Characterizing user archetypes and discussions on Scored.co

Andrea Failla1,2*, Salvatore Citraro2, Giulio Rossetti2, Francesco
Cauteruccio3

1 Department of Computer Science, University of Pisa, Pisa I56127, Italy

2 Institute of Information Science and Technologies “A. Faedo” (ISTI),
National Research Council (CNR), Pisa I56127, Italy

3 DIEM, University of Salerno, Fisciano I84084, Italy

<EMAIL_ADDRESS>
## Abstract

In recent years, the proliferation of social platforms has drastically
transformed the way individuals interact, organize, and share information. In
this scenario, we experience an unprecedented increase in the scale and
complexity of interactions and, at the same time, little to no research about
some fringe social platforms. In this paper, we present a multi-dimensional
framework for characterizing nodes and hyperedges in social hypernetworks,
with a focus on the understudied alt-right platform Scored.co. Our approach
integrates the possibility of studying higher-order interactions, thanks to
the hypernetwork representation, and various node features such as user
activity, sentiment, and toxicity, with the aim to define distinct user
archetypes and understand their roles within the network. Utilizing a
comprehensive dataset from Scored.co, we analyze the dynamics of these
archetypes over time and explore their interactions and influence within the
community. The framework’s versatility allows for detailed analysis of both
individual user behaviors and broader social structures. Our findings
highlight the importance of higher-order interactions in understanding social
dynamics, offering new insights into the roles and behaviors that emerge in
complex online environments.

## Introduction

In the last decades, the proliferation of social platforms and the
opportunities tied to each of them have drastically transformed the way
individuals interact, share information, and form communities. This
unprecedented growth in the scale and complexity of online interactions is
largely due to social networks like X (formerly known as Twitter), discussion
fora like Reddit, and even more niche platforms, like the now-defunct Voat,
known for their explorations of censorship-free models from the point of view
of specific political groups [29]. Hence, understanding user behavior within
these platforms has become a crucial area of research in computational social
science [26]. By studying how users interact with each other and with others’
content, researchers can uncover patterns of influence spread, opinion
formation, and creation and dissolution of communities [14]. These insights
are not only academically interesting but also have practical implications for
designing better social platforms, enhancing user experience, and mitigating
issues such as misinformation and online harassment. Moreover, understanding
these behaviors can aid in developing strategies for marketing, public health
campaigns, and even political mobilization, making this research area highly
relevant in multiple domains. Furthermore, all of these aspects are even more
critical in the analysis of understudied platforms. Indeed, platforms such as
Scored.co [34]111https://scored.co, which have not been extensively explored,
offer unique social dynamics that may differ significantly from “mainstream”
platforms. Investigating these less-explored environments can uncover novel
patterns of user behavior and mechanisms of information dissemination. Also,
understudied platforms often cater to niche communities or specialized
interests, thus providing insights into subcultures and micro-level social
dynamics that might not be straightforwardly visible on larger social
platforms.

Understanding these dynamics becomes particularly important when addressing
the general challenges inherent in studying complex social platforms. Among
all of these, a significant one is the identification of roles that users play
within complex social structures. Indeed, role identification is crucial for
various applications, including targeted information dissemination [47] and
community detection [10]. In traditional social network analysis, roles are
often determined based on patterns of dyadic connectivity and interactions.
Nevertheless, in a discussion on a social platform, two users can interact
directly, e.g., by sharing comments, but also indirectly, i.e., through other
users. Hence, it is fair to assume that taking into account group dynamics and
higher-order interactions could help in a more reliable identification of the
roles played by users. A promising approach to encapsulate group interactions
is defined by the concept of a social hypernetwork [5, 1, 15], which allows
for the modeling of relationships among groups of nodes, generally called
hyperedges. Such a representation is particularly useful for studying social
platforms from a higher-order point of view. Despite its importance and the
existing methodologies designed for pairwise graphs, current literature about
the problem of role identification lacks comprehensive approaches for social
hypernetworks.

To address this gap, in this work, we formally introduce an approach for
defining higher-order roles in a social hypernetwork and characterize higher-
order interactions. We define the concept of an archetype, a general
characterization of higher-order roles that serves as a “template” for
identifying nodes representative of specific roles within the context of
hyperedges. These archetypes provide a structured way to categorize and
understand the diverse roles users play in group interactions. Then, we
propose a general hyperedge characterization function, which allows one to
characterize a hyperedge w.r.t. features of the nodes contained in it.

To validate the effectiveness of our proposed framework, we conduct an
exhaustive experimental campaign on the understudied social platform
Scored.co, which offers a rich, yet understudied dataset for analyzing user
interactions in a hypernetwork context, making it an ideal testbed for our
framework. Our experiments demonstrate the utility of our approach in
characterizing user roles within social hypernetworks.

Summarizing, the main contributions of this work are as follows:

  * •

We define the concept of archetype, that is, a high-level description of user
roles that serves as a “template” characterizing nodes representatives;

  * •

We introduce an approach to characterize higher-order entities, such as
hyperedges, taking into account exhibited features and their higher-order
dynamics;

  * •

We design an exhaustive experimental evaluation in which we assess the
effectiveness of our framework on the understudied social platform Scored.co.
Notably, this is also the first work studying the structural properties of
Scored.co.

The outline of this paper is as follows: in the Related Literature section, we
provide a detailed overview of related literature. In the Materials and
methods section, we provide the formalization of our proposed approach by
defining the concept of archetype first, and the hyperedge characterization
function after. In the Experiments section, we illustrate the experimental
campaign we carried out to evaluate the effectiveness of our framework.
Finally, in the Conclusion section, we draw our conclusions and delineate some
future works.

## Related Literature

#### Hypernetworks and Role Identification

The identification of roles within social networks stands as a fundamental
aspect for understanding the dynamics and function of these complex systems
[39]. In traditional social network analysis, roles are often determined based
on patterns of connectivity that provide insights into the influence,
responsibilities, and grouping of individuals within the network [2]. This
analysis is crucial for applications ranging from the characterization of
polarization [37] and user behaviors [11] to the analysis of biological
networks [43] and animal populations [3]. In different cases, role
identification is also framed within the task of discovering influential users
in a social network. In light of this, we refer the interested reader to the
comprehensive survey proposed in [2].

Nevertheless, extending role identification into hypernetwork scenarios poses
many challenges. Unlike traditional networks, hypernetworks consist of
interactions, represented by hyperedges, that can encompass multiple nodes
simultaneously. Higher-order interaction models can better represent complex
real-world systems [42, 5]; however, the complexity of higher-order
interactions can introduce difficulties in accurately defining and identifying
roles, as traditional centrality metrics and methodologies (e.g., community
detection algorithms) often fall short in capturing the multidimensional
nature of hyperedges [32, 7, 39]. Despite the relevance of such a task, to the
best of our knowledge, there are no existing papers that explicitly discuss
role identification within the context of hypernetworks. Given this gap in the
literature, the rest of the section will concentrate on providing an overview
of the methodologies and findings from the conventional settings in dyadic
interactions, which may serve as a baseline for future exploration into
hypernetwork-specific role identification.

