<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Archiving and Interchange DTD v1.0 20120330//EN" "JATS-archivearticle1.dtd">
<article xmlns:xlink="http://www.w3.org/1999/xlink">
  <front>
    <journal-meta>
      <journal-title-group>
        <journal-title>Italian Conference on Big Data and Data Science, September</journal-title>
      </journal-title-group>
    </journal-meta>
    <article-meta>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Cheick T. Ba</string-name>
          <email>cheick.ba@unim.it</email>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Alessia Galdeman</string-name>
          <email>alessia.galdeman@unimi.it</email>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Manuel Dileo</string-name>
          <email>manuel.dileo@unimi.it</email>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Christian Quadri</string-name>
          <email>christian.quadri@unimi.it</email>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Matteo Zignani</string-name>
          <email>matteo.zignani@unimi.it</email>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Sabrina Gaito</string-name>
          <email>sabrina.gaito@unimi.it</email>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Department of Computer Science “Giovanni degli Antoni”, University of Milan</institution>
          ,
          <addr-line>via Celoria 18, Milan, 20133</addr-line>
          ,
          <country country="IT">Italy</country>
        </aff>
      </contrib-group>
      <pub-date>
        <year>2022</year>
      </pub-date>
      <volume>2</volume>
      <fpage>0</fpage>
      <lpage>21</lpage>
      <abstract>
        <p>Web3, one of the arising paradigms which may rule the future Web, is also representing a source of big data stored in the underlying blockchains. Many diferent research fields are benefiting from these large collections of temporal and heterogeneous data, which capture diferent aspects of the interactions among people and between people and Web3 platforms. Specifically, since each piece of information is validated and timestamped, Web3 platforms are becoming an invaluable source for understanding the dynamics of these techno-social systems at a high temporal resolution. In this contribution, we focused on the analysis of the evolution of the networked structure of Web3 social networks through the lens of discrete choice models, and on the changes in the structure of the relationships after a shocking event has occurred on the platform - namely a hard-fork in the supporting blockchain. To support large-scale analysis, we represent Web3 platform data as temporal multigraphs manageable by modern graph database management systems. The main findings, which represent a summary of our efort in mining data from Web3 platforms, highlight some interesting aspects: i) when applied to Web3 social networks, discrete choice models allow us to decompose the evolution of social networks into diferent growing mechanisms, which are quite stable during the observation period; and ii) in a stratified context, such as Web3 platforms, interactions resulting from economic actions, such as transfers or loans of crypto-tokens, are as important as social relationships to predict how users will behave during a shocking event. These are a few examples of how Web3 social platforms may represent a challenging playground for a more in-depth understanding of the users' behaviors when social and economic interactions are strictly intertwined.</p>
      </abstract>
      <kwd-group>
        <kwd>Web3 social networks</kwd>
        <kwd>social network evolution</kwd>
        <kwd>link creation dynamics</kwd>
        <kwd>customer migration</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction</title>
      <p>In the last years, the actual structure of Web 2.0 has been questioned by novel paradigms which
are trying to reduce the over-centralization around a few big platforms and tech companies.
One of the ideas gaining momentum is Web3, i.e. the design of platforms and software systems
built on blockchain technologies to promote a decentralized Web. In fact, we are witnessing the
birth of decentralized counterparts of Twitter or Reddit, embodied by Hive, Mind, or Steemit;
but also services that are specific to the Web3 world, such as Decentralized Finance (DeFi),
Decentralized Autonomous Organizations (DAOs), and non-fungible token (NFT), a financial
asset, linked to data stored in the blockchain, that can be traded. Although the idea of Web3 is
at the heart of a heated debate between enthusiasts and skeptics, the platforms following this
paradigm ofer a great opportunity to researchers in diferent fields thanks to the huge volume
of high-resolution data stored in the supporting blockchains. Indeed, a broad set of data about
these techno-social systems can be easily accessible: by the nature of blockchains, data are
publicly available, validated, and afordable by interfacing with the API blockchain. Moreover,
data from Web3 platforms ofer two advantages: i) each piece of information is timestamped
since each blockchain block has a validation timestamp; and ii) each block reported multi-faceted
interactions - social, economic, financial - among people and between people and platform. So,
these data sources have all the features to face tasks and issues related to modern techno-social
networks and to support detailed and in-depth analysis of users’ traits. Specifically, here we
focus on a few issues - which summarize our efort in the recent years to mine Web3 platforms
related to the growth of Web3 social networks from the perspective of link creation mechanisms
and the efects of shocking events.</p>
      <p>
        Understanding and mining how the networks behind large techno-social systems grow
and react to exceptional events are fundamental elements for the comprehension of the main
processes driving the evolution of such systems and for the identification of specific patterns
of growth which are consequences of the platform design. In this regard, in the past years,
many models, mechanisms, and measures describing the network growth from a link formation
perspective have been proposed, however, most of these approaches rely on the assumption that
the growth is guided by a single parameterized mechanism. But, current techno-social networks
are the result of diferent and heterogeneous behaviors where diferent choices and mechanisms
occur [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ], an observation which is further emphasized by Web3 platforms, where social and
economic motivations mix together and determine the choice of users in both common and
unusual situations as user migration resulting from conflicts within the social network. For these
reasons, in this contribution, we adopt a modeling approach based on temporal multidigraphs
which allows us to represent the heterogeneity of the interactions expressed in Web3 social
platforms and a few machine learning methods able to decouple the mechanisms - social and
economical - driving the choice of creating new relationships or migrating to a new blockchain
in case of splitting event of the network determined by a hard fork of the blockchain. As a case
study, we focus on the Web3 social platforms supported by the Steem blockchain, whose main
social platform is Steemit, and by Hive, the blockchain born from a hard fork - splitting event
- of the Steem blockchain. Besides a few advances in the methodological aspects concerning
the application of discrete choice models to stratified social networks 1 and the prediction of
whether or not users migrate towards other platforms, the findings resulting from the analysis
have highlighted a few main aspects of the Web3 social platforms:
• by applying discrete choice models to the lifetime of Steemit, we observe that the
different mechanisms driving the choice of establishing new connections are quite stable
along the observation period, where the attitude towards reciprocating links and making
1Stratified network is one of the terms indicating multi(di)graphs, where vertices are connected by one or more
links, each of a specific type.
