Structural Similarities of Emotion-exchange Networks: Evidence from

18 Crisis Events

Ema Ku

sen

and Mark Strembeck

1,2,3

Vienna University of Economics and Business, Vienna, Austria

Secure Business Austria (SBA), Vienna, Austria

Complexity Science Hub (CSH), Vienna, Austria

Keywords:

Crisis Events, Emotion Analysis, Network Motifs, Online Social Networks, Twitter.

Abstract:

Online social networks (OSNs) play a signiﬁcant role during crisis events by offering a convenient channel

for information seeking, social bonding, and opinion sharing. In this context, people express their fear, panic,

shock, as well as gratitude, well-wishing, and empathy as a crisis event evolves over time. Though emotional

responses during crisis events have been studied both in ofﬂine and online settings, it is yet unclear which

communication structures are representative for the exchange of speciﬁc types of emotions. In this paper,

we report on new ﬁndings which indicate that not all negative emotions are exchanged in the same way. In

particular, we used emotion-exchange motifs to compare the structure of emotion-annotated communication

networks that resulted from 18 crisis events. Our ﬁndings clearly indicate that 1) exchanges of sadness on

the one hand, and joy/love on the other show more structural similarity than any other pair of emotions,

2) emotion-exchange networks can be clustered into two families, each of which includes different types of

emotions, 3) membership in the two families of emotion-exchange networks ﬂuctuates over time. A related

data-set is available for download from IEEE DataPort, DOI: 10.21227/yajb-6y77.

1 INTRODUCTION

Emotions motivate human behavior (Holyst, 2016)

and inﬂuence physiological and mental health

(Abdul-Mageed and Ungar, 2017). For example, they

trigger a ﬂight reaction when people face danger or

provoke tears and sobbing when experiencing loss

and helplessness. In this light, emotions play a crucial

role in crisis events, which are described as sudden,

threatening, and traumatic events which cause intense

feelings of danger, shock, panic, and fear (Flynn,

1997). Thereby, emotions considerably shape the col-

lective experience of an event (von Scheve and Ismer,

2013).

Since online social networks (OSNs) are predom-

inantly networks of people, human emotions can sig-

niﬁcantly inﬂuence user behavior and information dif-

fusion in OSNs. In this context, (Scheve, 2014) in-

dicated that the study of emotions and their roles in

OSNs may reveal dynamic processes and structures

that emerge due to interactions between OSN users.

For example, previous studies demonstrated that emo-

tions conveyed in OSN messages may boost or de-

crease the diffusion rate of a message within a so-

cial network (Kim et al., 2013; Tsugawa and Ohsaki,

2015). Other ﬁndings, such as (Berger, 2011), indi-

cate that emotions of the same affective valence

(e.g.,

anger and sadness) are not exchanged in the same way

and inspire different reactions in ofﬂine settings.

Although the existing body of literature provides

valuable insights into the emotions expressed during

various types of events, their inﬂuence on the pro-

cess of emotional contagion and message diffusion,

as well as the emergence of collective emotions, there

is a lack of studies which systematically examine

the underlying communication structures that arise

from emotional messaging. In this context, emotions

exchanged between pairs of users (so called dyads)

has been well studied. Yet, as noted by (Scheve,

2014), emotions exchanged within a dyadic structure

may further propagate to other connected individu-

als. Multiple authors further noted that strongly ex-

perienced emotions, such as anger or fear are shared

Affective valence is a term which distinguishes be-

tween pleasant (positive) or unpleasant (negative) emotions.

For example, negative emotions include anger, sadness,

fear, and disgust, while positive emotions include joy, trust,

and anticipation.

Kušen, E. and Strembeck, M.

Structural Similarities of Emotion-exchange Networks: Evidence from 18 Crisis Events.

DOI: 10.5220/0010397000250036

In Proceedings of the 6th International Conference on Complexity, Future Information Systems and Risk (COMPLEXIS 2021), pages 25-36

ISBN: 978-989-758-505-0

with others as a form of one’s coping mechanism

(Fraustino et al., 2012). This phenomenon is rooted

in psychology and is referred to as the social sharing

of emotions (Rim

e et al., 1991). Through such a pro-

cess, emotions that are propagated from a dyad to a

larger group of people form a network structure.

In this paper, we report on a study that investigates

how emotions contribute to the underlying topologi-

cal structure of OSN messaging networks. In particu-

lar, we examine how emotions contribute to the emer-

gence of families of emotion-exchange networks. Our

ﬁndings clearly indicate that seemingly similar emo-

tions, such as the negative emotions of anger and sad-

ness, do not only inspire different reactions in terms of

forwarding or endorsing a message, but that the way

they are exchanged also results in structurally differ-

ent communication networks.