#### Role Identification in Pairwise Networks

The general task of role identification consists in capturing the multifaceted
characteristics of a node’s role in a pairwise network. The work in [22]
identifies roles in undirected, unweighted networks by evaluating node
importance using correlated indicators like degree and centrality measures. A
node’s role is then determined by comparing its indicator relationships to
statistical correlations within the overall network. While this work shares
the task of role identification with ours, the process does not involve group-
based indicators leveraging the concept of “groups” such as communities or
subgraphs. The work in [6] frames the node role identification tasks as a node
classification approach based on random walks. Similarly, framed within a
classification tasks, the authors in [9] focus on the so-called “answer-
person” role on Reddit, characterized by users who predominantly respond to
questions posed by others, with minimal engagement in broader discussions.
Both the works in [6] and [9] share a similar aim with ours. Nevertheless,
they rely on supervised approaches on pairwise graphs. Also, the methods might
not be straightforwardly generalized to higher-order interactions.

The approach proposed in [8] focuses on the identification of node roles in
dynamic social networks as a sequence of different types of activities, by
leveraging pattern subgraphs and sequence diagrams. Doing so, the authors are
able to capture roles such as the “gossipmongers”, i.e., users who replicate
every received message at least three times. The work in [8] can be considered
as orthogonal to ours, as an hypergraph mining approach could also be applied
in our context to enhance role identification. The authors in [18] outline a
process for identifying user roles in Enterprise Social Networks (ESNs), using
a mix of design science research and data mining, involving data collection,
preparation, and evaluation, with user roles identified through statistical
analysis, including PCA and clustering. The work in [18] shares a similar
focus with ours, although using a different methodology. The identification of
emergent leadership roles is addressed in [41], where the authors examine
collaboration patterns between teams and propose the so-called “leadership
index”, a combination of centrality measures including closeness and
betweenness. In [47], the authors propose a mixed-methods methodology for user
role identification, focusing on dynamic user profiling. Several types of
special users are defined and identified to support information dissemination.
The work in [47] proposes an approach based on computational methods and
questionnaire-based evaluation to quantitatively describe user features. Such
work parallels ours in the sense that it considers the network’s features,
too. In [10], the authors study community and user stereotypes in Reddit.
Here, with the term stereotype, the authors refer to the tendency to classify
people into groups and to associate each group with a general idea or a label.
The authors propose a rule-based approach based on different quantitative
views of the data, and define author stereotypes on the basis of two
orthogonal taxonomies, namely, the number of posts, and the number of comments
of an author. While the work in [10] and ours share some similarities, the
employed methodologies are substantially different. The former defines
stereotypes based on a single quantitative measure called score, which is
inherent to the social platform itself. Instead, our approach proposes a
general framework in which the characterization of users and the
identification of their role are both defined by their feature-rich, higher-
order surroundings. In [25], the authors identify five distinct social roles
in a specific community on Reddit. Among them, we cite the “knowledge broker”,
i.e., a member who introduces knowledge to the community by sharing links, and
the “translator”, i.e., a member who contributes academic knowledge. While the
contribution in [25] is notable and similar to ours for considering various
aspects of user characterization, these roles are specific and applicable only
to the analyzed community.

Finally, it is worth mentioning embedding-based methodologies [46], which
could potentially be adapted to hypernetwork scenarios. For instance, in [38],
the authors introduce a technique that incorporates node attributes to
generate embeddings that capture the similarities based on neighborhood
structures. Instead, in [13], the authors leverage both node and structural
embeddings to detect nodes impersonating social bots. Indeed, node embeddings
based on structural properties and exhibited attributes attracted substantial
interest in the last years [24]. While these methods use embedding techniques
that effectively summarize and exploit the structural information within
traditional networks, their application to hypernetworks might not be
straightforward. Our approach diverges from embedding-based methods in the
sense that it is specifically tailored to the unique features of nodes within
hypernetworks, such as their exhibited features w.r.t. the hyperedges
containing them. By focusing on this, without relying on an embedding, our
methodology seeks to offer a more direct and fitting analysis of node roles.

#### “Understudied” Social Platforms

We conclude this bird’s-eye view of the related literature by focusing on the
last contribution of our paper, that is the study of an understudied platform.
Indeed, the reasoning provided in the above discussion of related work is also
valid for this aspect. In fact, there is a moderate number of works on
understudied platforms, and generally these are limited to present a dataset
collection about the considered platform [34, 17, 36, 28]. For instance, a
large-scale dataset of the social platform Scored.co has been presented in
[34], in which the authors studied aspects such as posting activity and user
characterization, as well as the phenomenon of user migration from other
platforms. A recent social platform, called Bluesky, has been studied in [17,
36]. In the former work, the authors presented a comprehensive study of the
social structure of the platform, as well as posting activity and content
analysis. Also, the complete post history of over 4M users has been released.
Similarly, the latter work studied users’ political leaning and ideological
polarization on BlueSky while also presenting a characterization of the
network topology over time. Finally, in [28], the authors released a dataset
targeting the Indian microblogging platform Koo. The dataset consists of more
than 72M posts and 75M comments, with related features such as shares and
likes. Also, a thorough overview of the platform is presented, consisting of a
discussion of the news ecosystem on the platform, hashtag usage, and user
engagement.

## Materials and methods

In this section, we introduce our framework to characterize nodes and
hyperedges in a social hypernetwork, as well as the definition of roles,
called archetypes, in such a network. We start by providing some background,
which is useful to understand the frame of our context. Then, we introduce the
definition of archetypes and our method to calculate them. Finally, we detail
the proposed framework to characterize nodes and hyperedges.

### Background

Fig 1: A toy hypergraph. Nodes are labelled with capital letters. Nodes A, B,
C and D are connected by a hyperedge of size 4. Nodes C and E, D and E, D and
F, and E and F are pairwise connected.

A hypergraph $H=(V,E)$, $V=\\{v_{1},\dots,v_{n}\\}$ is the set of nodes,
$E=\\{e_{1},\dots,e_{m}\\}$ is the set of hyperedges, where $e_{j}\subseteq
V$, for $j=1,\dots,m$. A visual representation of a hypergraph is depicted in
Fig. 1. The order of $H$ is $n=|V|$, while the size of $H$ is $m=|E|$. We
denote with $E_{v_{i}}$ the set of hyperedges containing $v_{i}$, that is
$E_{v_{i}}=\\{e_{j}\in E:v_{i}\in e_{j}\\}$. Given a hyperedge $e_{j}\in E$,
its size is the number of nodes belonging to it, that is $|e_{j}|$. The degree
of a node $v_{i}$, denoted as $deg(v_{i})$, is the number of neighbors of
$v_{i}$; a node $v_{k}\in V$ is the neighbor of node $v_{i}$ if and only if
there exists at least one hyperedge $e_{j}$ which $v_{i}$ and $v_{k}$ both
belong to. The hyperdegree of a node $v_{i}$, denoted as $hdeg(v_{i})$, is the
number of hyperedges to which $v_{i}$ belongs. A graphical depiction of a
hypergraph is given in Fig. 1.

We use a hypergraph $H$ to model a social hypernetwork. Here, nodes are users
of the social hypernetwork, while a hyperedge represents a discussion between
users. In what follows, we will refer to the social hypernetwork simply as
hypernetwork.

Moreover, features can be associated with users, and these are generally based
on the content the users interact with and the discussions they participate
in. To formalize them, we employ a set of features $F=\\{f_{1},\dots,f_{l}\\}$
characterizing the nodes in $H$. Given a node $v_{i}\in V$,
$F_{i}=\\{f_{1_{i}},\dots,f_{l_{i}}\\}$ represents the values of each feature
of $v_{i}$, that is $f_{k_{i}}$ indicates the value of the $k$-th feature of
$v_{i}$. We assume features can be either numerical or categorical and that
numerical ones are always normalized. Also, with $H_{F}$, we indicate the
hypergraph equipped with the set of node features $F$.