      </p>
      <p>connections with users with many common relationships are the leading factors;
• it is possible to predict, with reasonably good performances, whether or not a user will
migrate to a new Web3 platform born by a fork. Specifically, these outcomes have been
reached even with the only information on the network structure, without including
textual or external data such as the trend of cryptocurrencies. Moreover, in a stratified
context with diferent types of connection, interactions resulting from economic actions,
such as transfers or loans of crypto-tokens, are as important as social relationships to
predict how users will behave during a shocking event, such as a hard fork.
The paper is organized as follows. Section 2 provides a brief introduction of Web3 social
platforms and an overview of the related studies. In Section 3 we describe how we model
and manage data from Web3 social platforms. Sections 4 and 5 report the main findings of
the growth of the Web3 platforms by applying discrete choice models and a discussion about
predictability of user migration after a shocking event, such as a hard fork of the underlying
blockchain.</p>
    </sec>
    <sec id="sec-2">
      <title>2. Backgrounds and related works</title>
      <p>Diferent services and platforms lie under the umbrella of the Web3 paradigm, but they all have
the usage of blockchain technology as a common factor. Hereby we introduce the reader to a
specific type of Web3 platform: Web3 social platforms or networks, broadly speaking online
social networks or blogging platforms that rely on a blockchain to validate and persist all the
interactions and actions established by their users.</p>
      <p>Web3 social platforms. By Web3 social platform, we denote a web application which i)
ofers a set of “social actions” - following, commenting and voting - facilitating online
interactions among accounts; and ii) whose core functions are ground in an underlying blockchain
that guarantees the persistence and the validity of the operations. One of the most interesting
consequences of this architecture is a strong link between economical aspects and online social
behaviors, in fact, most of the current Web3 social platforms implement: i) a token ecosystem
based on blockchain technology for promoting high-quality content and users, and validating
social and economic operations; and ii) a rewarding system for distributing the wealth of the
platform. In particular, the rewarding system defines the set of rules and mechanisms regulating
the distribution of tokens among the users who actively participate in the platform activities.
In most of these platforms, rewards are assigned to accounts that publish content - posts or
comments - and accounts that promote content through upvoting, downvoting or sharing.
Specifically, content promotion is based on a stake-based voting system, where the voter decides
how much of its economic power - the amount of gained crypto-tokens - to put behind a vote.</p>
      <p>
        In the landscape of Web3 social platforms, most of the research studies have been focused on
Steemit. Launched in 2016, Steemit has been one of the most widespread Web3 social platforms
and it is considered a pioneer for the Web3 ecosystem since it has introduced the seminal
concepts of rewarding system and proof-of-stake consensus algorithm for block validation. In
detail, the platform is hosted on a blockchain called Steem, and implements three diferent
tokens: STEEM, Steem Dollar - (SBD), and Steem Power - SP, where the last is on the basis of the
internal rewarding system and the first two tokens are tradable on exchange markets. Steemit
has gathered the interest of researchers for its characteristics and has been dissected in many
aspects. For example, a few studies have focused on the features of diferent types of social
networks resulting from diverse interactions or specific subsets of accounts ([
        <xref ref-type="bibr" rid="ref2 ref3">2, 3</xref>
        ]). In particular,
Chonan [
        <xref ref-type="bibr" rid="ref4">4</xref>
        ] and Kim et al. [
        <xref ref-type="bibr" rid="ref5">5</xref>
        ] have focused on the structure of Steemit “follow” network and its
characteristics. Also, Guidi et al. [
        <xref ref-type="bibr" rid="ref6">6</xref>
        ] have delved into a study of the follower–following graph,
and have studied other operations in Steemit [
        <xref ref-type="bibr" rid="ref7">7</xref>
        ]. Aside from social relationships, they have also
focused on block producers (witnesses) and highlighted their social impact on the platform [
        <xref ref-type="bibr" rid="ref8">8</xref>
        ].
As for economic aspects, Ciriello et al. [
        <xref ref-type="bibr" rid="ref9">9</xref>
        ] and Thelwall et al. [
        <xref ref-type="bibr" rid="ref10">10</xref>
        ] have analyzed the relationship
between rewards and content, while Li et al. [
        <xref ref-type="bibr" rid="ref11">11</xref>
        ] have analyzed the rewarding system in Steemit
from a network perspective. Additional information provided by the underlying blockchain
has been exploited in other studies; for instance, users’ content has been also used for facing
text mining [
        <xref ref-type="bibr" rid="ref12">12</xref>
        ] and bot detection [
        <xref ref-type="bibr" rid="ref13">13</xref>
        ] tasks. Finally, a few recent works have also taken into
account temporal information to investigate network dynamics. For instance, Jia et al. [
        <xref ref-type="bibr" rid="ref14">14</xref>
        ] focus
on the difusion of content, while in our previous works we discussed the interplay between
cryptocurrency price and the link creation process [
        <xref ref-type="bibr" rid="ref15">15</xref>
        ], the impact of user migration on the
social networks [
        <xref ref-type="bibr" rid="ref16">16</xref>
        ] and the role of groups in this phenomenon [
        <xref ref-type="bibr" rid="ref17">17</xref>
        ], and the bursty dynamics
of the link creation process [
        <xref ref-type="bibr" rid="ref18">18</xref>
        ].
