“Evacuate everyone south of that line” Analyzing structural communication patterns during natural disasters

In this paper, we analyze more than 16 million tweets that have been sent from 6.1 million Twitter accounts and are related to nine natural disasters. As part of our analysis, we identify eight basic emotions conveyed in these tweets. We found that during natural disasters, social media messages at first predominantly express fear, while sadness and positive emotions increase in the immediate aftermath of the event. In this context, positive emotions contribute to the social phenomenon of emotional bonding and are often related to compassion, gratitude, as well as donations for disaster relief. In our analysis, we found that the users’ emotional expressions directly contribute to the emergence of the underlying communication network. In particular, we identified statistically significant structural patterns that we call emotion-exchange motifs and show that: (1) the motifs 021U and 021D are common for the communication of all eight emotions considered in this study, (2) motifs which include bidirectional edges (i.e. online conversations) are generally not characteristic for the communication of surprise, sadness, and disgust, (3) the structural analysis of a set of emotions (rather than a single emotion) leads to the formation of more complex motifs representing more complex social interactions, and (4) the messaging patterns emerging from the communication of joy and sadness show the highest structural similarity, even reaching a perfect similarity score at some point during the data-extraction period.


Introduction
Over the past few years, a number of severe natural disasters happened around the globe. From hurricanes and earthquakes to tsunamis and landslides, these disasters caused communication blackouts, catastrophic damages to critical infrastructures, lack of resources, and humanitarian crises. During disaster events, the information that people have access to considerably shapes their behavior and attitudes towards the event [1]. Online social networks (OSNs) provide a vital communication medium where the ones affected by a disaster can share information, seek help, and bond emotionally. Recent studies have suggested that OSNs are a good source of data to study general sentiment during natural disasters [2]. Moreover, [58] showed that disaster events create a need for human conversation, turning OSNs into conversational and collaborative platforms for disaster communication.
Since a natural disaster causes a sense of urgency [11] as well as the feelings of danger, fear, panic, and shock [6,54], and may cause depression in those affected [47], the OSN discourse in such events is characterized by a high intensity of negative emotions such as fear and sadness. In fact, [47] showed that victims of a natural disaster may suffer from a depression even weeks after the disaster happened and, as a result, seek for collective bonding to share their emotions with those who went through a similar experience. Such an expression of negative emotions commonly serves as a coping mechanism and, as pointed in [45], can improve a person's mental well-being.
However, in addition to such negative emotions, positive emotions (e.g., joy and relief) are also frequently communicated during disaster events. According to numerous studies [14,17,20,29,31], positive emotions may even prevail over the negative ones because they help to increase the feelings of hope, gratitude, and empathy.
In this paper, we examine the emotions communicated by Twitter users during nine natural disasters that occurred in 2017 and 2018. In particular, the events we analyzed for this paper are hurricane Harvey, an earthquake in Mexico, hurricane Maria, an earthquake in Costa Rica, an earthquake in Iran and Iraq, a mudslide in California, windstorm Friederike in western Europe, the wildfire in Nairobi, as well as hurricane Irma.
A recent study found that user (communication) behavior plays a significant role in the dynamics of network structures [70]. In this paper, we explore the influence of expressed emotions, as one important aspect of observable user behavior on OSNs, on the structure of the underlying communication network. In our study, we focus on the communication patterns that emerge as Twitter users directly exchange emotional messages during the nine disaster events. We call such patterns emotionexchange motifs and show that characteristic motifs emerge as Twitter users communicate emotions. Furthermore, we found that the communication structures representing collective coping (conveying joy and sadness) are structurally more similar than the structures emerging from any two negative emotions (e.g., fear and anger).
A network motif is defined as a subgraph that occurs significantly more often in a real-world network as compared to the subgraph patterns that can be found in a corresponding null model [40]. The concept of network motifs was initially proposed in 2002 by Milo et al. [40], who described motifs as basic building blocks of complex networks. Ever since, the concept has been applied to various types of networks, such as biological networks [71] and co-authorship networks or animal social networks [64]. However, the application of network motifs in studying patterns that emerge as people communicate emotions over OSNs has generally been understudied.
This paper is a part of our ongoing research effort for investigating the influence of emotions on the emergence of local communication patterns during crisis events (see [35] for an analysis of terror and shooting attacks, and [37] for an analysis of riot events). The novel concept of emotion-exchange motifs plays a central role in this research endeavor. In particular, emotion-exchange motifs are statistically significant and frequently recurring patterns that are formed when the individuals affected by a crisis event exchange emotional messages. To the best of our knowledge, this line of work is the first to combine human emotions and network motifs to reveal the basic building blocks of emotional social media conversations.