### Archetypes for Nodes Characterization

The first aim of our approach is the definition of archetypes. An archetype
serves as a “template” to represent nodes characterized by a certain subset of
features from the set $F$. The concept of an archetype is pivotal in
characterizing higher-order node roles based on subsets of hyperedges. Often,
the study of a representation of nodes in a social network involves the
definition of a taxonomy or a more thorough analysis of the behavior of such
nodes [10]. Instead, our definition of archetype enables a more general
characterization of possible behavioral dynamics occurring among nodes, and
does not rely on a single attribute.

Let $F_{A}=\\{f_{1},\ldots,f_{p}\\}\subseteq F$ be a subset of features. Then,
an archetype $A$ is defined as a tuple of values based on the features
indicated by $F_{A}$. Formally, let $A=\langle
a_{1},a_{2},\ldots,a_{p}\rangle$, where $a_{j}$ is the value of the $j$-th
feature from $F_{A}$ for the archetype $A$. Then, each $a_{k}$, for
$k=1,\ldots,p$, represents a particular value of the $k$-th feature from
$F_{A}$ that characterizes the nodes associated with this archetype. As an
example, let $F_{A}=\\{f_{\texttt{sent}},f_{\texttt{tox}}\\}$, where
$f_{\texttt{sent}}$ (resp., $f_{\texttt{tox}}$) is the value of a quantitative
feature indicating the average sentiment value (resp., average toxicity value)
expressed by a user. Such features are extensively used in various data
science-based studies and can be easily computed via classical methods such as
VADER [23] and Detoxify [20]. Suppose $f_{\texttt{sent}}\in[-1,1]$, where $-1$
(resp., $1$) indicates a mostly negative (resp., mostly positive) average
sentiment, and $f_{\texttt{tox}}\in[0,1]$, with higher values indicating a
high degree of toxicity. Then, various archetypes could be defined based on
these features. For instance, we could define the archetype
$A=\langle-1,0.5\rangle$ that describes a template for users that are
extremely negative and are toxic on average, and we could name this archetype
as _Cinically Commenter_ ; instead, the archetype $A=\langle 1,0.5\rangle$
would be a template for users that are extremely positive and exhibit moderate
toxicity, and we could name it as _Overzealous User_. Also, it is noteworthy
that, for the sake of presentation, here the definition of archetype is only
given w.r.t. nodes. Nevertheless, in case of features being also available for
hyperedges, then the same definition applies, and archetypes for the latter
can be defined.

Essentially, an archetype $A$ can be viewed as a prototypical example of nodes
that share similar feature values. To simplify the analysis and categorization
of archetypes, instead of taking into account the feature values directly, we
can map them into categorical values, indicating the state of the feature for
the particular archetype. This approach involves setting a series of
thresholds $T=\langle t_{1},\dots,t_{p}\rangle$, where the value $t_{j}$ has
the same domain of the feature $f_{j}$ in $F$, a set of labels $L$ and a
labeling function $\iota$. Then, given an archetype $A=\langle
a_{1},\dots,a_{p}\rangle$, by applying to each feature $a_{j}$ the
corresponding threshold $t_{j}$ from $T$ via the labeling function $\iota$, we
derive the archetype $A_{T}=\langle a^{t}_{1},\dots,a^{t}_{2}\rangle$, where
$\iota(a_{j},t_{j})=a^{t}_{j}$ is a label in $L$. Practically speaking,
$A_{T}$ represents the same archetype as $A$, but its representation is now
built over a specific set of labels. Let us take the aforementioned archetype
$A=\langle 1,0.5\rangle$, defined over the set of features
$F_{A}=\\{f_{\texttt{sent}},f_{\texttt{tox}}\\}$, and representing Overzealous
Users. Suppose we set $T=\langle 0,0.75\rangle$, and we set
$L=\\{\texttt{low},\texttt{high}\\}$. Also, suppose we define the labeling
function $\iota$ as

$\iota(a_{j},t_{j})=\begin{cases}\texttt{low}&\text{if}\ a_{j}\leq t_{j}\\\
\texttt{high}&\text{otherwise}\end{cases}$

Therefore, in this example, we derive
$A_{T}=\langle\texttt{high},\texttt{low}\rangle$, which can be seamlessly
interpreted as representing users exhibiting a high sentiment value and a low
toxicity value. Note how the labeling depends on the thresholds $T$, thus
allowing for flexibility that can accommodate different contexts of analysis.

Finally, we are now able to state when a node is represented by a given
archetype. Given an archetype $A=\langle a_{i},a_{2},\dots,a_{p}\rangle$,
based on a subset of features $F_{A}=\\{f_{1},\ldots,f_{p}\\}\subseteq F$, we
want to effectively understand what nodes are represented by it. Let $v_{i}\in
V$ be a node, and let $F_{A}(v_{i})=\langle
f_{i_{1}},f_{i_{2}},\dots,f_{i_{p}}\rangle$ be the feature vector of node
$v_{i}$ according to the features selected in $F_{A}$. The node $v_{i}$ can be
considered as represented by the archetype $A$ if $F_{A}(v_{i})$ is
sufficiently close to $A$, according to a predefined distance metric $d$. We
express it as $d(F_{A}(v_{i}),A)\leq\epsilon$ where $\epsilon$ is a small
positive threshold value that determines the acceptable distance between the
node’s feature vector and the archetype. Note that both $A$ and $F_{A}(v_{i})$
can be considered as vectors of the same length $p$; thus, classical distance
metrics, such as the cosine similarity [40], can be used. Furthermore, as we
will see in the experiments, in the simplest case also a feature-wise
comparison can be used to assess when a node can be considered as represented
by a given archetype.

#### A Characterization for Archetypes

To comprehensively understand and categorize user archetypes, we decide to
observe them through three different expressions, namely, (i) emotional, (ii)
psycho-emotional, and (iii) moral expressions. By leveraging well-established
psychological theories and lexicons, we aim to create detailed profiles that
reflect the peculiar ways in which users interact and participate within the
social platform. In what follows, we describe in detail these three
expressions, which we will subsequently use in our experiments.

##### Emotional Profiles

We aim to characterize archetypes based on the emotions they express. To do
so, we refer to the psychological theory of emotions [35] developed in 1980 by
the American psychologist Robert Plutchik. This theory identifies eight basic
emotions — joy, trust, fear, surprise, sadness, anticipation, anger, and
disgust — and claims that all other emotions derive from a mixture of these
primary ones. To quantify feelings expressed by Scored users, we leverage the
NRCLexicon (National Research Council Lexicon) [31], a resource containing
over 14,000 English words and their associated emotional ratings according to
Plutchik’s theory. This dictionary is further expanded in
222https://github.com/metalcorebear/NRCLex to include WordNet synonyms,
reaching over 27,000 terms. For each of the users’ texts, we compute emotion
scores, and normalize them in [0, 1]. In this context, 0 indicates texts that
do not elicit any emotion, while 1 signifies texts that strongly evoke the
specified emotion.

##### Psycho-emotional Profiles

We also characterize how user archetypes relate to their surrounding social
environments. To do so, we refer to the PAD model (Pleasure, Arousal,
Dominance) introduced by Mehrabian and Russell in 1974 [27]. According to the
PAD model, three dimensions characterize the perception an individual has of
the environment in which she finds herself. Pleasure (sometimes referred to as
valence) concerns whether an individual perceives the environment as enjoyable
or not. Arousal measures how stimulating the environment is for the
individual. Dominance indicates whether the individual feels in control of the
environment. To operationalize these dimensions, we leverage the VAD Lexicon
(Valence, Arousal, Dominance) [30]. This resource contains over 20,000 English
terms, along with their associated valence/pleasure, arousal, and dominance
values. For each of the three dimensions, we associate each text with the
total score of its words. Then, we normalize results in [0,1], where 0 implies
an absence of the corresponding dimension, and 1 implies the strong presence
thereof.

