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arXiv:1608.03656v1 [cs.SI] 12 Aug 2016
Easier contagion and weaker ties make
anger spread faster than joy in social media
Rui Fan1, Ke Xu1and Jichang Zhao2,*
1State Key Lab of Software Development Environment, Beihang University
2School of Economics and Management, Beihang University
∗Corresponding author: jichang@buaa.edu.cn
(Dated: August 15, 2016)
Abstract
Similar to face-to-face communication in daily life, more and more evidence suggests that human
emotion also spread in online social media through virtual interactions. However, the mechanism
underlying the emotion contagion, like whether different feelings diffuse unlikely or how the spread
is coupled with the social network, is rarely investigated. Indeed, because of the costly expense
and spatio-temporal limitations, it is challenging for conventional questionnaires or controlled ex-
periments. While given the instinct of collecting natural affective responses of massive connected
individuals, online social media offer us an ideal proxy to tackle this issue from the perspective of
computational social science. In this paper, based on the analysis of millions of tweets in Weibo, a
Twitter-like service in China, we surprisingly find that anger is more contagious than joy, indicat-
ing that it can sparkle more angry follow-up tweets and anger prefers weaker ties than joy for the
dissemination in social network, indicating that it can penetrate different communities and break
local traps by more sharings between strangers. We conjecture that easier contagion and weaker
ties could together make anger spread faster than joy, which is further justified by the diffusion of
bursty events with different dominant emotions. To our best knowledge, for the first time we quan-
tificationally disclose the difference between joy and anger in dissemination mechanism and our
findings would shed lights on personal anger management in human communication and collective
outrage control in cyber space.
1
I. INTRODUCTION
Emotions have a substantial effect on human decision-makings and behaviors [22]. Emo-
tions also transfers between different individuals through their communications and interac-
tions, indicating that emotion contagion, which make others around experience the similar
emotional statuses, could possibly promote social interactions [34, 37] and synchronize col-
lective behavior, especially as the individuals are embedded in social networks [42]. From
this perspective, better understanding of the emotion contagion can essentially help up-
grade emotion management and disclose collective behavior patterns. However, the detailed
mechanism of emotion contagion in context of the social network still remains unclear.
Conventional approaches like laboratory experiments are pervasively employed to testify
the existing of emotion contagion in realistic circumstances [21, 28, 41]. However, to unravel
the detailed mechanism beyond the emotion contagion is much more challenging. It is hard
for the controlled experiments to establish a large social network, stimulate different emo-
tions simultaneously and then track the propagation of emotions in real-time. Meanwhile,
in order to study the coupled dynamics between the social structure and emotion contagion,
properties like relationship strengths should be considered, while which might further import
uncontrolled contextual factors and fundamentally undermine the reliability of the experi-
ment. We argue that it is extremely difficult for conventional approaches to investigate the
spread mechanism in the context of large social network and long-term observation, and
the footprints of natural affective responses from massive individuals in online social media
indeed offer us a new and computational perspective [23, 33, 34].
It is not easy to differentiate online interactions from face-to-face communication in terms
of emotion contagion [17]. More and more evidence from both Facebook and Twitter in
recent years consistently demonstrates the existing of emotion contagion in online social
media [10, 13, 14, 25, 26, 31, 32]. Kramer et al. for the first time provide the experimental
evidence of emotion contagion in Facebook by manipulating the amount of emotional content
in the News Feed [32]. Later Ferrara and Yang disclose the evidence of emotion contagion
in Twitter [19]. Instead of controlling the content, they measure the emotional valence of
the content and show that posting positive and negative tweets both follow significant over-
exposures, indicating the spread of different feelings. Evidence from both studies suggests
that even in the absence of non-verbal cues of in-person interactions [19], emotions like
2
positive and negative feelings can still transfer from one user to others in online social media.
