# Estimating Emotion Contagion on Social Media via Localized Diffusion in
Dynamic Graphs

Trisha Mittal
University of Maryland
<EMAIL_ADDRESS>Puneet Mathur
University of Maryland
<EMAIL_ADDRESS>Rohan Chandra
University of Texas, Austin
<EMAIL_ADDRESS>Apurva Bhatt
ShareChat, India
<EMAIL_ADDRESS>Vikram Gupta
ShareChat, India
<EMAIL_ADDRESS>Debdoot Mukherjee
Meesho, India
<EMAIL_ADDRESS>Aniket Bera
University of Maryland
<EMAIL_ADDRESS>Dinesh Manocha
University of Maryland
<EMAIL_ADDRESS>
###### Abstract

We present a computational approach for estimating emotion contagion on social
media networks. Built on a foundation of psychology literature, our approach
estimates the degree to which the perceivers’ emotional states (positive or
negative) start to match those of the expressors, based on the latter’s
content. We use a combination of deep learning and social network analysis to
model emotion contagion as a diffusion process in dynamic social network
graphs, taking into consideration key aspects like causality, homophily, and
interference. We evaluate our approach on user behavior data obtained from a
popular social media platform for sharing short videos. We analyze the
behavior of $48$ users over a span of $8$ weeks (over $200$k audio-visual
short posts analyzed) and estimate how contagious the users with whom they
engage with are on social media. As per the theory of diffusion, we account
for the videos a user watches during this time (inflow) and the daily
engagements; liking, sharing, downloading or creating new videos (outflow) to
estimate contagion. To validate our approach and analysis, we obtain human
feedback on these $48$ social media platform users with an online study by
collecting responses of about $150$ participants. We report users who interact
with more number of creators on the platform are $12\%$ less prone to
contagion, and those who consume more content of ‘negative’ sentiment are
$23\%$ more prone to contagion. We will publicly release our code upon
acceptance.

##  1 Introduction

Online social media platforms like Facebook, Twitter, and Reddit not only
connect millions of people, but they also significantly impact society by
sparking political discussions [54], aiding disaster response [44, 63, 53],
and physically mobilizing people towards different causes [68, 8]. In contrast
to these positive effects, a recent study led by Facebook [41] highlighted one
of the most subtle and least combated problems of digital content on social
media–emotion contagion, which is defined as follows [28, 24]:

Emotion contagion (EC) is a diffusion of emotions (positive or negative) and
opinions over users in a social network such that the emotions and opinions of
a “perceiver” become more similar to those of the “expressor” as a result of
exposure to them.

Figure 1: We propose a computational approach to estimate emotion contagion of
digital content (short video with audio posts) in online social networks. For
instance, consider a user $c$, ”perceiver” (marked in red), on a social media
platform engaging with $m$ users over a period of $t$ days. We analyze the
inflow, i.e., the content consumed by $c$, and the outflow, i.e., the actions
that $c$ takes (like, share, comment, follow, unfollow, download, create new
content) in the same $t$ days. Our algorithm models the contagion phenomenon
as a diffusion process and quantitatively estimates the degree to which the
neighbor’s ($1\dots m$) emotions and content unintentionally match or
influence.

Emotion contagion can occur as a result of any type of exposure to the
emotions of others. This can be broadly classified into non-digital (face-to-
face or telephonic) and digital (social media) conversations. We now formally
define Digital Emotion Contagion:

Digital Emotion Contagion (DEC) is when EC occurs by sharing and expressing
opinions on online platforms via multimodal digital content such as posts on
Reddit and Facebook, tweets on Twitter, photos on Instagram, etc.

While in both non-digital and digital emotion contagion, the emotions and
opinions of “perceivers” change as a result of exposure to “expressors”, the
exposure is a lot more intense and frequent on digital media platforms (Figure
1) as all interactions on social media platforms are $1:n$ opposed to $1:1$
conversations in non-digital world. There are two main concerns with digital
emotion contagion. First, users have little control over the content they
consume on online social media platforms, putting them at risk of consuming
harmful content [60, 6]. Second, social media platforms are known to
incentivize emotion-rich content, leading to a self-reinforcing loop of
enhanced emotion contagion [28].

Social network analysis has previously focused on problems including hate-
speech detection and filtering [56], violent content flagging [2] and viral
post prediction [65]. These problems have seen significant progress owing to
the easy availability of huge datasets. However, prior work in emotion
contagion research has been restricted to proving its existence on social
media platforms [24, 41], with very limited work on estimating emotion
contagion. This is partly due to the absence of datasets capturing causal user
behavior on social media, which prohibits collaborative research. This is
primarily because this requires tracking user activity on social media
platforms over a time span which is very sensitive data to publicly release.
Prior works have also presented various hypotheses [47, 35, 15, 7, 30] about
factors responsible for causing emotion contagion on social media.

Furthermore, emotion contagion is not a widely understood term among social
media users. Instead the closest concept that is well-understood is influence.
While influence is often intended, contagion occurs without the knowledge of
the perceiver or expressor. Such similarities in shared emotions and opinions
can be expressed on platforms using various mechanisms (watching, liking,
commenting, sharing, downloading a post, creating a new post, following and
unfollowing other users, etc.). Emotion contagion is, at its core, a diffusion
process, which can be characterized based on the following key aspects [58]:

  1. 1.

Contagion is a causal effect on an ego’s outcome at time $t$ of his alters
outcome at time $s\leq t$.

  2. 2.

Homophily is ubiquitous and intransigent in the context of contagion, and it
is the tendency of people who are similar to begin with to share network ties.

  3. 3.

In a dyadic conversation, the contagion effect is well-defined, however social
networks represent a paradigmatic opportunity for interference, where more
than one subject could be responsible for subject’s outcome.

Our work focuses on estimating emotion contagion, a fairly nascent, but
important line of research in social network analysis. Several prominent
studies [28, 24] have indicated that the focus in emotion contagion research
should be to estimate contagion.