##### Moral Profiles

We aim to characterize archetypes based on the moral dimensions that emerge
from the content they produce. We rely on the Moral Foundations Theory, a
psychological framing rooted in cultural anthropology that postulates the
existence of five universal moral dimensions [19]: authority/subversion,
care/harm, fairness/cheating, loyalty/betrayal, and sanctity/degradation. Each
dimension is composed of a virtue (e.g., loyalty), and a corresponding vice
(e.g., betrayal). Virtues can be understood as follows, while vices can be
considered their opposites. The concept of authority can be defined in
relation to specific traits, such as deference to higher authorities, in order
to maintain group cohesion. Similarly, the concept of care can be understood
in terms of nurturing and protection. Fairness can be conceptualized in terms
of equal treatment and reward. Loyalty can be understood in relation to the
prioritization of one’s group and alliances. Finally, sanctity can be defined
in terms of the maintenance of the sacredness of the body and the avoidance of
moral contamination. We operationalize this framework via the eMFD (Extended
Moral Foundations Dictionary), a lexicon containing more than 3,000 words
[21]. Each word has an associated score in [-1, 1] for each foundation,
ranging from strong vice outage (-1) to strong virtue outage (1).

### Analyzing Higher-Order Entities

While archetypes are a particular yet effective way to analyze entities within
the social platform, they mainly focus on the node features, whereas
interactions are not taken into account. Hence, we define here a general
characterization function to characterize nodes and hyperedges according to
their exhibited features and higher-order dynamics. Without loss of
generality, we propose the definition of such a function w.r.t. hyperedges.
The same can be also applied to nodes.

Let $H_{F}=(V,E)$ be a hypergraph equipped with the node features set $F$. We
denote with $\omega$ a function which we call the hyperedge characterization
function. The need for a function such as $\omega$ addresses the challenge of
characterizing a hyperedge w.r.t. the nodes contained in it. Let us recall
that our approach deals with analyzing higher-order entities. To do so, we
exploit the representation of node relationships via hyperedges. While it
effectively captures the higher-order structural interactions between nodes,
it might not be sufficient in acquiring insights into the semantics of such
interactions. Therefore, we focus on the latter aspect through a
characterization of hyperedges that is based not only on the contained nodes
but also on their features. Formally, the domain of our hyperedge
characterization function is $E$. $\omega$ takes in input a hyperedge $e\in E$
and returns a value $\omega(e_{j})$, which we call its characteristic value.
Such value depends on the actual implementation $\omega$: in fact, $\omega$ is
general, and different approaches can be exploited to accommodate the
hyperedge characterization. Furthermore, to address the aforementioned
challenge, there are cases in which $\omega$ should be defined to consider the
values of each node’s features contained in the considered hyperedge. Given a
feature of interest $f_{k}$, we write $\omega^{k}$ to denote that the actual
implementation of $\omega$ considers the feature $f_{k}$.

In the following, we propose various specializations of $\omega$ and a brief
rationale for each of them. Some of these specializations are used in the
Experiments section. We separate them in three families, namely, (i)
numerical-only definitions, (ii) categorical-only, (iii) structural-based
ones. In describing each of them, we assume we are interested in
characterizing a hyperedge $e\in E$. Also, there are different specializations
that are intended to be exploited when the analysis we are carrying out is
feature-oriented. Therefore, in these cases, we assume having a feature
$f_{k}$ of interest.

##### Numerical-only specializations

The following specializations are intended to be used when numerical features
are considered within the investigation. Therefore, here we assume the feature
$f_{k}$ of interest is numerical. Some specializations are:

  * •

Statistics Descriptors: common statistics descriptors such as mean, median,
mode, variance, and standard deviation of the feature $f_{i}$ among the nodes
in $e$ can be easily computed. For instance, the mean would be simply defined
and denoted as $\omega_{\text{avg}}=\frac{\sum_{u\in e}f_{i_{u}}}{|e|}$.

  * •

MAD: calculates the Mean Absolute Deviation of the feature $f_{i}$ among the
nodes in $e$, that is $\omega_{\text{mad}}(e)=\sum_{u\in
e}\frac{|f_{i_{u}}-\omega_{\text{avg}}|}{|e|}$.

  * •

Gini Coefficient: employs the Gini Coefficient to compute the dispersion of
the values of $f_{i}$ among the nodes in $e$, that is
$\omega_{\text{Gini}}(e)=\sum_{u\in e}\sum_{v\in e,u\neq
v}\frac{|f_{i_{u}}-f_{i_{v}}|}{2\overline{f_{i}}|e|^{2}}$.

##### Categorical-only definitions

Different from the previous ones, the following specializations are intended
to be used when categorical features are considered. Therefore, here we assume
the feature $f_{k}$ of interest is categorical. Some specializations are as
follows:

  * •

Entropy: measures the cohesion of the values of $f_{i}$ among the nodes in
$e$. We define and denote it as $\omega_{\text{entr}}(e)=-\sum_{u\in
e}r_{i_{u}}log(r_{i_{u}})$, where $r_{i_{u}}$ denotes the proportion of the
value of feature $f_{i_{u}}$ over all nodes in $e$.

  * •

Gini Impurity: measures the probability of incorrectly classifying a randomly
chosen element in the dataset if it were randomly labeled according to the
distribution of all categories in the dataset. Here, we employ it on the
feature $f_{i}$, thus we define and denote it as
$\omega_{\text{GiniImp}}(e)=1-\sum_{u\in e}r_{i_{u}}^{2}$, where $r_{i_{u}}$
denotes the proportion of the value of feature $f_{i_{u}}$ over all nodes in
$e$.

##### Structural-based specializations

The structural-based specializations focus on characterizing a hyperedge based
on its exhibited structural properties rather than only focusing on the
features of the contained nodes. Some proposed specializations are the
following:

  * •

Hyperedge Size: the measure is simply given by the size of the hyperedge $e$,
that is $\omega_{\text{size}}(e)=|e|$, regardless of the feature $f_{i}$.

  * •

Purity: Here, the measure indicates the homogeneity of the values of $f_{i}$
in $e$, that is $\omega_{\text{purity}}(e)=\frac{max({count(f_{i_{u}}):u\in
e})}{|e|}$.

  * •

Cohesion: the characterization of the hyperedge $e$ is given by the mean
pairwise similarity of the value of the feature $f_{i}$ for each pair of node
$u,v\in e$. Formally, given a similarity function $sim(\cdot,\cdot)$ defined
for two features, we define
$\omega_{\text{cohes}}(e)=\frac{2}{|e|(|e|-1)}\sum_{u\in e}\sum_{v\in e,v\neq
u}sim(f_{i_{u}},f_{i_{v}})$.

  * •

Interaction potential: the hyperedge $e$ is characterized by its capacity to
create external connections, i.e., connections that span outside the
hyperedge. It measures the extent to which the hyperedge facilitates
interactions beyond its mere composition. Formally,
$\omega_{\text{intpot}}(e)=\frac{|\\{v\in V\setminus e:\exists u\in e,v\sim
u\\}|}{|e|}$, where $v\sim u$ indicates that $v$ and $u$ are neighbors within
a hyperedge different from $e$. The denominator can be $|e|$, i.e., only the
nodes in $e$ are taken into account, or $|V\setminus e|$, i.e.,
$\omega_{\text{intpot}}$ is sensitive to the order of the hypergraph.