In fact, through posting, reposting and other virtual interactions, users in online social media
express and expose their natural emotional states into the social network in real-time as the
context evolves. Hence being an ubiquitous sensing platform, the online social media collects
emotion expression and dissemination in the most realistic and comprehensive circumstance
and thus provides us an unprecedented proxy to obtain universal insights of the underlying
mechanism of emotion contagion in social network.
However, in the previous study, emotions in online social media are usually simplified into
the positive and the negative [5, 6, 19, 32] and many fine-grained emotional states, especially
the negative ones like anger and disgust are neglected. In fact, negative feelings like anger
on the Internet might greatly dominate online bursts of societal issues or terrorist attack
and play essential roles in driving the collective behavior during the event propagation [11,
44]. Aiming at fill this vital gap, in this paper, we categorize the human emotion into
four categories [18, 44], including joy, anger, disgust and sadness and try to disclose the
mechanism underlying their spread. Fine-grained emotional states enrich the landscape
of emotion contagion and make it possible to systematically understand the underlying
mechanisms between social structures and propagation dynamics.
In this paper, we employ over 11 million tweets posted by around 100 thousand users
of a half year in Weibo, a variant of Twitter in China to perform the computational and
quantificational investigation of emotion contagion. Surprisingly, we find that among the
four emotions we study, joy and anger demonstrate significant evidence of contagion and
anger is the most contagious mood, indicating that under the same volume of exposure,
angry messages will sparkle more follow-up retweets or tweets than joy in the near future.
Besides, from the view of coupled dynamics with the social structure, different measures
of relationship strengths consistently show that anger prefers weaker ties than joy in the
dissemination, indicating that angry tweets can break local traps and arrive the global
coverage with greater odds. We conjecture that easier contagion and weaker ties could make
anger spread faster than joy in online social media, then over 40 million tweets from 616
online bursts in China further solidly testify this argument. In these sudden events, we
find that negative ones with anger as the dominating emotion arrives their diffusion peaks
with shorter intervals and higher velocities than joyful counterparts. Our findings about the
emotion contagion will be insightful for personal anger management and collective behavior
3
understanding in realistic scenarios either online or offine.
II. RESULTS
In this study, 11,753,609 tweets posted by 92,176 users from Sept., 2014 to Mar., 2015
are collected, including the following network of these users. Through a Bayesian classifier
trained in [44], each emotional tweet in our data set can be automatically labeled to joy,
anger, disgust or sadness. Then the diffusive probability and structure preferences are
accordingly investigated in the social network of around 100 thousand subjects. Finally the
realistic bursts in Weibo will be employed to testify the conjecture that anger spreads faster
than joy, in which 40,005,242 tweets of 616 different events are employed to perform the
computational analysis [36].
A. Anger is more contagious than joy
Rather than manipulating the content users receive [31], we measure the emotion con-
tagion through the extent to which a user will be influenced emotionally by the tweets she
received in Weibo during a certain period, i.e., an observation window. Similar to [19], it
is assumed that the emotion that users are exposed to in the recent past will stimulate
similar emotional status and which can be reflected by users’ newly posted tweets. Each
individual in Weibo can be embedded into a online social network with nodes being users
and directed links being following relationships, for example, if a user u(follower) follows
a user w(followee), a tie will be established from uto w, indicating that tweets posted by
wwill be flooded to uin real-time. Supposing the observation window is ∆ hours, a vector
v(tu) = (panger , pdisgust, pj oy, psadness) represents the emotion distribution of tweets exposed
to uwithin ∆ before posting the tweet tu. Note that we omit the tweets with total exposure
less than 20 tweets to ensure the reliability of the measurement. By averaging over each
dimension of all tweets’ exposure vectors, a vector vall can be obtained to reflect the baseline
of emotion distribution before any tweet is posted in Weibo. While for a certain emotion
i(i= 1,2,3 or 4), by averaging over each dimension of all tweets with emotion i, a vector
viis similarly obtained to stand for the average emotion distribution before any tweet with
emotion iis posted in Weibo. Then for emotion i, the difference (denoted as di) on dimen-
4
0.5
1.0
1.5
2.0
1 2 3 4 5 6 7 8 9 10 11 12
∆
Difference (%)
a
47
48
49
50
51
52
1 2 3 4 5 6 7 8 9 10 11 12
∆
Percentage (%)
b
Anger
Disgust
Joy
Sadness
Figure 1. Contagion of different emotions. (a) The contagion tendency of different
emotions declines with the length of observation window (in hours). (b) The percentage of
influenced tweets for both anger and joy rises with the growth of observation window and
the fraction of influenced tweets in anger even exceeds 50% when ∆ >4 hours.