The remainder of this paper is organized as follows. In "Related work" we provide an overview of related work, followed by a brief description of the natural disaster events that have been analyzed for this paper (see "Events of study"). We describe our research method in "Methods" and provide the results in "Results". A discussion on the results is given in "Discussion". We conclude the paper and provide directions for future work in "Conclusion".

Use of Twitter during natural disasters
In recent years, a number of studies analyzed the communication behavior in numerous natural disasters. For example, the 2009 Marseille fire [8], the 2011 and 2013 floods in Brisbane [24], hurricane Irene [39], the 2015 Chennani flood [43], typhoon Haiyan in the Philippines [60], the 2011 Tohoku earthquake and tsunami in Japan [42], hurricane Sandy [51,68], the South East Queensland flood [27], and hurricane Harvey [70], to name just a few.
So far, the role of social media during natural disasters has predominantly been explored in terms of situational awareness. For example, [8,44,51,67] found that people tend to broadcast and re-share (retweet) informative messages that contain references to locations affected by a hazardous event. By doing so, the ones affected by a natural disaster may collectively advance their understanding of the situation and prepare for evacuation [30]. News reports even indicate that more people consulted social media channels rather than the 911 emergency number to seek help during hurricane Harvey 1 .
Moreover, people do not only spread informational tweets but also express their sympathy and well-wishes to the victims [60], praise individuals (such as members of the local fire brigade) or organizations for their help and support [38], use Twitter to coordinate disaster relief efforts [60], and share their personal experiences during a disaster event [60]. Thus, online social media can be regarded as a platform for emotional support-seeking and, to a certain degree, a therapeutic channel for those affected by a disaster event. In this context, [15,45,46] found that people are coping with the traumatic experience via social media messages and publicly mourn those who did not survive. Moreover, [47] found that mental trauma resulting from a natural disaster is experienced collectively rather than individually (such as a death of an individual's family member) which encourages people to bond and share their emotions with those who have also been affected.
Since natural disasters can be classified as highly traumatic events [48] and involve a sense of urgency and danger, people predominantly experience negative emotions [53]. For example, [57] found that OSN posts sent during a natural disaster predominantly convey negative emotions such as anger, fear, and sadness. Moreover, [49] found that the expression of negative emotions changes over time. By conducting a series of user studies, [49] showed that negative emotions are more intense when they are immediately experienced compared to the emotional intensities reported when retelling stories about the event. In this respect, online social media are a convenient source of data for emotion analysis as researches may analyze the emotional expressions in near-real time.

Application of network motifs in the study of OSN communication patterns
Recently, network motifs have also been applied to examine the formation of human communication patterns. One such study [72] found that star motifs are representative for a network derived from Facebook wall postings. Furthermore, [21] analyzed the structural differences of communication networks derived from Twitter and Facebook and found that Twitter communication is characteristic for a short lasting in-star motif (i.e., a single user is frequently mentioned by many users), while Facebook exhibited longer message-sending behavior between the same set of users. In addition, our previous work studies the emergence of emotion-exchange motifs in social media communication involving human users as well as social bots [35][36][37].

Events of study
All events in our study can be classified as natural disasters and though these disasters differ in their particularities, they exhibit common characteristics such as causing injuries, threat to life, infrastructure damage, and distress [66].
Hurricane Harvey (August 2017) became a tropical storm on August 17, 2017, crossing the Windward Islands, Barbados, and Saint Vincent. It gradually weakened when it reached the Caribbean Sea and became a tropical storm on August 19. However, the storm rapidly intensified on August 24 and eventually became a Category 4 hurricane. San Jose Island (Texas) was reached at its highest intensity leaving 68 dead. Afterwards, Harvey progressed to Louisiana on August 29 as a Category 3 hurricane. It dissipated on September 3 after causing an estimated damage of $125 billion.
Hurricane Irma (August/September 2017) hit the Caribbean as a category 5 hurricane killing 37 people. Subsequently, the storm hit Cuba (ten dead) and the US (12 dead), affecting a total amount of 1.2 million people and leading to considerable damages in the infrastructure. It was later reported to be the most powerful Atlantic storm in a decade, causing damages of about 67 Billion US dollars.