      </p>
      <p>
        Hard fork and user migration. Web3 social platforms may ofer data about a
phenomenon which is peculiar to blockchain-based systems. Indeed, in these systems situations
where miners/validators change the consensus protocol may happen, leading to what is known
as blockchain fork. Specifically, two types of fork may occur: i) soft forks, where changes retro
compatible with the previous consensus protocol are introduced so that new blocks are added
to the same chain; and ii) hard forks, where miners do not consider as valid the blocks validated
with the new protocol so that two diferent branches are created if validators do not reach a
consensus on which protocol to use. In the latter case, the members of the original branch may
opt to migrate to the platform based on the new branch, leading to a phenomenon denoted as
user migration. User migration is a “universal” process spanning both centralized and
decentralized online social media but is not fully understood yet, especially in the Web3 world. Most
of the studies are based on centralized social platforms. For instance, Kumar et al. [
        <xref ref-type="bibr" rid="ref19">19</xref>
        ] have
analyzed user migration patterns, by matching user accounts through external data. Newell
et al. have conducted an analysis of user activity during a cross-platform migration through
surveys to understand the motivations behind migration. Other works have focused on users
migrating across communities on the same platform, showing non-random migration patterns
in Facebook groups [
        <xref ref-type="bibr" rid="ref20">20</xref>
        ]. A more in-depth analysis has been conducted [
        <xref ref-type="bibr" rid="ref21">21</xref>
        ] on Reddit, where
user migration across COVID-19 subreddits has been analyzed through diferent time scales.
All previous studies are based on data collected from centralized social platforms, however only
one work [
        <xref ref-type="bibr" rid="ref16">16</xref>
        ] has focused on user migration in Web3 social platforms, as a consequence of a
hard fork. Also in this case, Steemit represents a reference point since it experienced a hard
fork as a reaction to a hostile takeover of the Steem blockchain, leading to the new branch Hive.
      </p>
    </sec>
    <sec id="sec-3">
      <title>3. Modeling and managing Web3 social platform data</title>
      <p>Web3 social platforms make available to their users a rich set of operations to support diferent
kinds of interaction, namely interaction actions. From a network perspective, interaction actions
- comments, likes, reacting and following - result in diferent types of relationships connecting
accounts/users. Interaction actions in Web3 social platforms have two further important features
inherited from blockchain: i) each interaction action has a timestamp corresponding to the time
the block containing the action has been validated and recorded into the chain, and ii) interaction
actions are not merely social, rather also related to economic or financial operations, such as
borrowing or transferring tokens or assets between accounts. The latter aspect makes Web3
social platforms complex techno-social systems with diferent intertwined layers of actions.</p>
      <p>
        Formally, interaction actions are represented as a set of tuples  = {(,  , ,  )} where  and
 are accounts, who interact through an action of type  , validated by the blockchain at time
 . Given the temporal information associated to each tuple in  , we build two diferent kinds
of sequence of directed multigraphs [
        <xref ref-type="bibr" rid="ref22">22</xref>
        ], which describe the evolution of the platform: i) a
sequence of incremental directed multidigraphs, and ii) a sequence of diferential snapshots,
where each snapshot captures the network generated by the interaction actions occurring only
in a given time window. To cope with issues treated in this work, here we detail the incremental
approach. Specifically, we consider an evolving edge-labeled multidigraph  represented by a
sequence &lt;  1, ...,   &gt; where each   = (  ,   , ,   ) is a weighted edge-labeled multidigraph,
and  is the maximum timestamp in  . Through multidigraphs we include in the model diferent
types of relations expressed by  . Each multidigraph of the sequence is defined by the following
elements:
•   : the set of users  which belong to at least one interaction action (,  ,   ,  ) ∈  such
that   ≤  ;
•   : the set of triple (,  ,  ) with ,  ∈   and  ∈  , denoting a specific action type taking
value on the set  of actions made available by the blockchain;
•   ∶   → ℝ: a weighting function which returns the number of interaction actions of
type  involving  and  occurring before or at the timestamp  .
      </p>
      <p>Finally, it is worth noting that the above definition does not take into account the meaning of
operations, especially complementary operations, such as “follow” and “unfollow” where the
latter determines a removal of the link created by the former operation. This way actions can
only increase the state of a multidigraph, while semantic constraints can be introduced in a
successive phase of the analysis.</p>
      <sec id="sec-3-1">
        <title>3.1. FlowChains: a platform for gathering and managing Web3 social data</title>
        <p>Handling data produced by Web3 social platforms requires an efort not only in modeling and
representing temporal and heterogeneous data but also in designing and developing scalable
analytics platforms which have to gather data from diferent blockchains and manage
largescale multidigraphs. To this aim and to support our analysis of the temporal aspects of Web3
social platforms, we have developed FlowChains, an analytics platform for Web3 social and
trading data, whose architecture is depicted in Figure 1. The core of the architecture is the
event streaming platform Apache Kafka which collects data through a set of Kafka Connectors.
Each Kafka Connector handles a specific stream of blocks gathered through the APIs released
by Web3 platforms and applications. Then, syntactically diferent operations coming from
diferent blockchains which express the same interaction action are grouped in the same Kafka
topic. This aggregation step facilitates the alignment among the data produced by the rich set
of blockchains. Finally, the interaction actions belonging to a specific topic are transformed
into a temporal annotated link in a graph database management system. In FlowChains the
graph database is Neo4J, the leading solution for handling and managing large-scale multigraph.