sion ibetween vall and vican intuitively reflect the contagion tendency, i.e., the significance
of contagion, of iin Weibo. Higher diimplies that emotion iwill stimulate more tweets with
the same emotion in the near future than the average level, suggesting it is more contagious
from the perspective of emotional influence.
As can be seen in Fig. 1(a), dang er and djoy are significantly higher than that of other
emotions, which indicates that both emotions can spread in the social network, especially
for anger which possesses the highest significance as compared to the baseline. For example,
danger is about 2.1% when ∆ = 1, which means that users received 2.1% more angry tweets
than ordinary time before they post an angry message. However, the significance of contagion
is relatively low for disgust and sadness, especially for disgust, suggesting the possibility of
contagion is trivial. Because of this, in the following content we only focus on anger and joy.
Note that dialso decrease as ∆ grows, because the influence of the emotion decays with time
and thus users are easier to be influenced by messages they received in more recent hours,
which is consistent with our intuition. While even ∆ grows, anger persistently shows the
most significant difference, indicating that it is more contagious than joy and is a stronger
stimuli in emotion expression of human in the social network.
Emotion influence is closely entangled with emotion contagion. When emotion spread in
5
the social network, connected individuals could influence each other emotionally and later
might lead to the clustering of emotion, i.e., networked individuals demonstrate homophily
in sentimental statuses. For example, Bollen et. al find that happiness of users is assorta-
tive across Twitter [7] and Bliss et. al reveal that average happiness scores are positively
correlated between friends within three hops [5]. Particularly, Fan et. al even show that in
Weibo anger possesses stronger correlation than joy for friends within three hops, suggesting
that anger is more influential than joy [18]. Inspired by this, similar to the metric presented
in [19], here we also evaluate the contagion tendency of anger and joy from the perspective
of emotion influence. For each tweet tuwith emotion iposted by u, we calculate the Eu-
clidean distance ej(j= 1,2,3 or 4) between v(tu) and vj(j= 1,2,3 or 4). We define tuis
an emotionally influenced tweet, i.e., tuis stimulated by emotion icarried by tweets that u
received within ∆ if the emotion with the smallest distance is i. Then for anger and joy,
the one with higher percentage of influenced tweets will be more influential and contagious.
As shown in Fig. 1(b), anger possesses the higher percentage of influenced tweets than joy,
indicating that as compared to joy, it is easier to be stimulated by tweets that users are
exposed to. Meanwhile, as ∆ grows both emotions’ influenced percentages increase because
users are exposed to more tweets when ∆ is large, while anger persistently possesses the
higher percentage than joy and the gap is even enlarged for greater ∆.
We further investigate the emotion contagion from the view of emontionally influenced
users. Specifically, all users are sorted in the descending order of the percentage of their
influenced tweets, i.e., the faction of influenced tweets in their tweeting timelines. The
top and bottom 15% users are then defined as the high susceptible and the low susceptible,
respectively. As can be seen in Fig. 2, low susceptible users are easier to be affected by anger
while high susceptible users are more inclined to be stimulated by joy. Different from [19],
in which it is claimed that both high and low susceptible users are more susceptible to
positive feelings than the negative, however, our results demonstrate that in fact anger, one
of the negative emotions, is more susceptible than joy for low susceptible users. It means
that a fine-grained emotion category can lead to new insights in discussing the emotion
contagion and anger, out of expectation, is more contagious than joy. Meanwhile, relatively
lower number of followers for the low susceptible user indicates its higher occupation than
the high susceptible in the soical network and given the power-law like distribuiton of the
number of followers, it is further suggested that anger is more contagious for the majority
6
0
20
40
60
80
Low susceptible High susceptible
Percentage (%)
Anger
Joy
Figure 2. Influenced percentage of anger and joy in both high and low susceptible users,
respectively.