Main Contributions: We present the first computational approach for estimating
emotion contagion in dynamic social network graphs. The input to our approach
consists of a graph, $\bm{\mathcal{G}}$, where each node represents a user $i$
with profile $p_{i}$ and each edge between users $i,j$ represents the tie
strength between $i$ and $j$. The objective of the approach is to compute the
emotion contagion value, $\bm{\xi}$, for each node in $\bm{\mathcal{G}}$. The
novel aspects of our work include:

  1. 1.

We estimate emotion contagion by computationally modeling the key drivers of
emotion contagion: causality, homophily, and interference. Despite the
availability of many approaches that detect these factors, no method was
previously known that could quantify them.

  2. 2.

Our diffusion approach models dynamic graphs; put simply, edges are bi-
directional with different weights for each direction. Prior work on detecting
emotion contagion operate on static uni-directional graph networks.

We analyzed $48$ users’ activity over a span of $8$ weeks and estimated the
emotion contagion on them. We obtained the user behavior data from a popular
social media video sharing platform. To validate our analysis, we obtain $150$
human feedback responses via user studies conducted based on the activity of
these $48$ users. The user study corroborates our approach’s results and
quantifies homophily, causality, and interference.

##  2 Related Work

Section 2.1 highlights some of the recent work on analyzing social media
content for various applications. In Section 2.2, we go over the theory of
emotion contagion. In Section 2.3, we specifically focus on digital emotion
contagion and discuss the challenges of existing research directions on
emotion contagion in social media. Lastly, Section 2.4 elaborates on prior
literature in opinion propagation on social networks.

###  2.1 Analyzing Social Media Content

The past two decades have witnessed an increase in the number of social media
platforms, encouraging millions of users across the globe. The amount of
content being generated and shared on these platforms is enormous and has
given rise to many interesting research problems. One such direction is in
automated systems for moderating content like hate speech [55, 14], violent
content [3] and fake news [31, 1] on social platforms. Such platforms have
also shown how useful they can be in response to disaster assessment [32] and
management [38]. Other interesting research problems analyze content shared on
these platforms to understand the dynamics of content likeability and social
validation for content creators [59], influence and opinion propagation for
social media marketing [12, 69], and the components that can make content
trend and go viral on social media [65, 26]. In this work, we analyze another
such aspect, emotion contagion, on social media platforms.

###  2.2 Theory of Emotion Contagion

Prior works have suggested that humans instinctively tend to align with the
emotional states they perceive around them [21, 34, 5]. Various studies have
concluded that emotions can be contagious [66], as a response to which
individuals show behavioral, attentional, and emotional synchrony [34]. Prior
literature has also associated emotion contagion to feelings of empathy and
sympathy [34, 19] and emotional arousal [51, 62, 50]. The study of emotional
contagion has been the focus of various disciplines because different types of
interactions, such as commercial transactions, team communication, and
human–robot interactions, can transfer emotions [46, 13, 42, 48, 49].
Marketing research on emotional contagion has focused on understanding how
positive or negative emotions converge in positive or negative consumer
behavior [19, 41, 25, 16]. More recently, emotion contagion through social
media has been of heightened interest because of the high engagement on these
platforms.

###  2.3 Digital Emotion Contagion

Most prior works [41, 24, 23, 15] have conducted controlled experiments on
social media platforms and confirmed the presence of emotion contagion and its
manipulative effects on individuals. Similarly, [67] and [37] show that the
content we consume on social media affects not only the emotions that we
express on these platforms but also our general well-being. As discussed in
prior literature [28], contagion can occur due to three mechanisms: (i)
mimicry, (ii) activation, and (iii) social appraisal. More specifically,
digital media platforms are known to incentivize competition for attention and
positive reinforcement in the forms of likes or shares [10, 9], and expressing
emotions is an extremely useful way to attract attention. As a result, such
emotion-rich digital activities lead to self-reinforcing loops that enhance
emotion contagion over time. [64] developed Tweet Moodifier, a Google Chrome
extension that enables Twitter users to filter and visually mark emotional
content in their Twitter feed to make them aware of and reflect on the
emotion-rich content being consumed.

###  2.4 Diffusion Models for Social Media Analysis

Diffusion models have increasingly been used to investigate how information
propagates among people for various problems in social media analysis. More
specifically, some of the classical learning models for opinion propagation
and diffusion are threshold models [29], with more recent generalisations by
[39], and the De Groot or Lehrer-Wagner model [17, 45]. Diffusion can be
mathematically defined as an optimization problem with single objective of
optimizing the goal of spreading information and capturing the rate of
information dispersion. There are many factors which may influence the effects
of information diffusion across social networks. Studies pointed out that
diffusion-related behaviors are mainly caused by social infectivity and
homophily [70, 4]. Information flow using diffusion models on social media
with respect to viral tweets [36], pandemic information [52, 20], and fake
news and misinformation [43] has been widely studied.

##  3 Background and Problem Statement

To further enhance the readability and understanding of the paper, we first
formally define the problem statement in Section 3.1. In Section 3.2, we
include a brief background on the mathematical diffusion process on which we
base our approach. We then elaborate more on the key aspects of the contagion
phenomenon and the factors that have been known to cause stronger contagion on
social media as we use this as a base to build our model in Section 3.3.

###  3.1 Problem formulation

Users on this social media platform have regular access to videos where they
may watch videos belonging to a set of topics, $\mathcal{S}$, or perform an
action from an action set $\mathcal{A}$, or both. Currently, we observe the
following actions: play, like, download, share, create, follow, and unfollow.
Each user $i$ has a watch history,
$\mathcal{W}_{i}\in\mathbb{R}^{t\times\lvert\mathcal{S}\rvert\times n_{i}}$,
indicating the videos that $i$ has watched over the past $t$ days, and an
action history,
$\mathcal{U}_{i}\in\mathbb{R}^{t\times\lvert\mathcal{S}\rvert\times n^{a}}$,
where $a\in\mathcal{A}$ denoting the actions that $i$ has performed during
those $t$ days.