The choice of Neo4J has been dictated by the fact that it natively supports multiedges between
two vertices, complex attributes can be assigned both to vertices and links, and it follows the
schema-free paradigm so allowing a certain level of flexibility in the data model.</p>
      </sec>
      <sec id="sec-3-2">
        <title>3.2. Web3 social platform datasets: Steemit and Hive</title>
        <p>Through the FlowChains platform, we were able to collect a large dataset covering the lifespan
of two important blockchains Steem and Hive, at the basis of the two Web3 social platforms:
Steemit and Hive blog. Specifically, the blockchain Hive has originated by a hard fork of Steem
on the 20th of March 2020, after a 51% attack. Although they are two diferent blockchains
both Steem and Hive have released more than 50 operations in common. Among them, we
are interested only in operations generating interaction actions, of which a subset has been
reported in Figure 1b. These actions have been further grouped into two main categories: i)
ifnancial and ii) social operations. Financial operations are for rewards and token management,
and asset and share transfer; whereas social operations correspond to posting, rating, voting,
sharing and following. From the modeling perspective, this aggregation corresponds to defining
 as {,  } .</p>
        <p>The details about blocks and operations for both platforms have been gathered through
oficial public APIs. Moreover, due to the implementation of the hard fork, data between the
two blockchains are identical up to the fork event. From there, Hive and Steem have recorded
diferent data, as they have become two separated entities. So, we collected operations from
the very first block on Steem blockchain, produced on 24th March 2016, up to January 2021.
For Hive, we start from the first block after the fork (20/03/2020), and up to January 2021.
Overall, from Steem, we extracted 993,641,075 operations related to social interaction actions
and 72,370,926 operations related to financial actions; from Hive we have a total of 206,224,132
social actions and 4,041,060 financial actions. It is worth noting that both blockchains record
the operations with a three-second granularity.</p>
      </sec>
    </sec>
    <sec id="sec-4">
      <title>4. Mining the growth of Web3 platforms</title>
      <p>
        The understanding of how online social networks grow and evolve is a central issue in temporal
network analysis, however, traditional approaches have failed to catch the complexity of
such phenomenon, especially when online social networks are the result of a mix of growth
mechanisms based on diferent aspects, from social to economic or financial. Recently, a few
approaches based on discrete choice models [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ] have shown promising results as the possibility
of decoupling the diferent mechanisms which drive the formation of social networks. The
fundamental idea behind these approaches is that we can think of the formation of a directed
link (,  )
      </p>
      <p>
        as a choice made by  to connect with  , where the set of possible choices for  is the
set of all other nodes. For further details about discrete choice models applied to social network
formation we refer the reader to Overgoor et al.’s seminal work [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ]. Essentially, the underlying
inference problem is an estimate of the parameter   which characterizes a random utility
function a node  uses to choose the target node  , i.e.  ,
=     +  , , where   is a vector
of features for the node  and  models the noise in choosing among the alternatives. In our
analysis we apply a conditional logit model with a linear utility function so that the likelihood
function is convex with respect to the parameters  :  can be inferred by eficiently maximizing
the likelihood by using gradient-based optimization methods. In the context of conditional
logit choice models, the parameters  represent the importance of a specific feature in   for
the choices made by  ; while the features summarize the diferent mechanisms which may act
during the formation of the network. Here we leverage the above model and its interpretation
by applying it to diferent snapshots of the Steemit lifespan so to highlight if the choice model
is stable. Moreover, we take into account features based on social and financial actions so to
ifnd the main aspects driving the evolution of Web3 social platforms.
      </p>
      <p>Experimental setting.</p>
      <sec id="sec-4-1">
        <title>To investigate the stability of the choice model and the utility</title>
        <p>
          function parameters, first we identify a set of dates - 2017-03-15, 2017-04-15, 2017-05-15,
201706-15, 2017-07-15, 2017-08-15, 2017-09-15 - which correspond to specific stages of the growth of
Steemit, as shown in [
          <xref ref-type="bibr" rid="ref15">15</xref>
          ]. Then, we proceed by transforming the temporal links of type “follow”
into choice data: given an interval [ ,   ], we extract    from the sequence of multidigraphs   .
        </p>
        <p>Finally, from the set of “follow” links created in [ ,   ], we extract  elements which corresponds

to the choices (,  ) . On the other hand, alternative choices have to be selected. Indeed we have
to estimate the utility assigned by node  to other alternatives, to approximate the likelihood
function. To speed up the computation, a negative sampling of the alternatives is applied, i.e.
for each positive choice (,  ) , we randomly select  nodes not connected to  in [  ,   ]. Once,
the choice data have been selected, we compute for each pair (,  )
basis of the information provided by   and infer the parameters  .</p>
        <p>the feature vector   on the</p>
        <p>Parameters inferred for the conditional logit model. Each column represents a stage of the evolution of
3. Hops (HS): length of the shortest path between  and  in the social network;
4. Reciprocity (RS): boolean flag indicating whether ( , ) ∈ 


;
5. Common neighbors - social(CNS): number of in-neighbors in common between  and
 in the social network;
6. Friends of friends (FoFS): boolean flag indicating if CNS is diferent from 0;
7. In financial (IF) : boolean flag indicating whether  is in the financial network;</p>
      </sec>
      <sec id="sec-4-2">
        <title>8. In-degree - financial(DF) : number of transactions received by node  ;</title>
      </sec>
      <sec id="sec-4-3">
        <title>9. Transactions (TF): number of transactions exchanged between  and  10. Common neighbors - financial (CNF) : number of neighbors in common between  and  in the financial network.</title>
        <p>Results.</p>
        <p>In Table 1 we report the parameters of the conditional logit choice model which
has achieved the best performance in terms of accuracy, i.e. the choice model whose random
utility function is  , =  1 log() + 
2
  + 
3 + 
4
   + 
5
( ) + 
6
  +  , . Each
column reports the weights -  - users have assigned to a particular feature when they chose
to connect to other nodes during a specific stage of the growth of the Steemit social network.