of the social network that joy.
Being more contagious and more susecptible to the majority indicate that anger could be
transfered faster than joy, because it will inspire more follow-up tweets under the same in-
tensity of stimuli. However, the mechanism underlying emotion contagion also relies heavily
on structure of the social network and thus how structure functions on contagion of joy and
anger indeed deserves further explorations.
B. Anger prefers weaker ties than joy
The dynamics of emotion contagion is essentially coupled with the underlying social
network that providing channels for disseminating the sentiment from one individual to
others. Except the willingness of posting an angry or joyful tweet after exposed to anger
or joy from followees, another key factor that determines the user’s action is that on which
relationship the contagion will happen with higher likelihood. Specifically, the prediction of
which friend will retweet the emotional post in the future will be insightful for the contagion
modeling and control.
The social relationship, or the tie in social network, can be measured by its strength, which
7
is instrumental for spreading both online and real-world human behaviors [8]. The strength
of a tie in online social media can be intuitively measured through online interactions, i.e.,
retweets, between its two ends. Here three metrics are presented to depict tie strengths
quantificationally. The first one is the proportion of common friends [38, 46], which is
defined as cij /(ki−1 + kj−1−cij ) for the tie between users iand j, where cij is the
number of common friends, kiand kjrepresent degrees of iand j, respectively. Note that
for the metric of common friends, the social network of Weibo is converted to undirected
with each link representing the possible interaction between both ends. The second metric
is inspired by the reciprocity in Twitter-like services and higher ratio of reciprocity indicates
more trust and more significant homophily [47]. Hence for a pair of users, the proportion
of reciprocal retweets in the total flux between them is defined as the tie strength. The
third metric is the number of reweets between two ends of a tie in Weibo and greater values
stand for more frequent interactions. Note that different from the previous two metrics,
the retweet strength is time-evolving and we only count the retweets happening before the
corresponding emotional retweet. And in order to smooth the comparison between anger
and joy, the retweet strength, denoted as S, is also normalized by (S−Smin)/(Smax −Smin),
in which Smin and Smax separately represent the minimum and maximum values in all
obervations.
By investigating each emotional retweet, i.e., reposting an angry or joyful tweet posted
by the followee, we correlate emotion contagion with tie strengths. As can be seen in
Fig. 3, all the metrics consistently demonstrate that anger prefers weaker ties than joy in
contagion, suggesting that angry tweets spread through weak ties with greater odds than
the joyful ones. It is well known that weak ties play essential roles in diffusion of social
networks [24], especially in break the local trap caused by communities in terms of bridging
different clusters together [16, 38, 45]. For example, a typical snapshot of emotion contagion
with four communities are demonstrated in Fig. 4, in which anger disseminates through
more weak ties of inter-communities than joy. Because of this, as compared to joy, anger
has more chances to penetrate different communities through its preference on weak ties in
emotion contagion. And more communities lead to more global coverage, indicating that
anger could reach broader dissemination than joy over the same time period.