######  Problem 3.1.

Given as input a user $c$ (“perceiver”), with corresponding watch history
$\mathcal{W}_{c}$ and action history $\mathcal{U}_{c}$, in a time period of
$t$ days, we want to estimate the emotion contagion on $c$, denoted as
$\bm{\xi}_{c}$, caused by its neighbors (“expressors”).

We model emotion contagion among users $c$ via diffusion in a graph
$\bm{\mathcal{G}}=\left(\mathcal{V},\mathcal{E}\right)$. Each edge between $c$
and a user $1\leq i\leq m$ is bi-directional and weighted. We describe this
diffusion process in the following section.

Emotion contagion can be modeled as a diffusion process over the social graph
network. However, prior models fail to capture the computational aspects of
emotion contagion in large networks due to the following two bottlenecks:

Aspect | Factors | References
---|---|---
Homophily | Connection Strength | [47]
Age, gender, demographics | [35]
Causality | Time Gap b/w Content Consumed and Action Taken |
Interference | Sentiment | [15, 7, 30]

Table 1: Factors affecting emotion contagion: We summarize factors suggested
by prior literature that are known to cause stronger contagion. We model these
factors in our approach (discussed in detail in Section 4.3)

  * •

Size of the graphs: The cost of global diffusion to compute and store the
histories and user profiles grows according to $\mathcal{O}(n^{2})$ and
$\mathcal{O}(n^{3})$, respectively.

  * •

Static edge weights: Static edge weights are easier to compute but do not
accurately reflect the dynamic relationship between two users. Most prior
works limit the edge weights to number of common friends, number of hops
between connections, etc. Such information, though easily available, does not
reflect the dynamic relationships between humans.

Figure 2: Overview: Given an input user $c$ (“perceiver”) and the set of $m$
neighbors of $c$, denoted as $\mathcal{M}$, we want to estimate the emotion
contagion, $\bm{\xi}_{c}$, that $\mathcal{M}$ causes $c$ (“expressors”). We
begin by creating a graph of the social network, $\bm{\mathcal{G}_{c}}$ with
$m+1$ nodes ($1$ central user node $c$ and $m$ nodes corresponding to $m$
neighbors). A dynamic process is allowed to occur where any neighbor $i,1\leq
i\leq m$, may create content, and the central user $c$ consumes that content
and may perform an action $a\in\mathcal{A}$ (part of Figure 2 outlined in
blue). We proceed by using a combination of deep learning and social network
analysis to model the various factors that characterize emotion contagion:
homophily, causality, and interference—and compute the inflow
($\mathcal{I}_{i}$) and outflow ($\mathcal{O}_{i}$) corresponding to any
random neighbor $i$ (shown in green). Finally, we estimate the emotion
contagion value by subtracting the outflow from the inflow (Section 4.2).

###  3.2 Diffusion Process

We can model dynamic processes arising in information systems, such as traffic
networks [57], by performing diffusion on the associated graph structures
described in the previous section. Let $\bm{\Phi}$ and $\bm{T}_{ij}$ represent
the matter to be diffused and the velocity at which matter travels between
nodes $i$ and $j$. The diffusion is described as

$\frac{d\bm{\Phi}}{dt}=-\bm{\widetilde{L}}\bm{\Phi}=-\left(\bm{\widetilde{D}}-\bm{\widetilde{A}}\right)\bm{\Phi}$
(1)

Equation 1 is the well-known diffusion equation [40]. We use
$\bm{\widetilde{L}}$ to denote the weighted Laplacian representation of
$\bm{\mathcal{G}}$. $\bm{\widetilde{D}}$ and $\bm{\widetilde{A}}$ represent
the weighted degree and adjacency matrices of $\bm{\mathcal{G}}$,
respectively. From Equation 1, it follows that the diffusion from a user $i$
to its neighbors $j$ is given as,

$\begin{split}\frac{d\bm{\Phi}_{i}}{dt}&=-\sum_{j}\left(\delta_{ij}\bm{\widetilde{D}}_{ii}-\bm{\widetilde{A}}_{ij}\right)\bm{\Phi}_{j}\\\
&=-\left(\sum_{j}\bm{T}_{ij}\bm{\Phi}_{i}-\sum_{j}\bm{T}_{ij}\bm{\Phi}_{j}\right)=-\sum_{j}\bm{T}_{ij}\left(\bm{\Phi}_{i}-\bm{\Phi}_{j}\right),\\\
\end{split}$ (2)

where $\bm{T}_{ij}$ denotes the edge weight. The second equality follows from
the definition of the degree matrix and the fact that
$\bm{\widetilde{A}}=\bm{T}$. $\sum_{j}\bm{T}_{ij}\bm{\Phi}_{i}$ and
$\sum_{j}\bm{T}_{ij}\bm{\Phi}_{j}$ represent the outflow $\mathcal{O}_{i}$
($j$ to $i$) and inflow $\mathcal{I}_{i}$ ($i$ to $j$), respectively.

###  3.3 Factors Affecting Emotion Contagion

Prominent studies [28, 24] have propounded factors that can indicate strong or
weak emotion contagion on online digital platforms. These factors are also
summarized in Table 1. Various studies suggest that positive emotions are more
prone to contagion than negative emotions [15, 30]. It has also been shown
that stronger ties between the expressor and perceiver lead to stronger
contagion [47]. On the other hand, perceivers’ personalities [11] (easily
influenced/agreeable), their online activities [18], and their demographic
features like age, gender, and culture [35] have proven to influence the
degree of emotion contagion online.