Mexico earthquake (September 2017) was an earthquake of magnitude 7. Costa Rica earthquake (November 2017) occurred on the coast of Costa Rica (southeast of Jaco) on November 12, 2017, with a magnitude of 6.5 causing three deaths.
Iran-Iraq earthquake (November 2017) an earthquake of magnitude 7.3 occurred on the Iran-Iraq border on November 12, 2017 and became one of the deadliest earthquakes in 2017 resulting in more than 400 deaths and over 7000 injured victims. Moreover, it damaged or destroyed considerable parts of the urban infrastructure (esp. running water, electricity) leaving over 70,000 people in need of shelter.
Southern California mudslides (January 2018) occurred in early January 2018 after a heavy rain period. The mudslide demolished homes in Montecito and caused over 20 deaths.
Friederike windstorm (January 2018) hit Central Europe, as well as the British Islands, France, Benelux, Northern Italy, Poland and parts of Eastern Europe in early 2018 causing heavy snowfall and blizzards. The heaviest losses occurred, however, in Germany and the Netherlands between January 17 and 18, 2018, causing at least eight deaths and damages amounting to one billion Euros in Germany alone.
Lang'ata wildfire (January 2018) occurred in the Lang'ata area of Kenya's capital Nairobi on January 28, 2018 killing three people and leaving hundreds of people homeless. Table 1 summarizes basic information on each of the nine data-sets included in our study.

Methods
Our research method comprises seven steps.
1. Data extraction and pre-processing: We used Twitter's Search API to extract publicly available tweets sent during the nine natural disaster events. During preprocessing, we removed duplicate entries and tweets that are uninformative with respect to emotion detection (such as tweets that contain URLs only). After the preprocessing step, our data-set comprised 16,843,947 tweets sent from 6,109,374 different Twitter accounts (see Table 1). Privacy of sensitive user data, such as personal identifiers, is an important aspect that needs to be considered while extracting, storing, and analyzing OSN data [4,12]. Prior to data analysis, we anonymized all personal identifiers (screennames/user IDs as well as @mentions that appear in the text of a tweet) by replacing them with a distinct hash value. All analysis tasks have been performed on the anonymized data-set.
2. Emotion detection: We applied our emotion detection procedure [32] which annotates the eight basic emotions with respect to Plutchik's wheel of emotions (anger, fear, sadness, disgust, joy, trust, anticipation, and surprise [50]). Our procedure relies on the NRC emotion-word lexicon [41] and the AFINN lexicon for the intensity of an affect [23], as well as a set of heuristics that people naturally use to detect emotions in written texts [59] (e.g. amplifiers, maximizers, downtoners, negation). When comparing the accuracy of our approach to the widely used sentiment analysis tool SentiStrength [61] (see, e.g., [22,52,55]), we achieved a better classification of negative emotions (0.85 vs. 0.73) but a comparatively worse accuracy for positive emotions (0.54 vs 0.61). However, also note that such a comparison is biased to a certain degree, because the detection and classification of positive emotions is a more difficult task than classifying negative emotions (see, e.g., [61]) and SentiStrength only identifies the emotional valence (positive or negative) of a text, while our approach explicitly identifies the eight basic emotions found in Plutchik's wheel of emotions.
3. Construction of the communication network: In general, Twitter users can directly send tweets to another user via @screenname. Following such traces, we reconstructed a directed communication network for each disaster event where every edge is annotated with respect to the dominant emotion that appeared in the corresponding tweet. Table 1 summarizes the number of vertices and edges in each of the nine communication networks. 4. Construction of a multiplex network: Next, we constructed a multiplex network for each day of data extraction, and each multiplex consists of eight layers (each layer corresponds to one of the eight basic emotions: anger, fear, sadness, disgust, joy, trust, anticipation, surprise). In addition, we aggregated the edges found on the negative emotion layers (anger, fear, disgust, and sadness) into an aggregated negative layer, and the edges found on the positive emotion layers (joy, anticipation, and trust) into an aggregated positive layer. We also derived a valence interlayer which captures the vertices found on each valence-specific layer (positive and negative) and their adjacent vertices that are active on the two aggregated valence layers. Finally, we aggregated all individual positive-and negative-emotion layers and layer surprise to derive an overall aggregated network. Figure 1 sketches the eight emotion-annotated layers and the four derived layers. 5. Null model construction: To detect emotion-exchange motifs, we generated synthetic random networks (null models) by applying the stub-matching algorithm over each of the eight emotion layers and each of the four derived layers of our multiplex network (see Fig. 1). In total, we generated 1000 null models for each layer by following the approaches described in [9,56]. Thus, over all days of the dataextraction periods for all nine events, we generated in total 1,704,000 null models that underwent the motif-detection procedure.