Both evidence from contagion tendency and relationship strength suggests that anger
could spread faster than joy, because it will stimulate more follow-up tweets and penetrate
8
0.00
0.01
0.02
0.03
Anger Joy
Common Friends
a
0.00
0.05
0.10
0.15
Anger Joy
Reciprocity (%)
b
0.000
0.005
0.010
0.015
Anger Joy
Retweets
c
Figure 3. Anger prefers more weak ties than joy. Three different metrics are averaged
over all emotional retweets in the dataset. Lower metrics for anger suggests that in
contagion anger disseminates through weaker ties than joy. Error bars represent standard
errors in (a) and (c), while in (b) there is no stand error beause the reciprocity is just a
ratio obtained from all emotional retweets.
more communities in the social network of Weibo. Next direct evidence from online bursts
in Weibo will be demonstrated to testify this conjecture further.
C. Anger spreads faster than joy
No moods are created equally online [15], the difference in contagion of positive and
negative feelings is a trending but controversial topic for years. Berger and Milkman reveal
that more positive content is more viral than negative content in study of NY Times [4]. Tadi
and ˇ
Suvakov find that for human-like bots in online social network, positive emotion bots are
more effective than the negative ones [42]. Wu et al. even claim that bad news containing
more negative words fades more rapidly in Twitter [43]. While Chmiel et. al point out that
negative sentiments boost user activity in BBC forum [11]. Pfitzner et. al state that users
tend to retweet tweets with high emotional diversity [40]. Ferrara and Yang demonstrate
that though people are more likely to share positive content in Twitter, negative messages
9
Figure 4. Emotion contagion in a sampled snapshot of the Weibo network with four
communities and links with more angry retweets will be orange and otherwise will be
green. It can be seen that anger prefers more weak ties bridging different communities
than joy. Besides, the left two communities dominated by anger and thus a large percent
of messages disseminate inter communities. While for the two right joy-dominated
communities, emotion tends to diffuse inside the community.
spread faster than positive ones at the level of contents [20]. Thus Hansen et al. conclude
that the relation between emotion and virality is much complicated [27]. Here we argue that
fine-grained division of human emotion, especially the negative, will enrich the background
of investigating the contagion difference. And in the meantime, explicit definitions of fast
spread will further facilitate the elimination of debates on this issue.
Over 600 bursty events are extracted from Weibo and for each event, the emotion occu-
pying more than 60% emotional tweets will be defined as the dominant emotion of the event.
In total we get 37 anger-dominated events and 200 joy-dominated events, as can be seen
Fig. 5(a), in which the volume of emotional tweets fluctuates with time and anger takes over
the majority. For an online burst, the fast spread means the volume of emotional tweets
grow quickly in the period from the awakening instant to the diffusion peak. Through a
parameterless approach presented in [30], we can precisely locate the instant of awakening
10
0
200
400
600
800
0 10 20 30 40 50
τ
Volume
Anger
Disgusting
Joy
Sadness
315 party
(xA, yA)
(xP, yP)
0
500
1000
1500
0 10 20 30 40
τ
Volume
(xA, yA)
(xP, yP)
0
2000
4000
6000
0 10 20 30 40
τ
Volume
a
b c
Figure 5. Illustration of the online bursts. (a) An example of an anger-dominated event
and the newly posted emotional tweets varies as time τevolves. (b) Examples of locating
the awakening and the peak for both anger and joy dominated events. xAdenotes the
instant of awakening, xPdenotes the peaking time and yAand yPstand for the volume of
emotional tweets at the instants of awakening and peak, respectively. The slope of the line
(blue) between points (xA, yA) and (xP, yP) can reflect the averaged velocity.
and peak. Then how fast the spread is can be reflected by the interval between the awak-
ening and the peak (shorter intervals suggest faster spread) or the averaged velocity of the
growth in diffusion from awakening to the peak (higher velocities indicate faster spread).
Specifically, as demonstrated in Fig. 5(b), regarding to interval, 1/(xP−xA) can reflect how
fast the spread is, while with respect to averaged velocity, it can be defined as the slope,
i.e., (yP−yA)/(xP−xA) and for both measures higher values suggest faster spread. The
averaged results over all anger and joy dominated events are listed in Table I and it can be
seen that both metrics testify significantly that anger-dominated events incline to arrive the
peak from the awakening more quickly than joy. We can conclude that anger indeed spreads
faster than the joy in social media like Weibo.