The remainder of this paper is organized as fol-

lows. In Section 2, we provide an overview of related

work followed by a description of our research proce-

dure in Section 3. Our ﬁndings are reported in Section

4 and discussed in Section 5. Section 6 concludes the

paper and provides directions for future work.

2 RELATED WORK

Structural similarity of networks has been studied

over a wide range of real-world networks, includ-

ing social networks, air navigation networks, or food

networks. Often, network structures are compared

via their global properties (network density, degree

distributions, average path length, network diameter,

transitivity, clustering coefﬁcients) and local (node-

centric) properties (such as various centrality mea-

sures; see, e.g., (Sun and Wandelt, 2014),(Shi and

Macy, 2016)). Other approaches analyze the nodes’

inﬂuence in order to compare different networks con-

sisting of the same set of nodes (Koutra et al., 2013),

or the spectral clustering of graphs (see, e.g., (Gera

et al., 2018)).

In recent years, approaches studying network mo-

tifs (Milo et al., 2002) led to many interesting in-

sights that could not have been found by comparing

global network properties alone. In this sense, net-

work motifs reveal the underlying functional prop-

erties of complex networks (Masoudi-Nejad et al.,

2012) that would otherwise remain hidden.

For example, (Milo et al., 2004) correlated the

signiﬁcance proﬁles (SPs) of network motifs found

in seemingly unrelated networks from different dis-

ciplines, such as WWW links, word-adjacency net-

works, genetic networks, and sensory transcription

networks. Moreover, (Klaise and Johnson, 2017)

compared food networks by correlating the SPs of

network motifs and applying a trophic coherence

measure which reveals how layered a network is.

Moreover, (Topirceanu et al., 2016) compared the

underlying structure of friendship graphs derived

from three online social networks (Facebook, Twitter,

Google+). Our paper follows a similar line of work

by exploring emotion-annotated communication net-

works derived from Twitter conversations.

3 PROCEDURE

Our research procedure includes seven main steps, as

depicted in Figure 1.

1. Data Extraction. We used Twitter’s Search API to

extract publicly available tweets that have been sent

during eighteen crisis events. In order to extract the

relevant tweets, we monitored Twitter and systemat-

ically selected a set of hashtags and key-terms asso-

ciated with each crisis event. The data was collected

from the ﬁrst day of an event and stopped when the

event did not produce a considerable number of mes-

sages anymore (usually after seven to fourteen days).

After collecting the raw data, we removed duplicate

entries and messages that were uninformative with

respect to emotion detection. Our ﬁnal data-set in-

cluded 23,308,071 tweets (see Table 1).

2. Emotion Detection. After data pre-processing,

we applied our emotion detection procedure (for de-

tails see (Ku

sen et al., 2017)) which determines the

presence and the intensity of the eight basic emo-

tions found in Plutchik’s wheel of emotions (anger,

fear, disgust, sadness, joy, anticipation, trust, sur-

prise). Our approach uses the NRC emotion-word

lexicon (Mohammad and Turney, 2013) to identify

the presence of each basic emotion and the AFINN

lexicon to boost or decrease the intensity of an affect

(Hansen et al., 2011). In addition, we also applied

a set of heuristics that people naturally use to detect

emotions in written texts including ampliﬁers, maxi-

mizers, downtoners, and negation. Moreover, the al-

gorithm also considers characteristic features that are

frequently found in OSN messages (especially emoti-

cons and common abbreviations). For example, the

tweet “@screenname I am so very sorry to hear the

sad news about lieutenant Arnaud Beltrame. He has

displayed the true courage.” conveys an explicitly

named emotion and was annotated in the following

way: sadness = 3, fear = 2, trust = 1, the remaining

emotions = 0 (whereby the values refer to the emo-

tion intensity). Another example illustrates emotion

annotation for a tweet where an emotion is implied –

“@screennameA @screennameB f***ing idiot! How

COMPLEXIS 2021 - 6th International Conference on Complexity, Future Information Systems and Risk

1-Data

extraction

Emotion

labeling

@-network

reconstruction

Null model

generation

Motif

detection

7 - Discovery of

network families

4 - Define a

multiplex

model

Figure 1: Research procedure.

many shootings will it take for you to wake up and

change the law about gun control? #guncontrol”

which was annotated in the following way: anger =

2, disgust = 3, fear = 2, all remaining emotions = 0.