##  4 Our Approach

In this section, we present our algorithm for estimating emotion contagion in
social networks. To begin, we give an overview of our approach in Section 4.1.
We describe our approach as a diffusion model in Section 4.2 and elaborate on
how we take into account, homophily, environmental confounding, causality, and
interference in Section 4.3

###  4.1 Overview

We describe our overall approach in Figure 2. Given an input user $c$
(“perceiver”) and the set of $m$ neighbors of $c$, denoted as $\mathcal{M}$,
we want to estimate the emotion contagion, $\bm{\xi}_{c}$, that $\mathcal{M}$
causes $c$ (“expressors”).

In our approach, we begin by creating a graph of the social network,
$\bm{\mathcal{G}_{c}}$ with $m+1$ nodes ($1$ central user node $c$ and $m$
nodes corresponding to $m$ neighbors). A dynamic process is allowed to occur
where any neighbor $i,1\leq i\leq m$, may create content and the central user
$c$ consumes that content and may perform an action $a\in\mathcal{A}$. This is
indicated by the part of Figure 2 outlined in blue. We proceed by using a
combination of deep learning and social network analysis to model the various
factors that characterize emotion contagion: homophily, causality, and
interference.

In the following sections, we describe our approach to modeling emotion
contagion as a diffusion process that addresses two bottlenecks, global
diffusion and static edge weights, enabling large-scale emotion contagion
modeling in large social networks.

###  4.2 EC in Localized Dynamic Graphs

####  4.2.1 From Global to Local Graphs:

Very little of the literature studying emotion contagion focuses on its
estimation due to the challenges of modeling diffusion on large social graphs.
The cost of global diffusion for computing and storing the histories and user
profiles grows according to $\mathcal{O}(n^{2})$ and $\mathcal{O}(n^{3})$,
respectively. Furthermore, global diffusion on these large graphs inevitably
includes nodes with large degrees, for example, nodes corresponding to
celebrities, athletes, and so on, which create bottlenecks. We instead perform
localized diffusion, focusing on selected central user nodes. This selection
may be targeted or, in the worst case, random. Due to the sparsity of
bottleneck nodes, localized diffusion helps in bypassing most bottlenecks.

For each central user $c$, we extract a star graph $\bm{\mathcal{G}_{c}}$
consisting of $\lvert\mathcal{V}_{c}\rvert=m+1$ user nodes with $c$ as the
central node and $\lvert\mathcal{E}_{c}\rvert=m$ edges.

####  4.2.2 From Static to Dynamic Edge Weights

We follow the speed-matching model used by Nagatani [57]. According to the
model, flow is represented by the concentration of matter at the source
multiplied by the velocity at the destination node. We set
$\bm{T}_{ij}\leftarrow u_{ij}\neq\bm{T}_{ji}\leftarrow u_{iji}$. Then the
dynamic equivalent form of Equation (2) becomes,

$\begin{split}\frac{\nabla\Phi_{i}}{\nabla
t}=\mathcal{I}_{i}-\mathcal{O}_{i}=\sum_{in=1}^{k_{in}}\Phi_{j}u_{ji}-\sum_{out=1}^{k_{out}}\Phi_{i}u_{ij}\\\
\end{split}$ (3)

####  4.2.3 Modeling the Inflow ($\mathcal{I}_{i}$) and Outflow
($\mathcal{O}_{i}$)

In this section, we use the concepts of localized diffusion on dynamic graphs
to define equations for the inflow and outflow terms. The inflow
$(i\xrightarrow{watch}c)$ describes the videos that are posted by $i$ and have
been watched by $c$, who may then choose whether or not to perform any action.
These actions are represented in the outflow $(c\xrightarrow{action}i)$. The
inflow and outflow represent the change in density at a particular node, which
corresponds to the rate of diffusion, or the strength of contagion. If, for a
particular user $i$, we consider the watch history,
$\mathcal{W}_{i}\in\mathbb{R}^{t\times\lvert\mathcal{S}\rvert\times n}$, till
time $t$, and we further restrict each entry of the watch history to be the
number of videos, $n$, then we can rewrite the watch history as the following
2D matrix,

$\mathcal{W}_{i}=\left[\begin{array}[]{cccc}\bm{n}_{11}&\dots&\bm{n}_{t1}\\\
\vdots&\ddots&\vdots\\\
\bm{n}_{1\lvert\mathcal{\mathcal{S}}\rvert}&\dots&\bm{n}_{t\lvert\mathcal{\mathcal{S}}\rvert}\\\
\end{array}\right]_{\lvert\mathcal{\mathcal{S}}\rvert\times t}$ (4)

Using Equation (4), the inflow corresponding to neighbor $i$ may be compactly
written as

$\mathcal{I}_{i}=\mathcal{T}W_{t},$ (5)

where $\mathcal{T}A$ is a trace function operator on a 2D matrix $A$, and
computes $\operatorname{Tr}{\left(\sqrt{A}^{\top}\sqrt{A}\right)}$ (sum of all
entries of $A$) with $\operatorname{Tr}{(\cdot)}$ is the matrix trace
operator. Similarly, the outflow can be represented by the 2D matrix,

$\mathcal{U}_{i}=\left[\begin{array}[]{cccc}\bm{\Gamma}(n_{11})&\dots&\bm{\Gamma}(n_{t1})\\\
\vdots&\ddots&\vdots\\\
\bm{\Gamma}(n_{1\lvert\mathcal{S}\rvert})&\dots&\bm{\Gamma}(n_{t\lvert\mathcal{S}\rvert})\\\
\end{array}\right]_{\lvert\mathcal{\mathcal{S}}\rvert\times t},\
\bm{\Gamma}(n)=\sum_{l=1}^{n}e^{-age}\delta_{f}\delta_{c}\delta_{e}$ (6)

which implies

$\mathcal{O}_{i}=\left(p_{i}^{\top}p_{c}\right)\mathcal{T}\mathcal{U}_{i}$ (7)

(a) Depiction of the number of followers for the $48$ users analyzed. (b)
Depiction of the choice of language for the $48$ users analyzed. (c) Depiction
of the gender distribution for the $48$ users analyzed. (d) Depiction of the
age distribution for the $48$ users analyzed.