From the analysis of the parameters and their trends we observe that:
• the weights of the diferent features are quite stable in each of the time windows. This
might be a possible indicator of the stability of the users’ behavior when choosing
to establish new relationships. It is also interesting to observe that the preferential
attachment mechanism, captured by the feature ()
, has lost its importance as the
network evolved;
• reciprocating links ( ) and making connections with users with at least one common
relationship (</p>
        <p>) have got the highest impact on the growth of the Steemit social
network. Specifically, while the choice of reciprocating links has been strong and stable
throughout the observation period, the mechanism based on common neighbors has
strengthened its importance as the network evolved;
• in the choice of link formation the financial features are marginal and almost irrelevant.</p>
        <p>In fact, most of the financial features are not even present in the formulation of the utility
function, and the only financial feature   got values close to zero during the whole
observation period.</p>
        <p>To sum up, through discrete choice models we are able to disentangle the complexity behind
the evolution of a Web3 social platform as Steemit, and identify which are the main growth
mechanisms that are leading the evolution of Web3 social platforms.</p>
      </sec>
    </sec>
    <sec id="sec-5">
      <title>5. User migration across platforms: when a shocking event happens</title>
      <p>In the previous section we dealt with a certain level of stability of the mechanisms leading the
evolution of Web3 platforms. In this section, we drastically change our setting by focusing on
the efects of a shocking event such as a hard fork of the blockchain supporting a Web3 social
platform - Steem in our case. Specifically, we are interested in the user migration consequent
to the hard fork. In the light of the data representation described in Section 3, modeling user
migration is quite straightforward: both the original blockchain - Steem - and the new branch
Hive - are described by two distinct evolution multidigraphs:   and   , respectively, with a
common ancestor representing the multidigraph at fork time   . Given these definitions, we
assign to each account a state. Specifically, a user  migrates - migrant - from platform  to 
after a fork, if after</p>
      <p>s/he does at least one action on  ; while a user  remains on the original
platform - resident - if s/he keeps performing actions on the platform  and no actions on  after
the fork event. We also introduce a third category - inactive users, i.e. people who are inactive
or have abandoned both platforms. So, for each user, we are interested in the predictability of
the choice to adopt a new platform given some user’s characteristics or activities. In particular,
we ask whether early signals indicating that s/he will move to a new platform exist. We cope
with these research questions by casting this issue into a machine learning task, specifically a
node classification task.</p>
      <p>Definition: User migration prediction task.
successive timestamps  ′, where  ′ &gt;   , we define the user migration prediction task as the
prediction of a node migration in one of the successive time steps.</p>
      <p>Given the graph   and considering the</p>
      <p>Indeed, the main goal is classifying a user as migrant or resident as a function of several
features related to the structure of the temporal multidigraph describing the platform; whereas
the assumption is that user features, at the network structure level, could be predictive of a
future user migration. It is worth noting that features are extracted by exploiting both financial
and social links.</p>
      <sec id="sec-5-1">
        <title>As features we selected the most common node-level features used</title>
        <p>in many network-based prediction tasks. Such features encode information about a node and
its neighborhood. Specifically, for each user in   , we compute in-degree and out-degree,

weighted in-degree, Pagerank, neighborhood average degree, and local clustering coeficient.
Alongside the structural information, we also include information on the status of nodes in
the neighborhood: i) the percentage of inactive neighbors, i.e. the number of neighbors whose
status is inactive at time   , divided by the total number of neighbors, and ii) the percentage
of resident neighbors, i.e. the number of neighbors whose status is resident at time  divided
by the total number of neighbors. In addition to the structural features, we compute a set of
features related to the activity of the users before the hard fork, mostly inspired by the similar
task of churn prediction: i) the number of active/inactive days in the three-month period before
the fork, ii) the average number of daily actions in the three-month period before the fork, iii)
the lifetime in the original blockchain, iv) the distance - in days - between the first and the
last action in the three-month period before the fork, and v) the average length of the activity
sessions2. These features have been extracted from the financial and social layers, i.e. subgraphs
of a multidigraph where links have a specific label, social or financial actions in this case.</p>
        <p>Experimental setting.</p>
        <p>The experimental context is given by the migration from Steem
to Hive. Hence, we rely on the Steem evolving multidigraph   , and its financial and social
layers. More precisely, we select the snapshot at fork time,   = 2020/03/20, at 2:00 PM. Then,
we obtain the labels migrant and resident by inspecting the sequences of multidigraph   and
  after the fork time. The two classes are imbalanced. For instance, social layer, where there
is a more severe imbalance, residents are 3/4x more than migrants (66.9 %, 33.1%); vice-versa in
the financial layer there are more migrants (56.1%) than residents (43.9%). In this case we deal
with the sample imbalance by oversampling through the SMOTE method.</p>
        <p>
          We perform the performance evaluation in a 5-fold cross-validation setting. For each fold,
we apply oversampling on the training portion of the fold. Then, we train a model, compute a
set of evaluation metrics and we average the performances over the five folds. To compare the
performances of the diferent learning algorithms, we compute the main evaluation metrics
for classification tasks: weighted F1, accuracy, precision, recall and AUC. For the classification
task, we rely on standard machine learning methods: Logistic Regression, Random Forest,
2An activity session corresponds to a bursty train of actions as described in [
          <xref ref-type="bibr" rid="ref18">18</xref>
          ]. In this case, we use diferent
thresholds to identify bursty trains.