Our algorithm was designed to run on multiple CPU

cores and thereby parallelizes the emotion detection

procedure.

Testing the Accuracy. To test for the accuracy of

our procedure, we deployed two independent human

raters. To mitigate potential bias in emotion detection,

we chose the raters who were personally not involved

in any of the crisis events studied in this paper. Their

task was to assign 0 (emotion not detected), 1 (emo-

tion detected), or 2 (unsure) to a sample of 150 tweets

(50 tweets from each type of a crisis event) selected

randomly from a subset of our data-set that includes

only directed messages (n=1,396,709 tweets), as the

directed messages are used to derive the communica-

tion network in the subsequent step. Upon annotating

the tweets, the raters reached a substantial inter-rater

agreement (Cohen Kappa 0.71) and after resolving

discrepancies between the two raters, we computed

the F-measure score for each emotion and achieved

0.84 for anger, 0.84 for joy, 0.73 for fear, 0.68 for

sadness, 0.67 for anticipation, 0.62 for disgust, 0.61

for trust, and 0.50 for surprise. The score for surprise

is inﬂuenced by the relatively low number of tweets in

which “surprise” is the dominant emotion as well as

the ambiguity of surprise which is neither a positive

nor a negative emotion and its interpretation highly

depends on the context of a tweet.

3. Construction of the Messaging Network. On

Twitter, each user can send a direct message to an-

other user via @screenname. Based on such @-

traces, we reconstructed a directed messaging (DM)

network for each event. We allow for the presence

of multiple edges (i.e., a user can send multiple mes-

sages to another user) and self-loops (i.e., a user can

mention him or herself in a tweet to bypass the char-

acter restriction imposed by Twitter). Moreover, we

label each edge according to the dominant emotion

conveyed in the corresponding message.

The resulting emotion-annotated networks already

show ﬁrst differences with respect to their global net-

work properties. For example, the networks repre-

senting anger-, fear-, and anticipation-exchange have

a comparatively large number of connected compo-

nents, compared to disgust- and surprise-exchange

networks (see Table 2). We also found that the aver-

age messaging rate per user (expressed as an average

node degree) assumes it’s highest value in the anger-

exchange network (degree

anger

= 1.70) and it’s low-

est value in the joy- (degree

joy

= 1.42) and sadness-

exchange (degree

sadness

= 1.39) networks.

4. Construction of a Multiplex Network. Next,

we derived one multiplex network for each day of

the data extraction period, separately for each event.

Each daily multiplex network consists of eight layers,

and each of these layers represents one of the eight

basic emotions. Moreover, in order to gain more in-

sight concerning the interlayer dependencies, we do

not only consider individual emotion layers (see Fig-

ure 2a) but also various derived layers. These de-

rived layers are: 1) a negative layer which includes

the edges found on the four negative emotion layers

(anger, fear, disgust, and sadness), 2) a positive layer

which includes the edges found on the three positive

emotion layers (joy, anticipation, and trust) (see Fig-

ure 2b)

. In addition, we derived a valence interlayer

which captures the vertices that are active on both de-

rived valence-speciﬁc layers (positive layer and neg-

ative layer) as well as those of their adjacent vertices

which are also active on the two derived valence lay-

ers (as shown in Figure 2c). Finally, we also aggre-

gated all positive- and negative-emotion layers as well

as surprise to derive the aggregated network (Figure

2d) for each day.

Note that “surprise” can be associated to positive as

well as negative emotions and is therefore treated sepa-

rately.

Structural Similarities of Emotion-exchange Networks: Evidence from 18 Crisis Events

Table 1: Basic information about the data-set used in our study: extraction period, number of tweets, vertices and edges of the

corresponding communication network, as well as hashtags and key-terms used for data extraction.

