(14)

Bipartite Random Graph Model. The BiRGM (Bipartite Random Graph Model) is the
bipartite variant of the traditional Random Graph Model. As for its
monopartite counterpart, the probability that any two nodes are linked is
equal for all the nodes and reads
$p_{i\alpha}=\frac{N_{\top}N_{\bot}}{L}\equiv p_{\text{BiRGM}}$ (where $L$ is
the empirical number of ‘bipartite’ edges). In this case, we have
$f_{\text{Ber}}(V_{\alpha\beta}^{j}=1)=p_{\text{BiRGM}}^{2}$ and the PMF
describing the behavior of $V_{\alpha\beta}$ is a Binomial, i.e.

$f_{\text{BiRGM}}(V_{\alpha\beta}=n)=\binom{N_{\top}}{n}(p_{\text{BiRGM}}^{2})^{n}(1-p_{\text{BiRGM}}^{2})^{N_{\top}-n}.$
(15)

##### Validating the monopartite projection.

The statistical significance of the similarity of nodes $\alpha$ and $\beta$,
thus, amounts at computing a p-value on one of the aforementioned probability
distributions, i.e. the probability of observing a number of V-motifs greater
than, or equal to, the observed one:

$\mbox{p-value}(V_{\alpha\beta}^{*})=\sum_{V_{\alpha\beta}\geq
V_{\alpha\beta}^{*}}f(V_{\alpha\beta}).$ (16)

After this procedure is repeated for each pair of nodes, an $N_{\bot}\times
N_{\bot}$ matrix of p-values is obtained. The choice of which p-values to
retain has to undergo a validation procedure for testing multiple hypotheses
at the same time: here, the False Discovery Rate (FDR) procedure is used. The
$m$ p-values (in our case, $m=N_{\bot}(N_{\bot}-1)/2$) are, first, sorted in
increasing order, p-value${}_{1}\leq\ldots\leq$p-valuem and, then, the largest
integer $\hat{i}$ satisfying the condition

$\mbox{p-value}_{\hat{i}}\leq\frac{\hat{i}t}{m}$ (17)

(where $t$ represents the single-test significance level - in our case, set to
0.05) is individuated. All p-values that are less than, or equal to,
$\mbox{p-value}_{\hat{i}}$ are kept, i.e. all node pairs corresponding to
those p-values will be linked in the resulting monopartite projection.

### Supplementary Note 3: Analysing a network mesoscale structure

#### Community detection: the Louvain algorithm

After the daily monopartite user networks have been obtained, the Louvain
algorithm [62] has been run to detect the presence of communities. This
algorithm works by searching for the partition attaining the maximum value of
the modularity function $Q$, i.e.

$Q=\frac{1}{2L}\sum_{i,j}\left[a_{ij}-\frac{k_{i}k_{j}}{2L}\right]\delta_{c_{i},c_{j}}$
(18)

a score function measuring the optimality of a given partition by comparing
the empirical pattern of interconnections with the one predicted by a
properly-defined benchmark model. In the expression above, $a_{ij}$ is the
generic entry of the network adjacency matrix $\mathbf{A}$, the factor
$\frac{k_{i}k_{j}}{2L}$ is the probability that nodes $i$ and $j$ establish a
connection according to the Chung-Lu model, $\bm{c}$ is the $N$-dimensional
vector encoding the information carried by a given partition (the $i$-th
component, $c_{i}$, denotes the module to which node $i$ is assigned) and the
Kronecker delta $\delta_{c_{i},c_{j}}$ ensures that only the nodes within the
same modules provide a positive contribution to the sum. The normalization
factor $2L$ guarantees that $-\frac{1}{4}\leq Q(\bm{c})\leq 1$. Moreover, a
reshuffling procedure has been applied to overcome the dependence of the
original algorithm on the order of the nodes taken as input.

#### Core-periphery detection

Core-periphery detection can be carried out upon adopting the method proposed
in [52] and prescribing to search for the network partition minimizing the
quantity called _bimodular surprise_ , i.e.

$\mathscr{S}_{\parallel}=\sum_{i\geq l_{\bullet}^{*}}\sum_{j\geq
l_{\circ}^{*}}\frac{\binom{V_{\bullet}}{i}\binom{V_{\circ}}{j}\binom{V-(V_{\bullet}+V_{\circ})}{L-(i+j)}}{\binom{V}{L}};$
(19)

as anticipated in the main text, $L$ is the total number of links, while $V$
is the total number of possible links, i.e. $V=\frac{N(N-1)}{2}$. The
quantities marked with $\bullet$ ($\circ$) refer to the corresponding core
(periphery) quantities, i.e. $V_{\bullet}$ is the total number of possible
core links, $V_{\circ}$ is the total number of possible periphery links,
$l_{\bullet}^{*}$ is the number of observed links within the core and
$l_{\circ}^{*}$ is the number of observed links within the periphery.

From a technical point of view, $\mathscr{S}_{\parallel}$ is the p-value of a
multivariate hypergeometric distribution, describing the probability of $i+j$
successes in $L$ draws (without replacement), from a finite population of size
$V$ that contains exactly $V_{\bullet}$ objects with a first specific feature
and $V_{\circ}$ objects with a second specific feature, wherein each draw is
either a ‘success’ or a ‘failure’: analogously to the univariate case,
$i+j\in[l_{\bullet}^{*}+l_{\circ}^{*},\min\\{L,V_{\bullet}+V_{\circ}\\}]$. The
method outputs the most statistically significant core-periphery structure
compatible with the network under analysis.

### Supplementary Note 4: Computing the polarization of non-verified users

Let $C_{c}$, with $c=1,2,3$, indicate the set of (both verified and non-
verified) users belonging to community $c$ and $N_{\alpha}$, with
$\alpha=1,2,3$ the set of neighbours of verified users belonging to the
community $c=\alpha$. A non-verified user _polarization_ is defined as

$\rho_{\alpha}=\max_{c}\\{I_{\alpha c}\\}$ (20)

where

$I_{\alpha c}=\frac{|C_{c}\cap N_{\alpha}|}{|N_{\alpha}|}.$ (21)

As it has been shown in [44], the polarization index reveals how unbalanced is
the distribution of interactions between non-verified users and verified
users: non-verified accounts basically focus their retweeting activity on the
tweets of verified users within the same community, thus providing a clear
indication of the community of which a non-verified user is likely to be a
member.