        </p>
        <p>Support Vector Machine with linear kernel, a Gradient Boosting classifier, and two multilayer
perceptrons - MLP - with 100-unit hidden layer and three hidden layers (128 units - 64 units
32 units), respectively.</p>
        <p>Results. In Table 2 we report the results for the user migration prediction task. In this
task, we are combining structural and activity-related features from both the social and financial
layers, fully leveraging both the evolving graphs. This latter aspect is resulted crucial for
improving the performances of all the models w.r.t. settings where features are taken from
a single layer only - financial or social - have been considered. By comparing the model, as
expected, the ensemble methods - Random Forest and Gradient Boosting - have obtained the best
performances, which in general are quite good for the task. In addition, we observe that SVM
and Logistic Regression have benefited from the addition of features coming from both layers.
In short, the results suggest that in a stratified context with diferent types of links, interactions
and features resulting from financial actions should be used together with social-based features
to enhance the predictability of users in the case of a user migration.</p>
        <p>Finally, we also performed a feature importance analysis to highlight the most predictive
features to identify the early signals of willingness to migrate. The features ordered by their
importance are depicted Figure 2. We observe that the most important features have been
extracted from both social and financial layers and concern both structural and activity-related
aspects. In fact, the average length of the session in the financial layer, and the neighbor degree
in both social and financial ones are among the most important features. To sum up, this
analysis on feature importance confirms the importance of taking into account information
derived from both types of interaction actions when we tackle the user migration prediction
task in Web3 social platforms.</p>
      </sec>
    </sec>
  </body>
  <back>
    <ref-list>
      <ref id="ref1">
        <mixed-citation>
          [1]
          <string-name>
            <given-names>J.</given-names>
            <surname>Overgoor</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A.</given-names>
            <surname>Benson</surname>
          </string-name>
          ,
          <string-name>
            <given-names>J.</given-names>
            <surname>Ugander</surname>
          </string-name>
          ,
          <article-title>Choosing to grow a graph: Modeling network formation as discrete choice</article-title>
          ,
          <source>in: The World Wide Web Conference</source>
          , WWW '19,
          <string-name>
            <surname>Association</surname>
          </string-name>
          for Computing Machinery, New York, NY, USA,
          <year>2019</year>
          , p.
          <fpage>1409</fpage>
          -
          <lpage>1420</lpage>
          . URL: https://doi.org/10.1145/3308558.3313662.
        </mixed-citation>
      </ref>
      <ref id="ref2">
        <mixed-citation>
          [2]
          <string-name>
            <given-names>R.</given-names>
            <surname>Ciriello</surname>
          </string-name>
          ,
          <string-name>
            <given-names>R.</given-names>
            <surname>Beck</surname>
          </string-name>
          ,
          <string-name>
            <surname>J. Thatcher,</surname>
          </string-name>
          <article-title>The paradoxical efects of blockchain technology on social networking practices</article-title>
          ,
          <source>in: Proceedings of the Thirty Ninth International Conference on Information Systems</source>
          , AIS,
          <year>2018</year>
          .
        </mixed-citation>
      </ref>
      <ref id="ref3">
        <mixed-citation>
          [3]
          <string-name>
            <given-names>A.</given-names>
            <surname>Kiayias</surname>
          </string-name>
          ,
          <string-name>
            <given-names>B.</given-names>
            <surname>Livshits</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A. M.</given-names>
            <surname>Mosteiro</surname>
          </string-name>
          ,
          <string-name>
            <given-names>O.</given-names>
            <surname>Litos</surname>
          </string-name>
          ,
          <article-title>A puf of steem: Security analysis of decentralized content curation</article-title>
          , ArXiv abs/
          <year>1810</year>
          .01719 (
          <year>2019</year>
          ).
        </mixed-citation>
      </ref>
      <ref id="ref4">
        <mixed-citation>
          [4]
          <string-name>
            <given-names>U. W.</given-names>
            <surname>Chohan</surname>
          </string-name>
          ,
          <article-title>The concept and criticisms of steemit</article-title>
          ,
          <source>CBRI Working Papers: Notes on the 21st Century</source>
          , Available at SSRN: http://dx.doi.org/10.2139/ssrn.3129410,
          <year>2018</year>
          .
        </mixed-citation>
      </ref>
      <ref id="ref5">
        <mixed-citation>
          [5]
          <string-name>
            <given-names>M. S.</given-names>
            <surname>Kim</surname>
          </string-name>
          ,
          <string-name>
            <given-names>J. Y.</given-names>
            <surname>Chung</surname>
          </string-name>
          ,
          <article-title>Sustainable growth and token economy design: The case of steemit</article-title>
          ,
          <source>Sustainability</source>
          <volume>11</volume>
          (
          <year>2019</year>
          )
          <fpage>167</fpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref6">
        <mixed-citation>
          [6]
          <string-name>
            <given-names>B.</given-names>
            <surname>Guidi</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A.</given-names>
            <surname>Michienzi</surname>
          </string-name>
          ,
          <string-name>
            <given-names>L.</given-names>
            <surname>Ricci</surname>
          </string-name>
          ,
          <article-title>A graph-based socioeconomic analysis of steemit, IEEE Transactions on Computational Social Systems PP (</article-title>
          <year>2020</year>
          )
          <fpage>1</fpage>
          -
          <lpage>12</lpage>
          . doi:
          <volume>10</volume>
          .1109/TCSS.
          <year>2020</year>
          .