## Experiments

In this section, we present an experimental evaluation carried out to assess
the efficacy of our framework. In what follows, we first provide a
characterization of the understudied dataset regarding the social platform
Scored.co. We study archetypes based on platform-specific and linguistic
features, and we illustrate how our proposed framework allows for a
comprehensive analysis of them. Then, we focus on the constructed
hypernetworks, and we provide a characterization of discussions, that is,
hyperedges, through our proposed hyperedge characterization function.

### Dataset

We focus on the Scored.co social platform, which hosts a network of
communities that users can create and join. The platform shares different
similarities with the more common platform Reddit333https://reddit.com. Users
can join communities related to various topics, from politics to memes, and
upvote content they like, and downvote content they dislike. The number of
upvotes minus the downvotes constitutes a post’s score, i.e., a value that
indicates the content’s usefulness and/or relevance to the discussion.

Interestingly, Scored.co acted as a shelter for many far-right/alt-right
communities after the 2020 massive Reddit bans [12]. Some of these maintained
their names and key figures, e.g., c/TheDonald, c/GreatAwakening, ultimately
acting as a continuation of the original ones. This platform has allowed users
to freely share their views without the risk of being banned. Scored.co is an
emerging yet understudied platform, potentially hosting dangerous content.
Despite its growing user base, it has received relatively little academic
attention compared to other social media platforms, as we pointed out in the
Related Literature section. The loosely moderated nature of some communities
can lead to the spread of misinformation, hate speech, and radical ideologies.
This makes Scored.co a platform of interest for researchers studying online
extremism, digital sociology, and the impacts of social media on public
discourse.

To build the dataset our experiments are carried out on, we collect data from
the Scored.co platform via the official
API444https://help.scored.co/knowledge-base/getting-started-with-the-api/. To
retrieve as much content as possible, we use a breadth-first search technique
by first gathering all posts and comments authored by C, one of the platform’s
admins, which is one of the most active users on the platform. Then, the
content is parsed to retrieve other users and their related content. We repeat
this procedure until no new user is found. Eventually, we find 207,554 unique
users (referenced to by their username), 4,398,074 posts, and 36,978,685
comments. Our data collection process started on June 9th, 2024, and ended on
June 22nd, 2024. The final dataset comprises higher-order interactions on
Scored.co starting from the platform’s launch on October 15th, 2019, and
ending on June 1st, 2024.

To improve reproducibility and share our findings, we release the dataset on
Zenodo [16]. The dataset is anonymized and provides:

  * •

Higher-order interactions extracted from discussion threads. Each
thread/hyperedge is labeled with the community it is extracted from (e.g.
c/TheDonald), and the year and month when the root post was created;

  * •

User profiles, namely a set of features characterizing each user at every time
stamp.

A Python data collection script is also enclosed in the repository. In the
first release of this dataset, only user/thread data leveraged in this study
is shared (i.e., 2023 data from the c/TheDonald community, see next section).
However, we plan to update it in the near future to include statistics and
interactions for all users, leveraging Zenodo’s versioning system. Our dataset
complies with the fair guidelines for data sharing [44], which are as follows:

  1. 1.

Findable. We release the data on Zenodo 555https://zenodo.org/, a service
managed by CERN that also assigns a DOI to the repository, ensuring
findability. Moreover, we indexed it also on the SoBigData Research
Infrastructure (URL: http://sobigdata.eu/), an EU-funded RI providing curated
datasets and algorithms advocating open science;

  2. 2.

Accessible. The dataset is freely accessible to anyone with an internet
connection;

  3. 3.

Interoperable. All data is released in CSV files, which can be read and
manipulated with most programming languages;

  4. 4.

Reusable. Files, fields, and data collection methods are described in a
dedicated document released within the repository, ensuring reusability.

### Higher-order Interactions and Analysis

Given the previously described dataset, we are now able to construct the
hypernetworks which constitutes the basis of the experiments. We start by
constructing a hypernetwork ${\cal H}=(V,E)$, where $V$ denotes the set of
Scored.co users who participated in at least a discussion, while $E$ denotes
the set of hyperedges encoding discussion threads. That is, a user $v$ appears
in $V$ if they participate in at least one discussion. Also, we discard all
hyperedges of size 2 due to the fact that we are interested in studying
higher-order interactions. This means that, for all $e\in E$, $|e|>2$. Since
discussion topics on Scored are varied, ranging from politics to sports,
memes, and more, we decided to center our analysis on discussions taking place
in c/TheDonald during 2023. This community is a controversial and highly
active online group that originally formed on Reddit before migrating to
platforms like Scored.co [12]. We chose it because it is the oldest and most
active community on the platform, covering 74% of all collected posts and
comments. This allows us to maintain topic continuity without sacrificing
large portions of the data. Note that ${\cal H}$ is a hypernetwork that
represents the whole dataset. To enable analyses on the time dimension, we
construct a hypergraph ${\cal H}_{t}=(V_{t},E_{t})$, for each month
$t=1,\dots,12$, containing users and discussions relative to month $t$.

In Table 1, we report summary statistics of all the constructed hypernetworks.
The table reports basic statics, such as nodes and hyperedges number $|V|$ and
$|E|$, respectively, the largest hyperedge size $max_{|e|}$, the average
hyperdegree $\overline{hdeg}$, and the average degree $\overline{deg}$. Also,
for each pair of adjacent timestamps $1\leq t,t_{+1}<12$, we report the
Jaccard similarity index between node sets. The last row of the table reports
the same information for the hypernetwork ${\cal H}$.

Table 1: Statistics of the constructed hypergraphs. From left to right: number of nodes, number of hyperedges, largest hyperedge size, average hyperdegree, average number of neighbors, and Jaccard similarity index between adjacent timestamps. The bottom row refers to the aggregated hypergraph $\mathcal{H}$. $t$ | $|V|$ | $|E|$ | $max_{|e|}$ | $\overline{hdeg}$ | $\overline{deg}$ | $Jaccard_{t,t+1}$
---|---|---|---|---|---|---
1 | 10889 | 28280 | 293 | 19.59 | 394.17 | 0.63
2 | 10018 | 24234 | 230 | 18.24 | 348.39 | 0.63
3 | 10245 | 26393 | 411 | 19.18 | 382.09 | 0.63
4 | 10203 | 25406 | 428 | 18.72 | 375.51 | 0.64
5 | 9922 | 25681 | 368 | 19.43 | 391.11 | 0.64
6 | 9594 | 24558 | 357 | 19.13 | 359.61 | 0.63
7 | 9400 | 23869 | 225 | 19.00 | 335.22 | 0.62
8 | 9449 | 24542 | 380 | 19.30 | 358.27 | 0.63
9 | 9022 | 24132 | 454 | 19.90 | 364.10 | 0.63
10 | 9179 | 29632 | 241 | 23.39 | 376.16 | 0.64
11 | 8865 | 24962 | 258 | 20.77 | 351.09 | 0.65
12 | 8402 | 22711 | 216 | 20.34 | 333.75 | -
all | 20937 | 321860 | 454 | 112.8 | 1090.89 | -