(e) We visually depict the temporal aspect of the data. The visualization has
been generated for one of the $48$ users for a period of $2$ weeks of the
total $8$ weeks of data. For every day the user comes online, we have the
videos played by the user (orange column on the left) and also the data
corresponding to like, share, download, create, follow and unfollow (stacked
column on the right).

Figure 3: Dataset Visualizations: To further understand the data used for
analysis, we depict user profiling statistics (neighbors, age, gender, and
language). We also show the temporality of the nature of the data used with an
example of one of the $48$ users and their activities on the platform for $2$
weeks.

We now define several key aspects that appear in the outflow equation
(Equation 6). First, we decay the action taken by $c$ exponentially consider
the temporal nature of the action. For example, if, on day $t$, $c$ likes a
video that was posted, in fact, on day $t-3$, then that action would be scaled
by $e^{-3}$. Next, the actions follow, unfollow, and create do not contribute
to the count directly and must therefore be modeled separately. $\delta_{f}$
is a step function with a value of $1$ if $c$ follows $i$ and $\frac{1}{2}$
otherwise. $\delta_{c}$ and $\delta_{e}$ denote the semantic and emotion
correlation scores between a video created by $c$ and all other videos up to
day $t$. For sentiment/emotion correlation, we use a context-based emotion
prediction method [emoticon]. We use the audio, video and background context
for inferring the sentiment. We obtain a single number $\pm 1$ referring to
positive or negative sentiment videos.

###  4.3 Modeling EC Factors

Part of the difficulty in estimating emotion contagion is attributed to the
challenges of modeling its underlying aspects: homophily, causality, and
interference. These aspects, absent in related concepts like virality and
influence, shape the contagion diffusion model. Estimating emotion contagion,
therefore, is equivalent to modeling these factors.

##### Homophily:

Consider two sports fans, Tom and Harry. Both are young students who speak the
same language, live in the same city, and follow each other on social media.
Their connection is further strengthened due to the fact that both Tom and
Harry react to each other’s posts related to sports. This is an example of
homophily with respect to personal demographics. We model this part of
homophily by creating vector representations of users’ information. Personal
information, such as age, gender, language, city, connection strength to the
central user, and so on, are first stored in a vector $\hat{p}$. We use
$\hat{p}_{c}$ and $\hat{p}_{i},1\leq i\leq m$ to denote the personal
information vector of the central user and his or her neighbors, respectively.
We then use multi-scale attributed node embedding [61] to generate embeddings,
$p_{c},p_{i}$ from these raw information vectors. We then take the dot
product, $p_{c}^{T}p_{i}$ to compute the correlation between the users.

Homophily not only considers the similarity between users, but also between
the content they consume and post online. Consider, again, the two sports fans
Tom and Harry, who regularly post news of soccer events. If Tom posts an
announcement for an upcoming match, Harry is likely to like, share, or even
save the details of the match. This is another example of homophily that
points to the audio-visual and emotional signals of the content posted by Tom
and consumed by Harry. Suppose, now, that Harry ends up attending that sports
event and posts a video of (part of) the match. The audio-visual, as well as
the sentiment, similarity of Tom’s announcement and Harry’s video is another
indicator of homophily.

We measure audio-visual and sentiment similarity ($\delta_{c}and\delta_{e}$,
respectively) between content using state-of-the-art deep learning models.
Specifically, given a video $v_{c}$ created by a central user $c$, we compute
it’s audio-visual and semantic correlation, represented by $\delta_{c}$, with
all the videos that $c$ has played. We use 3D convolutional networks [33] as a
feature extractor function, denoted by $\mathcal{D}(\cdot)$, to compute the
video embeddings and a python library [27] to compute audio embeddings. We
start by computing the correlation between the pair of vectors,
$\mathcal{D}(v_{c}),\mathcal{D}(v_{i})$ and
$\mathcal{Q}(v_{c}),\mathcal{Q}(v_{i})$,

$\bm{\rho}_{\mathcal{D}}=\frac{\operatorname{E}\big{[}\mathcal{D}(v_{c})\mathcal{D}(v)\big{]}}{\sigma\big{(}\mathcal{D}(v_{c})\big{)}\sigma\big{(}\mathcal{D}(v)\big{)}},\quad\bm{\rho}_{\mathcal{Q}}=\frac{\operatorname{E}\big{[}\mathcal{Q}(v_{c})\mathcal{Q}(v)\big{]}}{\sigma\big{(}\mathcal{Q}(v_{c})\big{)}\sigma\big{(}\mathcal{Q}(v)\big{)}}$
(8)

for every video $v$ that $c$ has played. Finally, we manually apply a
logarithmic scale to the correlation, according to our dataset. $\delta_{c}$
is computed as:

$\delta_{c}=-\textrm{age}\big{(}\log(1-\bm{\rho}_{\mathcal{D}})\big{)}-\textrm{age}\big{(}\log(1-\bm{\rho}_{\mathcal{Q}})\big{)}$
(9)

where the age parameter indicates the causality factor, which is explained
below. We note that Equation 9 is a hand-crafted heuristic chosen after
observing the given dataset. Learning this function using statistical learning
and deep learning techniques is a promising future direction but we defer that
to future work.

##### Causality:

Another factor used to estimate emotion contagion is the duration between when
a perceiver plays some content created by the expressor and when he or she
reacts to that content. Recall our case study from earlier; Harry, reacting to
Tom’s post, rather than a few days later, incurs different contagion levels;
an immediate reaction is a case of higher contagion compared to the latter
because of Harry’s response time. This example perfectly illustrates the
notion of causality: The faster a perceiver reacts to an expressor, the larger
the causality and, by our model, the higher the contagion. More formally, we
represent causality with the variable age indicating the reaction response
duration in days. Since contagion diffusion follows the standard linear decay
model, the effect of age decays exponentially. Hence, the term $e^{age}$
appears in Equation 7.