          <volume>3042745</volume>
          .
        </mixed-citation>
      </ref>
      <ref id="ref7">
        <mixed-citation>
          [7]
          <string-name>
            <given-names>B.</given-names>
            <surname>Guidi</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A.</given-names>
            <surname>Michienzi</surname>
          </string-name>
          , L. Ricci,
          <article-title>Steem blockchain: Mining the inner structure of the graph</article-title>
          ,
          <source>IEEE Access 8</source>
          (
          <year>2020</year>
          ). doi:
          <volume>10</volume>
          .1109/ACCESS.
          <year>2020</year>
          .
          <volume>3038550</volume>
          .
        </mixed-citation>
      </ref>
      <ref id="ref8">
        <mixed-citation>
          [8]
          <string-name>
            <given-names>B.</given-names>
            <surname>Guidi</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A.</given-names>
            <surname>Michienzi</surname>
          </string-name>
          ,
          <string-name>
            <given-names>L.</given-names>
            <surname>Ricci</surname>
          </string-name>
          ,
          <article-title>Analysis of witnesses in the steem blockchain</article-title>
          ,
          <source>Mobile Networks and Applications</source>
          (
          <year>2021</year>
          )
          <fpage>1</fpage>
          -
          <lpage>12</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref9">
        <mixed-citation>
          [9]
          <string-name>
            <given-names>R.</given-names>
            <surname>Zhang</surname>
          </string-name>
          , J. Park,
          <string-name>
            <given-names>R.</given-names>
            <surname>Ciriello</surname>
          </string-name>
          ,
          <article-title>The diferential efects of cryptocurrency incentives in blockchain social networks</article-title>
          ,
          <year>2019</year>
          .
        </mixed-citation>
      </ref>
      <ref id="ref10">
        <mixed-citation>
          [10]
          <string-name>
            <given-names>M.</given-names>
            <surname>Thelwall</surname>
          </string-name>
          ,
          <article-title>Can social news websites pay for content and curation? the steemit cryptocurrency model</article-title>
          ,
          <source>Journal of Information Science</source>
          <volume>44</volume>
          (
          <year>2018</year>
          )
          <fpage>736</fpage>
          -
          <lpage>751</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref11">
        <mixed-citation>
          [11]
          <string-name>
            <given-names>C.</given-names>
            <surname>Li</surname>
          </string-name>
          ,
          <string-name>
            <given-names>B.</given-names>
            <surname>Palanisamy</surname>
          </string-name>
          ,
          <article-title>Incentivized blockchain-based social media platforms: A case study of steemit</article-title>
          ,
          <source>in: Proceedings of the 10th ACM Conference on Web Science</source>
          ,
          <year>2019</year>
          , pp.
          <fpage>145</fpage>
          -
          <lpage>154</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref12">
        <mixed-citation>
          [12]
          <string-name>
            <given-names>K.</given-names>
            <surname>Kapanova</surname>
          </string-name>
          ,
          <string-name>
            <given-names>B.</given-names>
            <surname>Guidi</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A.</given-names>
            <surname>Michienzi</surname>
          </string-name>
          ,
          <string-name>
            <given-names>K.</given-names>
            <surname>Koidl</surname>
          </string-name>
          ,
          <article-title>Evaluating posts on the steemit blockchain: Analysis on topics based on textual cues</article-title>
          ,
          <source>in: Proceedings of the 6th EAI International Conference on Smart Objects and Technologies for Social Good, EAI</source>
          ,
          <year>2020</year>
          .
        </mixed-citation>
      </ref>
      <ref id="ref13">
        <mixed-citation>
          [13]
          <string-name>
            <surname>T.-H. Kim</surname>
            ,
            <given-names>H.</given-names>
            min Shin, H.
          </string-name>
          <string-name>
            <surname>Hwang</surname>
            ,
            <given-names>S.</given-names>
          </string-name>
          <string-name>
            <surname>Jeong</surname>
          </string-name>
          ,
          <article-title>Posting bot detection on blockchain-based social media platform using machine learning techniques</article-title>
          , ArXiv abs/
          <year>2008</year>
          .12471 (
          <year>2020</year>
          ).
        </mixed-citation>
      </ref>
      <ref id="ref14">
        <mixed-citation>
          [14]
          <string-name>
            <given-names>P.</given-names>
            <surname>Jia</surname>
          </string-name>
          ,
          <string-name>
            <surname>C.</surname>
          </string-name>
          <article-title>Yin, Research on the characteristics of community network information transmission in blockchain environment</article-title>
          ,
          <source>in: IEEE 4th Advanced Information Technology, Electronic and Automation Control Conference (IAEAC)</source>
          , volume
          <volume>1</volume>
          , IEEE, New York, NY,
          <year>2019</year>
          , pp.
          <fpage>2296</fpage>
          -
          <lpage>2300</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref15">
        <mixed-citation>
          [15]
          <string-name>
            <given-names>C. T.</given-names>
            <surname>Ba</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M.</given-names>
            <surname>Zignani</surname>
          </string-name>
          ,
          <string-name>
            <given-names>S.</given-names>
            <surname>Gaito</surname>
          </string-name>
          ,
          <article-title>The role of cryptocurrency in the dynamics of blockchain-based social networks: the case of steemit</article-title>
          ,
          <source>PloS One</source>
          (
          <year>2022</year>
          ).