From the analysis of this table, we can observe different insights. First off,
the aggregated hypernetwork $\mathcal{H}$ includes interactions among roughly
20% of all discovered users. Indeed, on average, users participate in 113
discussions (hyperedges) throughout the year, and in 18-20 discussions each
month. Scored.co users are exposed to $\sim 1K$ unique peers, with a monthly
average of 300-400, thus showing locally dense patterns consistently over
time. We can also observe how the largest hyperedge size exhibits some
variations but remains in the same order throughout the whole period. This
indicates the presence of a highly connected subgroup at certain timestamps.
The average hyperdegree $\overline{hdeg}$ remains relatively stable across
timestamps, indicating that on average, each node is part of $\sim 20$
hyperedges. The average degree $\overline{deg}$ remains fairly consistent,
too. To complement these statistics, we try observing with a more detailed
look the distribution of hyperdegree and hyperedge size, which are depicted in
Figures 2 (a) and (b), respectively. From the analysis of these figures, we
can see that both show the typical power-law behavior observed in many real-
world hypernetworks [33]. We observe how a few users participate in a large
number of discussions, while most users participate in just a few. The
hyperedge size distribution (Fig. 2 (b)) displays a similar shape, with mostly
small discussions and a few large ones. We also note how these patterns are
consistent over time, with 44% interactions of at least size 5, 15%
interactions of at least size 10, and 2% interactions of at least size 50.
Finally, in Table 1, we can observe that the overlap between adjacent
timestamps, calculated via the Jaccard similarity index between subsequent
node sets $V_{t}$ and $V_{t+1}$, is large and coherent over time, stabilizing
on 64% on average. Overall, the studied part of this platform emerges as a
locally dense online community with temporally stable structural patterns and
significant user engagement, which makes it interesting to study with our
approach.

Fig 2: Hyperdegree (a) and hyperedge size (b) distributions for the aggregated
hypergraph

### Identification and Analysis of Archetypes

We recall that a core aspect of our approach relies on identifying archetypes,
namely typical patterns that can give us approximate descriptions of
individual element behaviors. As we also noted in Archetypes for Nodes
Characterization section, archetypes can be easily defined for nodes and
hyperedges. In this section, we aim to characterize user behaviors. Therefore,
henceforth we refer to archetypes as related to nodes/users.

To define user archetypes, we combine platform-specific and linguistic
features. Specifically, we outline eight archetypes based on these features
and their values. The features we decide to use are, namely, (i) score, (ii)
sentiment, and (iii) toxicity. As far as the score is regarded, we compute the
average post score for each user, then we normalize values in $[0,1]$. For the
sentiment feature, we use the well-known VADER algorithm [23], a rule-based
sentiment classifier that assigns each text positive, negative, neutral, and
compound sentiment intensity values. Out of these, the compound sentiment is a
score in $[-1,1]$ going from the most extreme negative ($-1$) to the most
extreme positive ($1$) sentiment. For our purposes, we compute the average
compound scores for each user and rescale values in $[0,1]$. Moreover, for the
toxicity feature, we compute its values with Detoxify [20], a neural toxicity
detection model that returns the probability that a text contains toxic
language, and also in this case, we normalize the obtained values. Finally, to
discern between high and low values for each feature, we set a threshold of
0.5, such that when a feature has a value higher than this threshold, it is
considered high, and vice-versa.

The list of the eight archetypes defined is depicted in Table 2. Here, we can
observe how setting the various combinations of the state of a feature (high
or low) creates different archetypes. We defined these archetypes in order to
encapsulate the inherent semantics of the discussions taking place in the
studied dataset. For instance, the first row is the so-called Community Hero,
which represents users who consistently contribute positively to the
discussion by maintaining a positive and supportive attitude without engaging
in toxic behavior. A detailed characterization of these archetypes is given in
the following section.

Table 2: User Archetypes Based on Score, Sentiment, and Toxicity. Score | Sentiment | Toxicity | Archetype Name | #
---|---|---|---|---
H | H | L | Community Hero | 419
H | H | H | Controversial Star | 21
H | L | L | Respected Critic | 15286
H | L | H | Infamous Celebrity | 807
L | H | L | Benevolent Underdog | 267
L | H | H | Positive Provoker | 25
L | L | L | Quiet Critic | 3643
L | L | H | Malcontent | 469

#### Archetype Characterization

Having defined the archetypes, we are now able to provide a characterization
of them, based on multiple psychological and social dimensions. More in
detail, we describe the behaviors of these types with respect to the different
aspects highlighted in the A Characterization for Archetypes section. We
recall that these aspects are, namely, the (i) environment perception, the
(ii) emotions, and (iii) morality.

To control for class size imbalances, we compare average values for multiple
features across the top 10 most archetypal users for each archetype, i.e., the
most representative users for each category. We rank users according to their
typicality, which is defined as follows:

$Typicality(u)=\prod_{f}\alpha_{f}f(u)$ (1)

Here, $u$ is the target user; $f$ is a function computing $u$’s characteristic
score, sentiment, or toxicity; $alpha_{f}$ is a coefficient that equals 1 if
$u$’s archetype has a high value for $f$ and, conversely, -1 if $u$’s
archetype has a low value for $f$. As an example, a Community Hero’s
typicality is maximized when its score is 1, its sentiment value is 1, and its
toxicity value is 0. Thanks to the definition of typicality, we are now able
to characterize each archetype with respect to the aforementioned aspects.
Along with the characterization, in Fig. 3, we depict the profiles of each
archetype. The top part of the figure represents the profiles according to
Plutchik’s wheel of emotions. The middle part, instead, represents the
profiles according to the Pleasure/Arousal/Dominance model. Finally, the
bottom part depicts the profiles according to the Moral Foundations theory.

Fig 3: Archetype Profiles according to (a) Plutchik’s wheel of emotions, (b)
the Pleasure/Arousal/Dominance model and (c) Moral Foundations Theory.

##### Benevolent Underdogs.

With respect to their psychological features, Benevolent Underdogs are
characterized by high trust (0.18), joy (0.14), and anticipation (0.11), low
arousal (0.44) and high valence (0.66). These users have a positive and
optimistic outlook, showing happiness and hopefulness in their interactions.
From their feature values, a possible interpretation can suggest them as users
focusing on creating a supportive environment and emphasizing social cohesion.
It is important to note that, for this archetype as well as all the following
ones, these descriptors can lead only to qualitative suggestions and
interpretations of their behaviors.

##### Community Heroes.

Such users are characterized by high trust (0.17), joy (0.12), and
anticipation (0.14), low arousal (0.45) and high valence (0.64). Thus, their
psychological profile is similar to Benevolent Underdogs, with a generally
positive outlook. From a moral focus perspective, they mostly emphasize
loyalty and, to an extent, authority. Community Heroes and Benevolent
Underdogs essentially behave in the same way, although the former are more
recognized. Thus, we hypothesize that Community Heroes often provide support
in more prominent and/or critical situations, gaining greater acknowledgement
from the community.

##### Controversial Stars.

With respect to their psychological features, Controversial Stars show signs
of joy (0.13), trust (0.12), and anger (0.10), as well as high valence (0.60).
This indicates that while they have a positive emotional tone and are capable
of experiencing happiness and trust, they can also exhibit anger. This leads
to an interpretation of this archetype as an emotionally charged one, with a
tendency to express both positive and negative tones. Moreover, they mostly
emphasize loyalty and authority moral dimensions.

##### Infamous Celebrities.

Infamous Celebrities show high signs of anger (0.14), fear (0.14), and disgust
(0.10). Arousal (0.53) and Dominance (0.50) are average, while Valence is
slightly below average (0.48). Their complex psychological profile hints at
expressions of negative tones, perhaps toxic interactions. High levels of fear
could indicate a tendency to anticipate negative outcomes, which can make
their discourse more alarmist. Disgust contributes to a critical and often
harsh tone. Average arousal and dominance could suggest a moderate level of
engagement with the environment, whereas their slightly below-average valence
could be a sign of negative interactivity. Moral dimensions of care, fairness,
loyalty, authority, and sanctity display negative values. This moral outlook,
combined with their negative emotional profile, contributes to their
provocative, even controversial, behavior.