6. Motif detection: To detect emotion-exchange motifs (see [35][36][37]), we first applied the ESU subgraph enumeration algorithm [69] to enumerate all possible subgraphs of size k = 3 and subsequently the VF2 isomorphism testing algorithm [5] to check for the isomorphism between any two subgraphs. If two subgraphs were found to be isomorphic, they were placed in their respective isomorphism category (see Algorithm 1). Note that while the exact enumeration counts all existing subgraphs of a fixed size k, this accuracy comes at a high computational cost.
The emotion extraction as well as the motif detection procedures have been performed in parallel on four different machines: a machine with Intel Xeon CPU E3-1240 v5 @ 3.5 GHz (4 cores/8 parallel threads) and 32GB RAM, a machine with 2x Intel Xeon E5-2630 v3 @ 2.4 GHz (16 cores/32 parallel threads) and 288GB RAM, a machine with 2x Intel Xeon E5-2630 v4 @ 2.2 GHz (20 cores/40 parallel threads) and 256 GB RAM, as well as a machine with 2x AMD Epyc 7451 @ 2.3 GHz (48 cores/96 parallel threads) and 512 GB RAM. On these four machines, the emotion extraction and motif detection procedures for all nine data-sets took in total about 245 days and produced over 4.7 terabyte of data to analyze.

Emotions expressed during natural disasters
The integrated crisis mapping (ICM) model [25] is a theoretical framework which examines emotions that are likely to be experienced by the public as part of their coping strategy during different types of crisis events. According to the ICM, people experience a range of emotions when facing a crisis event. The corresponding list of emotions has been compiled from reputable mainstream US newspapers covering 259 news stories [26]. The model identifies four dominant emotions that occur during crisis events, namely anger, fear, anxiety, and sadness. So-called primary emotions are experienced instantly, while so-called secondary emotions occur in the aftermath of an event. The exact definition of what qualifies as a primary or a secondary emotion depends on the type of a crisis event. Thus, for example, riots and (violent) protests are characteristic for a primary emotion of anger and a secondary emotion of anxiety. Acts of terrorism or psychopathic acts (such as school shootings), on the other hand, instantaneously cause fear followed by sadness. Moreover, according to the ICM the emotions of fear and sadness are predominantly expressed during natural disasters 2 . In our analysis, the average emotional intensities ( ei ) of fear ( ei fear = 13.92 ) and sadness ( ei sadness = 10.80 ) dominate over the other six emotions (see Fig. 2). This finding can be generalized over all nine natural disasters in our study, where we found similarities with respect to the emotion intensities in each of the events. Figure 2 shows a positive value for Kendall's rank coefficient for each pair of events 3 .
The temporal analysis of emotional messages is shown in Fig. 3. In particular, we found that negative emotions of fear and anger are predominant at the beginning of a natural disaster event. In contrast, the emotion of sadness gradually increases its intensity as the consequences of a natural disaster are revealed over time and peaks towards the end of the data-extraction period (prevailing over anger and afterwards also over fear) (see Fig. 3). Positive emotions such as joy, trust, and anticipation, although not expressed as intensely as the negative ones, are also present throughout natural disaster events and on certain days even peak over the dominant negative emotions (e.g., trust peaks over sadness and anger from days 5 to 10). During natural disasters, emotional tweets attract more attention than neutral ones in terms of likes (mean(likes emotional ) = 1.98 ± 221.69 , while mean(likes neut ) = 1.79 ± 248.13 ). We also found that Pearson's coefficient is (weakly) positive with respect to the level of emotionality and the number of likes ( 5.79 × 10 −5 ). In contrast, neutral tweets result in comparably more repeated message spreading (retweeting) than the emotional messages ( RT neutral = 11066.25 ± 32002.86 vs. RT emotional = 6248.476 ± 16, 418.51 ). In this context, neutral messages are usually of informative nature where people share information related to the disaster event. In fact, [3] showed that people tend to retweet timely content and breaking news.
When distinguishing between positive (joy, trust, anticipation) and negative (anger, fear, sadness, disgust) emotions in our data-sets, user reactions in terms of liking a tweet and passing it forward (retweeting) differ considerably. As summarized in Table 2, tweets conveying a high intensity of positive emotions on average receive considerably more likes and retweets, while tweets conveying a high intensity of negative emotions are slightly longer (i.e., on average, they include more words).