Extraction Period Tweets Vertices Edges Hashtags

NATURAL DISASTERS

Harvey hurricane 23.8.-11.9.2017 7,931,488 281,724 494,046 #Harveyhurricane, #HurricaneHarvey, hurricane harvey,

hurricane houston, hurricane texas, #HarveySOS, #Har-

veyRescue, #Houstonﬂood

Irma hurricane 4.9.-18.9.2017 5,421,054 189,969 348,089 #IrmaHurricane, #Irma2017, #hurricaneIrma

Mexico earthquake 7.9.-28.9.2017 1,713,618 45,882 54,796 #mexicoEarthquake, #earthquakemexico, earthquake mex-

ico

Maria hurricane 21.9.-4.10.2017 1,258,515 60,353 97,916 #hurricaneMaria, #mariaHurricane, hurricane maria

Costa Rica earthquake 12.11.-2.12.2017 15,492 601 512 earthquake costa rica, #earthquake costarica, earthquake

#costarica

Iran-Iraq earthquake 12.11.-2.12.2017 272,670 7,639 9,451 #earthquake iran, earthquake iran, #earthquakeinkurdistan,

#earthquakeiran, #earthquakeiraq, #iraniraqearthquake,

#kurdistanearthquake, #prayforkurdistan

Southern California

mudslide

7.1.-27.1.2018 168,303 8,609 12,719 california ﬂood, #castorm, #Montecito, montecito, #mon-

tecitoﬂood, mudslide california, #mudslide california,

#santabarbara

Friederike windstorm 17.1.-28.1.2018 51,694 3,486 3,239 deutchland friederike, deutschland unwetter, ex-

tremeweather germany, extremeweather netherlands,

#friederike, germany hurricane, #orkanfriederike, wind-

storm netherlands

Lang’ata wildﬁre 28.1.-1.2.2018 11,113 695 915 #ﬁreKijijini, #langataﬁre

TERROR ATTACKS AND SHOOTINGS

Tehama County shoot-

ing

14.11.-02.12.2017 123,659 3,884 4,140 california shooter, kevin jason neal, #KevinJasonNeal,

northern california shoot, #RanchoTehama, #RanchoTe-

hamaShooting

Trebes (France) shoot-

ing

23.03.-08.04.2018 142,255 4,199 4,414 #ArnaudBeltrame, #Beltrame, #Carcassonne, #French-

Hero, #redouanelakdim, #Trebes, Arnaud Beltrame, Re-

douane Lakdim, Trebes France

YouTube HQ shooting 03.4.-10.4.2018 648,501 34,611 47,262 #NasimNajaﬁAghdam, #PrayersForYoutube, #San-

BrunoShooting, #shootingYoutube#YoutubeHQShooting,

#YoutubeHQ Tragedy, #youtubeshooter, #youtubeshoot-

ing, #YoutubeStrong

unster (Germany)

van attack

7.04.2018-14.04.2018 62,883 1,824 2,737 #MuensterAttack, #MuensterGermany, #Muensteramok-

fahrer, #Muensteramokfahrt, #MuensterAnschlag, #pray-

formuenster

Santa Fe school shoot-

ing

18.05.-25.05.2018 967,674 30,093 50,208 #DimitriosPagourtzis, #EnoughIsEnough, #SantaFe,

#SantaFeGunControl, #SantaFeGunControlNow,

#SantaFeGunViolence, #SantaFeHighschool,

#SantaFeShooting, #SantaFeStrong, #TexasShooting

RIOTS

Hamburg G20 summit 6.7-17.7.2017 653,568 25,429 58,768 #G20HH2017, #G20Hamburg, #G20HAM17, #G20HAM,

“#G20 #Hamburg”, “Hamburg riot”, “Hamburg Unruhe”

Charlottesville riot 10.8-16.8.2017 2,202,682 84,638 152,209 #Charlottesville, #UnitetheRight, “Charlottesville riot”

Catalonia riot 28.9-16.10.2017 1,640,829 27,432 54,266 #Catalonia, #CatalanReferendum, #RepublicofCatalonia,

“Catalonia violence”, “Catalonia protest”, “#1oct Catalo-

nia”

Philadelphia Super-

bowl riot

4.2-10.2.2018 22,073 1,164 1,022 #PhillyBurning, #Phillyriot, “#superbowl #Philadelphia”,

“#Philadelphia #riot”, and “Philadelphia riot”

5. Null Model Construction. A general procedure

for detecting network motifs is to determine the pres-

ence of speciﬁc subgraphs in the respective real-world

network and compare them to the subgraphs found in

a synthetically generated network that resembles the

real-world network (a so-called null model). For our

motif detection procedure, we generated null models

for each of the daily real-world multiplex networks

by using the stub-matching algorithm. This algorithm

uses the concept of stubs deﬁned as “sown-off arrow

heads” (or dangling edges), which are rewired so that

the synthetically generated network preserves the de-

gree sequence of the corresponding real-world net-

work (Newman et al., 2001). In total, we generated

COMPLEXIS 2021 - 6th International Conference on Complexity, Future Information Systems and Risk

a) Individual layers b) Aggregated valence

layers

c) Valence interlayer d) Aggregated network

Figure 2: Individual emotion-annotated layers and the corresponding derived layers used in our analyses (green = positive

emotion layers, red = negative emotion layers, yellow = surprise).