##### Malcontents.

Malcontents are characterized by high values for disgust (0.13), and anger
(0.11). This is paired with below-average values for Valence (0.39) and
Dominance (0.45), and high Arousal (0.61). This emotional profile could reveal
a full negative profile. The archetype shows high arousal as well as strong
emotional responses and engagement, but also low valence and dominance. This
could mean the users belonging to it often display dissatisfaction, leading to
discontented interactions. Morally, Malcontents use vice-oriented language,
focusing on sanctity/degradation and care/harm. Their low values in these
areas could indicate strong criticism and a tendency to vent.

##### Quiet Critics.

The Quiet Critics’ psychological profile outlines an emotional landscape
characterized by high levels of sadness (0.11), fear (0.14), and anger (0.12).
These predominant features suggest a dissatisfaction with their environment.
Anger, although present, paired with low toxicity values, could suggest a
profile expressing criticism in a non-confrontational way rather than being
directly hostile. With average levels of Valence, Arousal, and Dominance,
their emotional responses are steady an moderated. From a moral perspective,
Quiet Critics’ language frequently involves vice-oriented terms, particularly
focusing on sanctity/degradation, care/harm, and loyalty/betrayal. Their
emphasis on sanctity could interestingly suggest a concern for moral purity,
whereas the focus on care/harm could highlight preoccupation with injustice.
Their attention to loyalty/betrayal could indicate a sensitivity to perceived
trust, which might align with their cautious-yet-critical nature.

##### Respected Critics.

The Respected Critics’ psychological profile is similar to those of the Quiet
Critics, mostly eliciting sadness (0.8), fear (0.14), and anger (0.12).
Sadness and fear highlight their anticipation of negative outcomes, possibly
making their critiques cautionary. Anger drives their behavior, moderated by
average levels of valence, arousal, and dominance. Their moral profile
resembles that of the Quiet Critics.

##### Positive Provokers.

Positive Provokers are characterized by high levels of trust (0.18) and joy
(0.13). They show average Dominance (0.54) and Arousal (0.49) values, as well
as high Valence (.60). Their high trust and joy could suggest they generally
expect positive interactions from others and have a positive disposition. The
high Valence reflects their overall positive emotional tone. However, despite
these positive traits, their high toxicity scores reveal a tendency to a
duality, that we could interpret as a confrontational/provocative
communication styleThis dichotomy of positivity and toxicity creates a complex
profile where users intentions may be good, but their execution can be
damaging to others.

#### Archetypes Transitions

In this section, we aim to explore the temporal dimension of user interactions
within the Scored.co community and understand whether significant transitions
exist between the identified archetypes. By analyzing these transitions, we
can gain insights into how user behaviors evolve over time. This analysis not
only helps in understanding the fluidity of user roles but also potentially
provides valuable information for targeted interventions and community
management.

In order to carry out this analysis, we propose the following methodology.
Given the imbalanced class sizes (see Table 2) throughout the observation
periods, we employ a null model to test the transition probabilities between
archetypes. This null model computes the expected transition probabilities on
a copy of our dataset where archetype labels are shuffled. The detailed steps
are as follows:

  1. 1.

We generate $N=500$ shuffled copies of the dataset, randomizing the archetype
labels while preserving the overall distribution of interactions and
activities;

  2. 2.

For each archetype pair $(A,B)$ in the shuffled copies we compute the
transition probability $P(B|A)$, which represents the likelihood of a user
transitioning from archetype $A$ to archetype $B$;

  3. 3.

We calculate the mean and standard deviation of $P(B|A)$ across all shuffled
copies. These statistics are used to compute $z$-scores and $p$-values for the
observed transition probabilities in the original dataset;

  4. 4.

Finally, transitions with $p$-values less than $0.01$ are considered
statistically significant, indicating that these transitions occur at a
higher-than-expected rate compared to the null model.

Fig. 4 depicts the observed statistically significant transitions, letting us
observe several insights from the transitions between archetypes. One notable
transition is from Benevolent Underdogs to Respected Critics, occurring at a
significant rate of 39.23%. Benevolent Underdogs are characterized by positive
sentiments and low post scores, typically engaging in supportive and
encouraging behaviors. This transition can indicate that even users who start
with low recognition can, through consistent positive contributions, build
credibility and eventually gain influence within the community. Community
Heroes, another archetype defined by high trust, joy, and engagement, show a
tendency to transition to Benevolent Underdogs or, more rarely, to Positive
Provokers. The slight shift to Benevolent Underdogs suggests that Community
Heroes, despite their initially high engagement and recognition, may sometimes
experience a reduction in visibility or engagement, leading them to adopt a
more low-profile but still positive role. Also, we observe an occasional drift
towards more toxic behaviors. Infamous Celebrities, which have high post
scores and negative sentiment, exhibit a significant probability of remaining
in their contentious roles (13.71%). However, there is also an 11.71%
likelihood of transitioning to Malcontents. This shift reflects a potential
decrease in engagement and influence, where high-profile negative behavior can
lead to more discontent and a less active state. This transition from Infamous
Celebrities to Malcontents suggests a trajectory where persistent negativity
can diminish a user’s central role within the community. Malcontents, who are
driven by negative emotions and low post scores, present an interesting case
with a substantial 33.29% chance of becoming Respected Critics. This
transition implies that their critical nature can eventually earn them
credibility, provided they moderate their toxic behaviors. Another significant
transition is observed from Quiet Critics to Respected Critics, with a
remarkably high probability of 43.29%.

Fig 4: Transition Probabilities across archetypes (expressed in percentages).
Only statistically-validated ones are shown ($p<0.01$).

#### Temporal Analysis of Archetype’s Higher-order Interactions

Above, we proposed a thorough characterization of a series of archetypes. At
this point, an interesting aspect to study is the dynamics of archetypes
within the social platform, as well as their evolution in time. To do so, we
now focus on temporal trends of archetypes by examining some features on a
monthly basis. We focus on two key metrics, that is, the average hyperdegree
$\overline{hdeg}$ and the average degree $\overline{deg}$ of all nodes
represented by each archetype.

We consider the archetypes defined in the previous section, and we analyze the
nodes each archetype represents in each month. More formally, for each
archetype and for each node $u$, we compute its hyperdegree $hdeg(u)$ and its
degree $deg(u)$, and we do this for each hypergraph ${\cal H}_{t}$,
$t=1,\dots,12$. In Fig. 5 we show the obtained results. The figure consists of
12 subplots, one for each hypergraph, corresponding to a different month. For
each subplot, the $x$-axis represents the average hyperdegree
$\overline{hdeg}$ of each archetype, while the $y$-axis represents the average
degree $\overline{deg}$ of each archetype. From the analysis of this figure,
different insights can be derived. First off, we can observe how the Respected
Critics archetype has a higher hyperdegree and degree than all other
archetypes. This is somewhat expected as their characterization encompasses a
considerable number of nodes, as we have seen in the A Characterization for
Archetypes section. It is straightforward to observe how there are pairs of
archetypes that are often collocated together w.r.t. these dimensions. This is
the case of Infamous Celebrity and Quiet Critic, which appear very close in
almost all monthly snapshots, although they are very different in size. The
relatively small number of archetypes such as Controversial Star and Positive
Provoker is also reflected in their average hyperdegree and degree values:
indeed, they remain stable during the months and have little to no
fluctuations. This is somewhat expected, considering that these archetypes are
characterized by emotionally charged and often provocative interactions,
leading to fluctuating levels of activity and influence. This variability
suggests that their presence is more dynamic, potentially driven by specific
events or contentious discussions that peak at different times. Also in this
case, these results could be somewhat enhanced by a more qualitative-oriented
approach: indeed, aspects such as the content shared between archetypes would
be of great importance in a more in-depth analysis of their interaction.
Nevertheless, we believe the provided observation already indicates different
implications. For instance, archetypes with stable engagement patterns are
likely to be reliable contributors, therefore they could be taken into account
in systematic operations of the platforms, such as moderation activities.
Also, archetypes that show fluctuating feature values might be highly
responsive to specific events or topics, which could fuel critical
discussions.