##### Interference:

Multiple neighbors may jointly influence the central user. While modeling
single expressor-perceiver connections has been explored in prior studies,
estimating contagion in the case of multiple perecivers and expressors is a
harder endeavor. In our approach, we address this issue by leveraging the
property of star traffic network graphs where the inflow and outflow are
isolated along individual edges. To model the effect of $N$ neighbors, we
simply sum the inflow and outflow along the $N$ distinct edges.

##  5 Dataset

To the best of our knowledge, there is no dataset available for detection and
estimation of emotion contagion, mainly because $i)$ this requires tracking a
user’s activity online for a consecutive time frame and $ii)$ contagion is not
a well-understood term to be able to collect human annotations. Hence, for our
purpose we extract users’ social media information (content they watch, like,
share, and download) from a popular video sharing platform designed for
professional and amateur content creators. We extract user activity for $48$
users over a span of $8$ weeks on the platform. We give more insights about
the data in Section 5.2. Due to the sensitive nature of the extracted
information, we have not released our dataset. That being said, to foster
reproducability, we provide details for extracting our data in Section 5.1.

###  5.1 Dataset Structure and Extraction Process

We select $48$ users who are active on the platform between November
$27^{\textrm{th}},2021$ and February $1^{\textrm{st}},2022$. For each day a
given user comes online, we extract the list of actions performed and their
timestamps, URLs of the videos watched, created, shared, or downloaded, user
IDs (masked), and the topic of the videos. We also retrieve user profiling
information of the $48$ users and their neighbors which includes age, gender,
number of followers, demographic location, language. In total, this involved
analyzing over $200$k short videos roughly watched, created, liked or shared
by these users.

###  5.2 Dataset Analysis

We visualize our data in Figure 3. We present distributions over user profile
information including followers, language, gender, and age in Figures 3(b),
3(c), and 3(d), respectively. In Figure 3(e) shows the activity for $1$
central user during a $2$-week period. At a high level, we use the orange
columns and multi-color stacked columns to calculate the inflow $\mathcal{I}$
and outflow $\mathcal{O}$, respectively. Visually, similar heights between an
orange column and its corresponding stacked column indicate higher contagion
($\mathcal{I}-\mathcal{O}\approx 0$), which occurs on two occasions—$12/24/21$
and $12/29/21$. We provide a more in-depth analysis of the data in Appendix A.

##  6 Experiments and Results

We describe the user study conducted to obtain ground truth for the data, and
analyze its responses, in Sections 6.1 and 6.2, respectively. We also discuss
the efficiency of our approach in terms of computational resources
highlighting the benefits of modeling localized emotion contagion in dynamic
social network graphs in Appendix B.2. We will publicly release our code upon
acceptance.

###  6.1 Obtaining Ground Truth via User Studies

In the absence of benchmark datasets and curated ground truth for detecting
and estimating emotion contagion, we conduct an extensive user study in the
form of multiple questionnaires. Each questionnaire was designed to address
three goals: $(i)$ to corroborate our approach’s results using human feedback,
$(ii)$ to understand people’s interpretation of the importance over different
actions, and $(iii)$ to emphasize the underlying aspects of emotion contagion,
namely, homophily, causality, and interference.

We prepared $10$ questions for each questionnaire. Questions $1-4$ (unique to
each questionnaire) ask participants to answer questions about a given central
user’s online activity including his or her engagements with neighbors,
question $5$ presents a scenario comparing different actions, and questions
$6-10$ (identical across questionnaires) inquire about a participant’s general
social media usage. We circulate anonymous web links to these questionnaires
and obtained approximately $150$ responses. In the following sections, we
analyze the responses to $5$ of the questionnaires sent out. Throughout a
questionnaire, we deliberately avoid the term contagion and, instead, use the
term influence. Due to lack of space, we attach full copies of these
questionnaires in the supplementary material.

###  6.2 Evaluation

We divide our analysis based on the three parts described above. In all
instances, a lower value for $\xi$ indicates higher contagion.

####  6.2.1 Analysis for Q$\bm{1-4}$: Does our approach estimate EC accurately
?

We analyze the questionnaire as case studies. Our objective through these
studies is to confirm that the contagion values obtained from our
computational model agrees with the participants’ responses.

Case Study $\bm{1}$: On a particular day, user A watched, and liked, $15$
videos posted by user B. On another day, user A watched $150$ videos posted by
user D, without reacting to those videos. User A followed both users B and D
afterwards.

In this study, we asked participants to report which user, between B and D,
had a greater influence on A in their opinion. Out of $17$ responses, $10$
indicated that B is likely to have had a bigger influence on A. This response
strongly agrees with our computational model, which indicates that contagion
caused by user B ($\xi_{B}=11.73$) is approximately $11\times$ more than that
caused by user D ($\xi_{D}=124.56$). From the case study, we may also conclude
that the “active” actions such as liking, sharing, etc. are stronger than
“passive” actions like watching.

Case Study $\bm{2}$: User A watches, likes, and shares all videos created by
Users B and C over a span of 8 weeks across various topics.

As before, participants must report which user, from their perspective, had a
greater influence on A. Unlike the previous one, however, this study does not
contain user activity information. The participants do, however, have access
to personal details about the users which includes age, gender, language,
location, and number of followers.

The response to this study was mixed. Of $28$ participants, $4$ chose B to
have a greater influence, $6$ felt otherwise, and $18$ indicated there was not
enough information to decide. Our model can explain why such a response was
received. While, objectively, C does indeed have a stronger contagion effect
than B ($\xi_{C}=86.41$ versus $\xi_{B}=133.50$), the profile embedding scores
of B ($0.61$) and C ($0.65$) are similar. From the demographic information, C
was closer to A in terms of age and language, but B was more popular with more
followers, hence confusing the participants trying to decide who had a more
similar profile to A.