Table 2: Mean value of global network properties: num-

ber of connected components (CC), node degree, network

diameter, eccentricity (ECC), and radius.

Layer CC Degree Diameter ECC Radius

Anger 225.01 1.70 1.89 3.42 0.44

Fear 222.01 1.58 1.70 2.94 0.45

Sadness 49.4 1.39 1.24 2.04 0.77

Disgust 39.6 1.44 1.20 2.21 0.83

Anticipation 219.01 1.51 1.73 2.82 0.57

Joy 95.8 1.42 1.30 2.06 0.72

Trust 119.99 1.57 1.56 2.76 0.64

Surprise 44.9 1.43 1.21 1.98 0.82

1000 synthetic networks for each of the 8 multiplex

layers and the 4 derived layers for each day of each

crisis event, resulting in 2,964,000 null models in to-

tal.

6. Motif Detection. In order to detect emotion-

exchange motifs (Ku

sen and Strembeck, 2019; Ku

sen

and Strembeck, 2020), we ﬁrst enumerated all pos-

sible subgraphs of a pre-deﬁned size k (in our case

k = 3)

by using the ESU subgraph enumeration algo-

rithm (Wernicke, 2006). Next, we performed an iso-

morphism test for the different subgraphs by apply-

ing the VF2 algorithm (Cordella et al., 2004). Since

isomorphism testing for each pair of subgraphs is re-

garded a general bottleneck when performing an exact

motif detection (in contrast to approaches that approx-

imate the number of motifs), we categorized the sub-

graphs according to their degree sequence to only test

the set of possible candidates (see Algorithm 1). Fi-

nally, we mapped each simpliﬁed emotion-exchange

motif

found in the input (real-world) networks to

We pre-deﬁned the size k = 3 to capture the smallest

possible group of nodes, as dyads would be trivial for this

type of an analysis. In future work, it would be interesting

to set k to other values (> 3). However, given the computa-

tional costs of the current procedure (with k = 3), detecting

motifs of larger sizes is infeasible and would require sig-

niﬁcant performance improvements of the motif detection

procedure.

Here, a “simpliﬁed emotion-exchange motif” disre-

gards self-loops and multi-edges.

one of the thirteen possible 3-node directed subgraph

classes and labeled them according to MAN-labeling

scheme (Davis and Leinhardt, 1972).

7. Discovery of Network Families. We followed the

approach suggested by (Milo et al., 2004) which uses

network motifs and their signiﬁcance proﬁles to com-

pare networks of different sizes. To account for the

temporal aspect of emotion-exchange motifs, we de-

ﬁned three time-frames for each crisis event: a) the

ﬁrst two days of a crisis event (referred to as time-

frame 1), b) the subsequent days 3-6 (referred to as

time-frame 2), and c) the remaining days of a cri-

sis event (referred to as time-frame 3). For each pair

of emotion-exchange networks, we computed Spear-

man’s ρ coefﬁcient while considering the temporal as-

pect. The results are presented for a p-value< 0.05.

In order to identify families of emotion-exchange net-

works, we used the complete linkage method for hier-

archical clustering.

4 RESULTS

Emotional Intensities During Crisis Events. Our

data analysis indicates that three negative emotions

are universally dominant during the crisis events

studied in this paper. The average emotional in-

tensities (ei) of fear (ei

f ear

=0.24) and sadness

(ei

sadness

=0.14) dominate over the remaining emo-

tions during natural disasters, fear (ei

f ear

=0.22)

and anger (ei

anger

=0.18) during riots, while fear

(ei

f ear

=0.29) and anger (ei

anger

=0.19) dominate

during terror attacks and shootings. Our empirical

ﬁndings complement those of (Flynn, 1997), who

found that people universally express emotions ac-

cording to particular phases across different types of

crisis events, with shock and fear being initially ex-

pressed with a high intensity. Such initial emotions

are subsequently followed by a wide range of other

emotions, depending on the particularities of a crisis

event and one’s personal coping strategy. For exam-

Structural Similarities of Emotion-exchange Networks: Evidence from 18 Crisis Events

Algorithm 1: Motif detection.