        </mixed-citation>
      </ref>
      <ref id="ref16">
        <mixed-citation>
          [16]
          <string-name>
            <given-names>C. T.</given-names>
            <surname>Ba</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A.</given-names>
            <surname>Michienzi</surname>
          </string-name>
          ,
          <string-name>
            <given-names>B.</given-names>
            <surname>Guidi</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M.</given-names>
            <surname>Zignani</surname>
          </string-name>
          ,
          <string-name>
            <given-names>L.</given-names>
            <surname>Ricci</surname>
          </string-name>
          ,
          <string-name>
            <given-names>S.</given-names>
            <surname>Gaito</surname>
          </string-name>
          ,
          <article-title>Fork-based user migration in blockchain online social media</article-title>
          ,
          <source>in: Proceedings of the 14th ACM conference on web science</source>
          ,
          <year>2022</year>
          .
        </mixed-citation>
      </ref>
      <ref id="ref17">
        <mixed-citation>
          [17]
          <string-name>
            <given-names>C. T.</given-names>
            <surname>Ba</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M.</given-names>
            <surname>Zignani</surname>
          </string-name>
          ,
          <string-name>
            <given-names>S.</given-names>
            <surname>Gaito</surname>
          </string-name>
          ,
          <article-title>The role of groups in a user migration across blockchain-based online social media</article-title>
          ,
          <source>in: 2022 IEEE International Conference on Pervasive Computing and Communications Workshops</source>
          and
          <article-title>other Afiliated Events (PerCom Workshops)</article-title>
          , IEEE,
          <year>2022</year>
          , pp.
          <fpage>291</fpage>
          -
          <lpage>296</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref18">
        <mixed-citation>
          [18]
          <string-name>
            <given-names>C. T.</given-names>
            <surname>Ba</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M.</given-names>
            <surname>Zignani</surname>
          </string-name>
          ,
          <string-name>
            <given-names>S.</given-names>
            <surname>Gaito</surname>
          </string-name>
          ,
          <article-title>Social and rewarding microscopical dynamics in blockchain-based online social networks</article-title>
          ,
          <source>in: Proceedings of the Conference on Information Technology for Social Good</source>
          ,
          <year>2021</year>
          , pp.
          <fpage>127</fpage>
          -
          <lpage>132</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref19">
        <mixed-citation>
          [19]
          <string-name>
            <given-names>S.</given-names>
            <surname>Kumar</surname>
          </string-name>
          ,
          <string-name>
            <given-names>R.</given-names>
            <surname>Zafarani</surname>
          </string-name>
          , H. Liu,
          <article-title>Understanding user migration patterns in social media</article-title>
          ,
          <source>in: AAAI</source>
          ,
          <year>2011</year>
          .
        </mixed-citation>
      </ref>
      <ref id="ref20">
        <mixed-citation>
          [20]
          <string-name>
            <given-names>M.</given-names>
            <surname>Senaweera</surname>
          </string-name>
          ,
          <string-name>
            <given-names>R.</given-names>
            <surname>Dissanayake</surname>
          </string-name>
          ,
          <string-name>
            <given-names>N.</given-names>
            <surname>Chamindi</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A.</given-names>
            <surname>Shyamalal</surname>
          </string-name>
          ,
          <string-name>
            <given-names>C.</given-names>
            <surname>Elvitigala</surname>
          </string-name>
          ,
          <string-name>
            <given-names>S.</given-names>
            <surname>Horawalavithana</surname>
          </string-name>
          ,
          <string-name>
            <given-names>P.</given-names>
            <surname>Wijesekara</surname>
          </string-name>
          ,
          <string-name>
            <given-names>K.</given-names>
            <surname>Gunawardana</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M. I. E.</given-names>
            <surname>Wickramasinghe</surname>
          </string-name>
          ,
          <string-name>
            <given-names>C.</given-names>
            <surname>Keppitiyagama</surname>
          </string-name>
          ,
          <article-title>A weighted network analysis of user migrations in a social network, 2018 18th International Conference on Advances in ICT for Emerging Regions (ICTer) (</article-title>
          <year>2018</year>
          )
          <fpage>357</fpage>
          -
          <lpage>362</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref21">
        <mixed-citation>
          [21]
          <string-name>
            <given-names>C.</given-names>
            <surname>Davies</surname>
          </string-name>
          ,
          <string-name>
            <given-names>J. R.</given-names>
            <surname>Ashford</surname>
          </string-name>
          ,
          <string-name>
            <given-names>L.</given-names>
            <surname>Espinosa-Anke</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A. D.</given-names>
            <surname>Preece</surname>
          </string-name>
          ,
          <string-name>
            <given-names>L. D.</given-names>
            <surname>Turner</surname>
          </string-name>
          ,
          <string-name>
            <given-names>R. M.</given-names>
            <surname>Whitaker</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M.</given-names>
            <surname>Srivatsa</surname>
          </string-name>
          ,
          <string-name>
            <given-names>D. H.</given-names>
            <surname>Felmlee</surname>
          </string-name>
          <article-title>, Multi-scale user migration on reddit</article-title>
          ,
          <source>in: Workshop on Cyber Social Threats at the 15th International AAAI Conference on Web and Social Media (ICWSM</source>
          <year>2021</year>
          ), AAAI,
          <year>2021</year>
          .
        </mixed-citation>
      </ref>
      <ref id="ref22">
        <mixed-citation>
          [22]
          <string-name>
            <given-names>P.</given-names>
            <surname>Holme</surname>
          </string-name>
          ,
          <string-name>
            <given-names>J.</given-names>
            <surname>Saramäki</surname>
          </string-name>
          ,
          <article-title>Temporal networks</article-title>
          ,
          <source>Physics Reports</source>
          <volume>519</volume>
          (
          <year>2012</year>
          )
          <fpage>97</fpage>
          -
          <lpage>125</lpage>
          . Temporal Networks.
        </mixed-citation>
      </ref>
    </ref-list>
  </back>
</article>