Case Study $\bm{3}$: User A regularly watches videos of the topic, ‘Albums &
Concerts’ created by various users on the platform for $4$ weeks, but does not
create videos on the same topic. In the $5^{\textrm{th}}$ week, User A created
the first $2$ videos of this topic.

The question put to participants changes slightly in this study; instead of
comparing the contagion tendencies between two users, we simply ask the
participants if they felt A was influenced by the videos he or she watched
during those four weeks. A majority ($20/28$) voted yes. To verify this, we
compared the contagion value in the ‘Anger’ topic of which A, similar to
‘Albums & Concerts’, watched many videos, but did not create any. We observed
that when A did not create videos despite watching videos of that topic for
four weeks, the contagion on A drops by a factor of $2$
($\xi_{\textrm{A\&C}}=39.00$ versus $\xi_{\textrm{Anger}}=21.64$).

####  6.2.2 Analysis for Q$\bm{5}$: Do actions contribute equally to EC?

Claim | User Study | Approach
---|---|---
follow/unfollow $>$ like/share/download | $73.2\%$ | $50\%$
create $>$ follow/unfollow | $57.1\%$ | $75\%$
create $>$ like/share/download | $64.7\%$ | $87.5\%$
create $>$ watch | $85\%$ | $98\%$

Table 2: User Study (Q$5$) Results: We summarize the results of Q$5$ and also
report the performance of our approach on $48$ users with randomly selected
creators.

Question $5$ compares the potential for causing contagion between pairs of
actions in $\mathcal{A}$. An example of such a question could be to compare
liking $10$ videos of a particular neighbor with creating $1$ video in the
same category. In this example, participants are asked to report which of the
two actions, in their opinion, had a greater influence on the central user. We
present $5$ such comparisons in Table 2. The first column contains the
question setup containing the pairwise action comparison. The second and third
columns indicate the percentage of participants and central users that agree
with the corresponding relation in the first column. We refer readers to the
questionnaires for exact language of the questions and options.

This experiment further serves to distinguish influence from contagion.
Actions that may seem influential over other actions may not necessarily cause
stronger contagion. For instance, $73.20\%$ participants indicated that follow
(or unfollow) induces a greater influence than actions such as like, share,
and download, whereas our analysis yielded only $50\%$ of the central users
who agreed with that assessment. Objectively, this may make sense since to
follow someone is a “stronger” response. Our contagion model additionally
takes into account profile similarity, age of the content, and causality to
determine contagion. In the instance considered above, the central users may
have followed users after considerable time passed since the former watched
the latter’s videos. Alternatively, the profiles of the central users and the
expressors might have been dissimilar.

Figure 4: User Study (Q6 - Q10) Results: Response summary to the last five
questions (same across all the questionnaires).

####  6.2.3 Analysis for Q$\bm{6-10}$: Is there a discernible relationship
between people’s social media usage and the factors characterizing EC?

We asked the following questions:

Q$6$: What do you think is the concept of “digital emotion contagion”?

Q$7$: Do you think the content you share on social media is affected,
influenced or based on the content you consume online? Additionally, do your
opinions often change based on the content you consume on social media?

Q$8$: What comprises of the people you follow on social media?

Q$9$: How do you decide to follow/subscribe a user on social media?

Q$10$: When do you like/share a content post on social media?

We summarize the results of the user study to questions $6-10$ in Figure 4. We
refer the readers to the questionnaires in the appendix for the options
corresponding to each question.

Questions $6$ and $7$ survey participants’ knowledge of digital emotion
contagion and its effects on participants. From the responses to question $6$,
$75\%$ of the participants are unaware of emotion contagion, misinterpreting
contagion, instead, with virality (option $1$) or posts intended to influence
their audience (option $2$). For question $7$, we found that that $57\%$ of
the participants believe the content they share online is not influenced by
what they consume while $42\%$ indicated otherwise. The lack of a clear
consensus among the participants reveals that there is little awareness of the
effects of contagion, emphasizing the importance of the proposed work.

S. No. |  Scenario | Approach Insights
---|---|---
$1$ |  Watch more ‘negative’ (sentiment) than ‘positive’ videos | $23\%\uparrow$
$2$ |  More neighbors | $12\%\downarrow$
$3$ |  More homophilic neighbors | $28\%\uparrow$
$4$ |  Topic diversity | $8\%\downarrow$

Table 3: Other Scenarios: We analyze some scenarios and generate results for
$48$ users and understand how emotion contagion changes with different
scenarios.

Our objective through questions $8,9,$ and $10$ was to discover the presence
of homophily, causality, and interference in emotion contagion. From the
responses to question $8$, participants follow their friends (option $2$),
family (option $3$), strangers whose content they relate to (option $4$), and
celebrities (option $1$) which are not necessarily homophilic in nature. Our
takeaway from Q$9$ is that actions on social media are causal in nature.
$71\%$ of the users reported that they take their time before ‘following’
people on social media. In Q$10$, $80\%$ participants reported that they base
low-effort actions like ‘like’ and ‘share’ mostly on the content of the
respective post (option $2$), followed by liking because posts were created by
close friends (option $1$) or for bookmarking for inspiration of future posts
(option $3$), indicating each relationship on social media leads to a
different level of engagement and hence will be contagious at varying levels.
Responses to these questions validate the need and the decision of taking into
consideration, aspects of homophilic connections, causality of actions, and
the interference of contagious connections.