1 Input: input network;

2 Output: list of motifs ;

3 Initialize: i = 0;

4 # ENUMERATE AND CLASSIFY SUBGRAPHS

5 def procedure: esu vf2(list layers)

6 foreach l in list layers do

7 subgraphs = esu(l)

8 foreach s in subgraphs do

9 subgraphs’ = subgraphs \ s

10 foreach s’ in subgraphs’ do

11 if vf2(s, s’) then

12 assign common isomorphism class

13 subgraphs’ = subgraphs’ \ s’

14 subgraphs = subgraphs \ s’

15 end

16 end

17 end

18 end

19 end procedure

20 # GENERATE LAYERS AND INTER-LAYERS

21 detect layers in input network

22 layer neg.add edges from(layer anger, layer sadness,

layer disgust, layer fear)

23 layer pos.add edges from(layer joy, layer anticipation,

layer trust)

24 foreach i in range(length(V(input network))) do

25 if v

∈ V(layer negative) & v

∈ V(layer positive) then

26 inter layer.add edges from(layer neg.edge containing(v

layer pos.edge containing(v

))

27 end

28 end

29 list layers = [layer anger, layer joy, ... , layer surprise, layer neg,

layer pos, interlayer, input network]

30 esu vf2(list layers)

31 # GENERATE NULL MODELS

32 while i < 1000 do

33 foreach l ∈ list layers do

34 null[l] = matching(l.in degree(), l.outdegree())

35 end

36 esu vf2(null)

37 i = i+1

38 end

ple, we observe an increase in the intensity of pos-

itive emotions during natural disasters when people

express well-wishing and prayers, as well as during

terror attacks and shootings when people express grat-

itude to the helpers and “heroes” (e.g., the local po-

lice), anger which is highly associated with blaming

mechanisms (Freyd, 2002) during riots, terror attacks

and shootings, and sadness which is communicated in

messages of compassion and condolences.

User Reactions to Emotional Content. Our ana-

lysis of user reactions to emotional content revealed

an increased retweeting behavior for fear-conveying

messages (mean(retweet

f ear

) = 403.84 ± 1078.04),

followed by messages of trust (mean(retweet

trust

) =

266.32 ± 475.94), as shown in Table 3. Anticipation-

conveying messages received on average the highest

number of likes (mean(likes

anticipation

= 6.9 ± 21.48),

while anger resulted in the highest tweeting rate

(mean(mssg.rate

anger

= 1.07 ± 0.19), closely fol-

lowed by fear (mean(mssg.rate

anger

= 1.07 ± 0.18).

These results indicate that basic emotions inspire re-

markably different user behavior, irrespective of their

affective valence.

Table 3: User reactions to emotional content. The retweet

and likes values are presented as mean values over each cri-

sis event and the extraction date, while the messaging rate

stands for the average number of daily messages sent by a

unique user during each crisis event.

Emotion Retweet Likes Mssg. rate

Anger 114.91 ± 213.86 5.58 ± 17.76 1.07 ± 0.19

Fear 403.84 ± 1078.04 1.68 ± 2.79 1.07 ± 0.18

Sadness 178.29 ± 346.81 1.26 ± 1.17 1.06 ± 0.16

Disgust 20.99 ± 38.3 0.95 ± 0.73 1.03 ± 0.11

Anticipation 176.19 ± 300.85 6.9 ± 21.48 1.01 ± 0.04

Joy 123.39 ± 273.27 3.34 ± 4.67 1.02 ± 0.07

Trust 266.32 ± 475.94 5.36 ± 8.18 1.04 ± 0.11

Surprise 65.36 ± 103.08 1.5 ± 1.37 1.02 ± 0.06

Emotion-exchange Motifs. In our data-set, the ex-

change of emotional messages during crisis events

is documented via 729,368 emotion-exchange motifs

that come in 1,480 shapes (isomorphism classes). For

presentation purposes, we only visualize the simpli-

ﬁed motifs in Table 4.

Since Twitter’s main purpose is that of a mes-

sage broadcasting service, the message-receiver mo-

tif 021U (f=596258; 729.37 per 1000 motifs) and

the broadcasting motif 021D (f=84139; 115.36 per

1000 motifs) appear most frequently in each of the

18 crisis events (see Table 4). These two motifs

also count a relatively high number of edges (ec)

(ec

021U

=5.53±2.52; ec

021D

=4.97±1.53) and exhibit a

relatively high variability with respect to the edge dis-

tribution (var

021U

=366; var

021D

=286).

Families of Emotion-exchange Networks. Over the

course of time, two sets of networks emerged that

form two families of emotion-exchange networks.