11
Measures Anger Joy
Time-difference 0.179 0.102
Slope 0.329 0.238
TABLE I. Averaged values over all anger and joy dominated events.
III. DISCUSSION
Bad is always stronger than good [3]. From the previous studies, it is profoundly disclosed
that anger is more influential than joy in Weibo [18] and the negative contents in Twitter
spread faster than positive ones [20]. However, in this study, by finely splitting the negative
feelings into anger, disgust and sadness, we for the first time offer the empirical evidence
that anger spreads faster than joy in social media, implying that anger on the Internet
should be considered primarily in either personal emotion management or collective mood
understanding.
The way how anger is expressed and experienced on the Internet is arousing attention.
It has been found from self-reports of rant-site visitors that posting anger produces relaxed
feelings immediately [35], which makes posting anger an effective way of self-regulation
in mood. However, considering the easy contagion of anger, more angry expressions on the
Internet might arouse negative shifts in mood of the crowd that connected to posters [35, 39].
Moreover, anger’s preference of weak ties will make it likely to spread to “strangers” in the
Internet. The users want to ease anger by posting on the Internet should be suggested to
underhand the possible impact to their online social network. Even in offline scenario, like
the “road rage” [1] at rush hours of China, in which anger spreads quickly between strangers
and might cause aggressive driving or even accidents. We suggest that in personal anger
management, the unexpected contagion to strangers should be seriously considered.
The online social media has already been the most ubiquitous platform for collective
intelligence, in which various signals generated from massive connected individuals provide
the foundation of collective behavior understanding. However, how emotion contagion affects
the aggregation of the individual behavior, particularly the individual intelligence, is rarely
considered. In fact from our findings, emotion spread, especially the anger’s fast contagion,
might imply a lot to the collective behavior in the cyber space, especially the crowdsourcing
12
results. It is even stated that emotion, such as anger, can be a threat to reasoning and
arguing [34]. For example, the outrages of massive emotional individuals, which would badly
bias the public opinion, might just come from the fast spread of anger, but not because the
event itself. Meanwhile, fast contagion of anger also offers a new perspective to picture
the emotional behavior of the crowd on the Internet. We suggest that for scenarios like
crowdsourcing or collective behavior understanding, angry users should be carefully treated
to omit their possible impact on the fair judgment of the observations in the epoch of big
data. Besides, diminishing weak ties will function effectively in controlling the diffusion of
the Internet outrages and make the crowd rational and smart.
Contrarily, happiness is believed to unify and clustering the community [12] and our
finding about the joy’s preference on less weak ties also supports this (see Fig.4), implying
that strong ties inside the community disseminate more joyful content in online social media.
Meanwhile, self-reports from Facebook users also testify that communication with strong ties
is associated with improvements in well-being [9], which further testifies that our findings
from the computational view is solid.
IV. CONCLUSION
Instead of self-reports in controlled experiments, the natural and emotional postings
in Weibo social network are collected to investigate the detailed mechanism of emotion
contagion from a new view of computational social science. For the first time, we offer the
solid evidence for the fact that anger spreads faster than joy in social media because of
being more contagious and more preferential on weak ties. Our findings shed lights on both
personal anger management and collective behavior understanding.
This study has inevitable limitations. It is generally accepted that emotion expression is
culture dependent and demographics like gender also matter [2, 29], suggesting that exploring
how anger spreads in Twitter and how the male and the female response differently to
emotion contagion will be of great significance in the future work.
13
ACKNOWLEDGMENT
This work was supported by the National Natural Science Foundation of China (Grant
Nos. 71501005, 71531001 and 61421003) and the fund of the State Key Lab of Software
Development Environment (Grant Nos. SKLSDE-2015ZX-05 and SKLSDE-2015ZX-28).
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