Fig 5: Monthly average hyperdegree (x-axis) and number of neighbors (y-axis)
for each archetype.

### Characterization of Discussions

We recall that one of the objectives of our approach is to analyze higher-
order entities. To do so, it offers the so-called hyperedge characterization
function $\omega$, which we presented in the Analyzing Higher-Order Entities
section. We are now able to leverage it to describe the dataset with regard to
some of the properties exhibited by the discussions.

First off, we focus on examining our dataset on a monthly basis, thus we
consider each hypergraph ${\cal H}_{t}$, $t=1,\dots,12$. We do not focus on
the overall hypergraph ${\cal H}$ due to the fact that we are interested in
observing how the structure and the interactions within Scored.co evolve over
time. Also, this approach allows for a more granular understanding of user
behavior and interactions. For each hypergraph ${\cal H}_{t}$, we compute the
s-betweenness hyperedge centrality [1]. This measure is a higher-order
extension of classical graph betweenness centrality, and is computed on the
line graph projection of the hypergraph to estimate the importance of
hyperedges. We recall that the line graph of a hypergraph is a graph that
represents the relationships between the hyperedges of the original
hypergraph. In particular, there is a node in the line graph for each
hyperedge in the hypergraph, and there is an edge between two nodes if the
corresponding hyperedges share at least one node. After the computation of the
centrality, we select the top 50 hyperedges in each hypergraph ${\cal H}_{t}$,
and for each of we compute some descriptive features based on the linguistic
productions of the contained nodes. In particular, we focus on the following
features, namely, (i) average word count, (ii) average unique word count, and
(iii) average purity w.r.t. user archetypes. These values can be easily
calculated via the $\omega$ function, specialized for each of them. For
instance, the specialization for the average purity is given by
$\omega_{\text{purity}}$ in the Analyzing Higher-Order Entities section.

In Fig. 6, we report the temporal trends of the average values of average word
count, average unique word count, and average purity for the top 50 most
prominent discussions. Note how the discussion here is another term for
hyperedge: in fact, in our setting, a hyperedge represents a discussion
between users in the social hypernetwork. From the analysis of this figure, we
can derive different insights. First off, the average word count graph, in the
left part of the figure, shows a relatively stable trend with slight
fluctuations, indicating a consistent level of engagement in discussions over
the year. There are some notable peaks, such as a slight increase around mid-
year followed by a step-down and a subsequent rise towards the end of the
year. Similarly, the average vocabulary size, which indicates the average
unique word count, mirrors the previous measure but remains consistently
lower, which is somewhat expected because of non-content words (e.g.,
articles, pronouns, etc.) appearing more frequently in texts. A slight
increase in the middle of the year is also depicted here, suggesting periods
of higher and lower lexical diversity in user interactions. The middle part of
Fig. 6 reports the trend for average subjectivity. We recall that this metric
evaluates how subjective (as opposed to objective) the discussions are. It
remains relatively stable throughout the year, which indicates that
discussions typically contain a balanced mix of personal opinions and factual
statements. Indeed, this calls for a more qualitative-oriented analysis of
these discussions, an approach often used in the content-based investigation
of social platforms [11]. Finally, the right part of the image depicts the
graph of the average purity w.r.t. the user archetypes. This refers to the
consistency of user behavior and content relative to the defined archetypes.
We can observe how this trend shows more variability compared to the previous
features. There are sharp declines in some months, suggesting periods of more
inconsistent behavior among users, while the different peaks could indicate
times when user behavior is more aligned with archetypes. While all these
insights are interesting, and show the applicability of our proposed approach,
more in-depth analyses could be performed, as also noted above. Nevertheless,
the various specializations of $\omega$ enable a series of different lenses
through social interactions can be studied, especially in understudied
platforms.

(a)

(b)

(c)

Fig 6: Average word count and average unique word count (a), average
subjectivity (b), and average purity w.r.t. user archetypes (c) for the top 50
most central discussions.

## Conclusion

The identification of node roles within complex networks is significant when
analyzing their dynamics and function. To advance in this context, in this
paper we proposed a multi-dimensional, general framework to characterize nodes
and hyperedges in a social hypernetwork. The aim of our framework is two-fold:
i) to characterize nodes and hyperedges taking into account their exhibited
features and higher-order dynamics, and ii) to define “archetypes”, serving as
a template to represent higher-order roles of nodes. Our framework consists of
different components, namely, hyperedge ensembles, hyperedge- and node-based
characterization functions. The combination of such components allows one to
analyze the social hypernetwork from a more general point of view; each
component can also be exploited in a standalone fashion, thus enabling a
detailed analysis of the single aspect it captures. To assess the
effectiveness of the framework, we carried out an exhaustive experimental
campaign on Scored.co, an understudied social platform, focusing on different
aspects such as the characterization of nodes as well as their behaviors and
surroundings.

This paper is a starting point for future research with various possible
extensions. First off, the framework can be applied as it is on other
(possibly understudied) social platforms such as Bluesky [17]. Second, it
would be interesting to compare archetypes based on the set of features
selected for defining them. Indeed, an approach to identify the archetype best
representing a particular set of nodes could be defined as an optimization
problem, and meta-heuristics solutions could be employed to solve it. Another
future direction would be studying role dynamics in crisis situations. Indeed,
we could apply the framework to study social hypernetworks in crisis
situations, e.g., natural disasters and pandemics, to understand how roles and
behaviors shift under stress and how information and support are mobilized [4,
45]. Exploiting the temporal component, we would integrate this framework
about higher-order roles in the recent multi-dimensional analysis of group
evolution in temporal data [14]. Finally, an interesting challenge would be
the analysis of cross-platform role identification, and in particular the
investigation of the consistency of identified roles across multiple social
platforms. This could help in understanding whether certain archetypes are
platform-specific or they can represent more universal roles in online social
interactions.

## Acknowledgments

This work is supported by (i) the European Union – Horizon 2020 Program under
the scheme “INFRAIA-01-2018-2019 – Integrating Activities for Advanced
Communities”, Grant Agreement n.871042, ”SoBigData++: European Integrated
Infrastructure for Social Mining and Big Data Analytics”
(http://www.sobigdata.eu); (ii) SoBigData.it which receives funding from the
European Union – NextGenerationEU – National Recovery and Resilience Plan
(Piano Nazionale di Ripresa e Resilienza, PNRR) – Project: ”SoBigData.it –
Strengthening the Italian RI for Social Mining and Big Data Analytics” – Prot.
IR0000013 – Avviso n. 3264 del 28/12/2021; (iii) EU NextGenerationEU programme
under the funding schemes PNRR-PE-AI FAIR (Future Artificial Intelligence
Research).

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