While the number of families remains constant over

time, the membership of networks in one of the two

families is ﬂuctuating over time. We name the fam-

ilies according to the initials of the core members

which include the networks whose membership to

a particular family is constant over all three time-

frames. The resulting families of emotion-exchange

networks are shown in Figure 5.

The ﬁrst family, is called the JSSIA (joy-

sadness-surprise-interlayer-aggregated) family,

and includes sadness- and joy-exchange networks

COMPLEXIS 2021 - 6th International Conference on Complexity, Future Information Systems and Risk

Fear

Anger

Sadness

Disgust

Joy

Anticipation

Surprise

Trust

Intensity

0.004

0.0005

0.03

0.01

0.002

0.0005

0.02

0.001

0.0001

Figure 3: Relative emotion intensities during natural disasters, shootings and terror attacks, as well as riots, normalized for

the range [0-1]. Positive emotions are depicted via dashed lines, negative via solid lines, and surprise via a dashed line. The

inlay plots show the daily intensity of aggregated positive (trust, joy, anticipation; green line) and aggregated negative (anger,

fear, sadness, disgust; red line) emotions.

(time-frame 1: ρ

joy−sadness

= 0.63; time-frame

2: ρ

joy−sadness

= 0.67 (albeit not signiﬁcant);

time-frame 3: ρ

joy−sadness

= 0.68), as well

as surprise (time-frame 1: ρ

joy−sur prise

= 0.74,

sadness−sur prise

= 0.73; time-frame 2: ρ

joy−sur prise

0.74, ρ

sadness−sur prise

= 0.67; time-frame 3:

joy−sur prise

= 0.45, ρ

sadness−sur prise

= 0.41).

Interlayer- and aggregated-emotion exchange net-

works share the membership with joy-, sadness-, and

surprise- in all time-frames, however with a larger

Structural Similarities of Emotion-exchange Networks: Evidence from 18 Crisis Events

Table 4: Basic information about the MAN-labeled motifs identiﬁed in the data-set – motif frequency (absolute and averaged),

prevalence rate per 1000, motif variability (absolute and averaged), as well as the mean edge count and its average standard

deviation.

Shape Frequency X:1000 Variability Edge count

021U

596258

(35074.00±58538.54)

729.37 366 (54.35±73.97) 5.53±2.52

021D

84139

(4674.38±7756.13)

115.36 286 (40.94±56.56) 4.97±1.53

021C

25640

(1508.23±3303.97)

35.15 219 (26.12±50.12) 3.76±0.84

030T

13240

(778.82±1518.81)

18.15 338 (37.94±74.29) 4.09±1.07

111D

4621

(385.08±872.08)

6.33 99 (12.83±27.53) 3.88±0.86

111U

3785

(270.35±556.35)

5.18 75 (9.07±18.29) 3.54±0.56

120U

997 (76.69±124.78) 1.37 26 (4.46±5.97) 4.42±0.39

120D

572 (63.55±134.78) 0.78 43 (7.00±13.45) 4.51±0.62

201

60 (15.00±16.02) 0.08 13 (4.25±5.19) 4.45±0.58

120C

31 (15.50±16.26) 0.04 8 (5.50±3.53) 4.68±0.26

030C

19 (9.50±2.12) 0.03 5 (3.00±2.83) 3.64±0.9

210

6 (3.00±1.41) 0.008 2 (1.50±0.71) 5.12±0.18

distance from the other three networks.

The second family, is called the PAF (positive-

anticipation-fear) family. The three consistent mem-

bers of the PAF family show a greater dissimilarity

among each other as compared to the closely corre-

lated core (joy-sadness-surprise) of the JSSIA fam-

ily. In the PAF family, two core networks of the

same affective valence (positive- and anticipation-

exchange networks) show the highest structural simi-

larity (time-frame 1: ρ

positive−anticipation

= 0.74; time-

frame 2: ρ

positive−anticipation

= 0.43; time-frame 3:

positive−anticipation

= 0.49).

The two dominant emotions during crisis events

(anger and fear) show a high ﬂuctuation with re-

spect to their family membership. While the ex-

change of fear is highly associated with the exchange

of positive emotions (see Figure 5) at the beginning

of a crisis event, the networks representing the ex-

COMPLEXIS 2021 - 6th International Conference on Complexity, Future Information Systems and Risk

0.125

Figure 4: Signiﬁcance proﬁles of the simpliﬁed motifs averaged over each day of each each crisis event.

change of fearful messages become structurally more

similar to the exchange of other negative emotions

(time-frame 2: ρ

negative− f ear

= 0.5), and anger (time-

frame 3: ρ

negative− f ear

= 0.62, ρ

anger− f ear

= 0.64)

over time. Anger initially highly resembles the aggre-

gated network (time-frame 1 ρ

anger−aggregated

= 0.53)

and eventually becomes more similar to the exchange

of fear (see time-frame 3 in Figure 5).