###  6.3 Scenario Specific Insights

Our approach offers flexibility to test, and generate, insights of contagion
in a wide range of settings. We examine four such settings summarized in Table
3. In the first experiment, we vary the sentiment of the content consumed by
central users. We find that the contagion increases when the content is more
negative than positive (Row $1$). In fact, such a finding was theoretically
hypothesized by Goldenberg and Gross [28]. In the second experiment, we
investigated the effects of increasing the number of homophilic neighbors for
each central user, and observed an increase in contagion (Row $3$). Finally,
in rows $2$ and $4$, we observe that contagion decreases when central users
interact with more expressors, who may not necessarily be homophilic, or
engage in more diverse topics, which decreases the exposure to content per
topic.

##  7 Conclusion

We shed light on a crucial, yet unexplored from a computational perspective,
research problem that affects millions of users. For the first time, using a
combination of deep learning and social network analysis, we showed we can
accurately estimate emotion contagion in dynamic social media networks. We
verified our approach by conducting a user study conducted with $150$
participants and comparing the participant responses to the outputs from our
approach.

There are some limitations to this work. Currently, we heuristically scale the
outflow by the audio-visual and semantic similarity (Equation 6). This
equation, fine-tuned to our dataset, may need to be adjusted for other
datasets. Second, we do not consider the environment of a user off the social
media platforms. The challenges of procuring users’ environment information
notwithstanding, such information contributes to the confounding aspect of
emotion contagion, but is not considered in this paper, since it requires
specialized data. In the future, we plan to explore ways of automatically
estimating the outflow equation from the data using machine learning. We
discuss ethical considerations taken with the handling of data in Appendix C.

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##  Appendix A More Data Analysis

Figure 5 lists the neighbor count for each central user; the highest being
$6,587$. A neighbor is any user whose content has been engaged with by a
central user, and who may not necessarily be a follower of, or follow, the
central user. Similarly, in Figure 6, we visually depict the breadth of topics
the $48$ users engaged in over the entire time span. Finally, in Figure 7 \-
Figure 13, we depict the frequency of each action in $\mathcal{A}$ by all $48$
users.

Figure 5: Depiction of the number of neighbors each of the $48$ users
interacted with over $8$ weeks. Figure 6: Depiction of the breadth of topics
the $48$ users engage in over $8$ weeks. Figure 7: Depiction of the number of
videos the $48$ users watched in over $8$ weeks. Figure 8: Depiction of the
number of videos the $48$ users created in over $8$ weeks. Figure 9: Depiction
of the number of videos the $48$ users liked in over $8$ weeks. Figure 10:
Depiction of the number of videos the $48$ users shared in over $8$ weeks.
Figure 11: Depiction of the number of videos the $48$ users downloaded in over
$8$ weeks. Figure 12: Depiction of the number of videos the $48$ users
followed in over $8$ weeks. Figure 13: Depiction of the number of videos the
$48$ users unfollowed in over $8$ weeks.

##  Appendix B More Experiments and Results

We first present more case studies for more analysis of Q$1-4$ in Section B.1.
Then in Section B.2, we discuss the efficiency of our approach in terms of
computational resources highlighting the benefits of modeling localized
emotion contagion in dynamic social network graphs.

###  B.1 More User Study Analysis

We add $2$ more case studies to extend our evaluation in Section $6.2.1$ for
Q$1-4$.

Case Study $\bm{4}$: User A watches a mix of ”Romantic Poetry” videos for a
month, often downloading and watching videos by users D and E. User A creates
a video in this category after 1 month. User A does not normally create many
videos in this category.

The focus of this study is to confirm the contagion resulting from having
created a video after watching many similar videos in the same category. This
time, we ask participants if both D and E were responsible for causing
contagion. An overwhelming majority replied affirmatively, which is also
corroborated by our model ($\xi_{D}=11.86,\xi_{E}=3.27$).

Case Study $\bm{5}$: User A watched 1 video posted by user C and unfollowed
user C afterwards. During the next 3 weeks, user A watched a few more videos
posted by user C and followed user C again.

The focus of this study is to confirm the contagion resulting from having
followed a user after watching their videos. As before we ask participants if
C is responsible for causing contagion. An overwhelming majority replied
affirmatively, which is also corroborated by our model ($\xi_{C}=2.53$). In
addition, we also note that the profile embedding similarity between the
central user A and user C is $0.63$.

###  B.2 Computation efficiency Analysis

Global diffusion involves simultaneously computing the contagion effects for
every central user for every neighbor simultaneously by diffusing through the
entire graph [22]. But the cost of storing the audio-visual information for
the entire graph scales with the number of central users and the average
number of neighbors per user. Empirically, we found that for a graph
consisting of $50$ central users, each with $1,461$ neighbors on average,
modeling the global diffusion would require approximately $4.22$ days and
$14.60$ TB of storage. Isolating the computation across central users and
neighbors, on the other hand, reduces the cost by a factor of
$\mathcal{O}(CM)$, where $C$ and $M$ denote the number of central users and
average number of neighbors per user, respectively. In our setup, computing
the emotion contagion requires approximately $2$GB and $5$ minutes.

Computing contagion locally offers several benefits in addition to reducing
the computational complexity. By performing local diffusion over selected
users, we avoid bottlenecks in global diffusion caused by including popular or
famous users who, though few, typically contain thousands or even millions of
followers (neighbors). Local diffusion also elegantly handles addition and
deletion of edges in realtime; a change in the edge list for a central user
$c$ does not affect local diffusion for all remaining central users. This is
not true in the case of global diffusion, where changes in the edge structure
in any part of the graph would necessitate restarting the diffusion process.

##  Appendix C Ethical Considerations

The dataset used in this paper sources videos from a popular social media
application for sharing short videos. These videos show users’ faces and their
user profiling information contains personal details such as age, gender,
language, and location. Given the sensitive nature of this dataset, we decide
against publicly releasing the data. We have, instead, provided directions to
replicate our data preparation process on other social media platforms. More
importantly, we do not collect any personal information of the involved human
participants in the user studies.