Structural Similarities of Emotion-exchange Networks: Evidence from 18 Crisis Events

Figure 5: Hierarchical clustering of emotion-exchange networks.

5 DISCUSSION

Our results clearly indicate differences between the

communication networks representing the eight ba-

sic emotions. We found that the eight emotions not

only inspire different user reactions/behavior during

crisis events, but that they are also different from a

structural point of view. Such an effect on the un-

derlying structure of Twitter’s direct messaging net-

work can be attributed to the functional role of emo-

tions. For example, as reported in previous studies,

fear is highly associated with an information seeking

and sharing behavior (Wollebaek et al., 2019) which

explains the high retweet rate of messages conveying

fear. This behavior is reﬂected in the underlying fear-

exchange motifs. Fear was characteristic for a high

signiﬁcance of the message receiver motif (111D) that

involves a mutual edge (i.e., it involves a discussion

between a pair of users). Another example is the ex-

pression of anger which structurally differs from fear

and does not persistently share the same family with

fear. Intense feelings of anger experienced during cri-

sis events are highly associated with blaming mecha-

nisms. According to (Freyd, 2002), people regularly

search for culprits who are to blame for a terror attack,

riots, or for the lack of help in the aftermath of natu-

ral disasters. In this context, we found that anger is

representative for a heated message-sending behavior

and is characteristic for message chains (021C) and

message receiver (021U) motif shapes.

Interestingly, message-exchanges representing joy

and sadness, which belong to two distinct affective

valence categories, show the highest structural simi-

larity compared to all other pairs of networks. A pos-

sible explanation for such a similarity lies in the ex-

pression of sympathy and condolences that both emo-

tions are associated with. According to (Batson et al.,

1991), messages of sympathy and condolences can be

seen as a form of altruism. We found that such al-

truistic messages are associated with the expression

of gratitude to individuals perceived as “heroes” (e.g.,

those who sacriﬁced themselves to save the lives of

others) or those who got injured, lost their homes, or

whose family members were victims of a crisis event.

This is reﬂected in the underlying motifs 021D (a

broadcaster motif) and 021U (a message receiver mo-

tif) rather than the discussion motifs (those that con-

vey mutual edges). Since the exchange of sadness and

joy is represented by the same set of motifs, we also

observed a more tightly correlated core of the JSSIA

family as compared to the PAF family.

6 CONCLUSION

In this paper, we studied the intensity of basic emo-

tions that were communicated during eighteen differ-

ent crisis events, including terror attacks, shootings,

riots, and various types of natural disasters. Prior

studies highlighted the general expression of fear and

shock as a crisis event happens, as well as the emer-

gence of a range of other emotions in the aftermath of

a crisis event. Based on a data-set counting over 23

million messages, our study empirically shows that

these ﬁndings also apply to message-exchanges hap-

pening in online social networks.

Moreover, we found that considerable differences

exist how emotions belonging to the same affec-

tive valence inﬂuence OSN communication behav-

ior. This is reﬂected in the user reactions to emo-

tional content. For example, while fear was highly

associated with increased retweeting behavior, anger

showed the highest messaging rate, and messages

conveying anticipation received most likes.

However, the main contribution of this paper is

an analysis of statistically signiﬁcant network struc-

tures that are representative for the exchange of

COMPLEXIS 2021 - 6th International Conference on Complexity, Future Information Systems and Risk

the eight basic emotions. To this end, we used

the novel concept of emotion-exchange motifs and

found that the exchange of sadness and joy are

structurally more similar than the exchange of any

other pair of emotions. Moreover, after cluster-

ing the emotion-exchange networks, two families of

networks emerged whose membership highly ﬂuc-

tuates over time. According to their core mem-

bers we named the two families JSSIA (joy-sadness-

surprise-interlayer-aggregated) and PAF (positive-

anticipation-fear), whereby JSSIA has a more tightly

correlated core compared to PAF.

In our future work, we plan to further examine

the emergence of temporal emotion-exchange motifs

to provide an even more ﬁne-grained analysis of the

underlying properties of human communication net-

works.

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