Our data-set includes a total of 729,698 messages that have directly been exchanged between a pair of users via @-mentions. In general, the emotions communicated via direct messaging (see Fig. 4) are comparable to the ones communicated via broadcast messages (Kendall's coefficient is a strong positive 0.85). Thus, since there are measurable similarities in the expression of specific emotions among the nine data-sets, we examine whether the direct messaging behavior is also comparable when users express emotions. To this end, we refer to the structural patterns (motifs) that emerge daily as groups of three users directly exchange messages (i.e., we analyze subgraphs of size 3, see also Table 3). 1 3

Emotion-exchange motifs
While directly exchanging emotional messages, Twitter users form statistically significant subgraphs that we call emotion-exchange motifs (see [35][36][37]). In total, we found 90,142,095 subgraphs which we categorized into 1824 isomorphism classes (i.e. isomorphic graphs are grouped together). Out of these 1824 isomorphism classes, 1410 are statistically significant for the input networks (emotion-exchange motifs) across all nine data-sets. For the sake of simplicity, Table 3 Frequency, variability, graph properties (min, max, and mean number of edges ± standard deviation), and event-wise occurrence of MAN-labeled motifs we classified the 1410 motifs according to the MAN-labeling scheme (mutual edges (M), asymmetric edges (A), non-edges (N) followed by a letter U = up, D = down, C = cyclic, or T = transitive, which distinguishes among different types of triads [7]) as shown in Table 3 (i.e., we currently disregard edge weights in a motif). As shown in Table 3, 12 of the 13 MAN subgraphs are statistically significant for the message-exchange during the nine natural disaster events. The most common motif is 021U (see Table 3) with a relatively low variability (with respect to its edge distribution). Two motifs occur in all nine data-sets (021D, 030T), while the motifs 201, 120C, 030C, 210 are representative for only two data-sets each. Thus, we do not consider 201, 120C, 030C, 210 common motifs with respect to their overall occurrence. One motif ( ID = 300 ) did not occur in any of the studied events.
Motif 120U has the highest average number of edges (mean(edge_ count)= 7.88 ± 4.81 ) while the maximum number of edges is found in motif 030T (max(edge_count)= 24 ). Though the theoretical minimum number of edges is 3 (i.e., one edge between each pair of vertices in a 3-subgraph), two motifs come with a minimum number of 4 and 5 edges (motifs 120C and 210, respectively).
The motif distribution on the eight layers (representing Plutchik's eight basic emotions) as well as the four derived layers of our multiplex network is shown in Table 4. On all layers, motif 021U is the most commonly occurring motif followed by 021D. For the other motifs, the distribution varies for each layer. Motif 021C is the third most frequent on the layers representing anger, fear, sadness, anticipation, and the derived layers negative, positive, interlayer, and aggregated while the layers disgust, joy, trust, and surprise show a relatively high presence of the motif 030T. Moreover, motif 210 only appears as Twitter users exchange mixed-emotion messages (i.e., positive as well as negative messages). Finally, motifs 210, 120C, and 201 appear only on the derived layers and are, thus, not representative for the communication of a single emotion (see Table 4). Figures 5,6,7,8,9 and 10 show the temporal occurrence of MAN-labeled motifs with respect to the 12 emotion-annotated layers of our multiplex network. The temporal evolution of specific motifs on the different emotion layers indicates characteristic differences among the motifs. Motifs 021D, 021C, 030T, 111U, 030C, 120U, 120D, 120C, and 210 peak within the first half of the data-extraction period (the latest on day 11) on all layers. In contrast, motif 021U does not show a general pattern. On the one hand, it peaks in the second half of the data extraction on layer anger; on the other, it peaks within the first week on the layers trust, fear, as well as the derived layers negative, positive, and interlayer. Motif 111D generally peaks within the first half of the extraction period with the exception for the joy layer where it peaks at the end of the data extraction period (see Fig. 7).
Furthermore, we found that certain motifs appear within a specific time-frame only. For example, motifs 201 and 120C (shown blue and black, respectively, in Figs. 11 and 12), only occur on the derived layers and within the first 14 days of the data-extraction period. Similar for motif 030C, which only appears within the first 11 days of the data-extraction period and only on the derived layers that involve positive emotions (i.e., positive, interlayer, and aggregated) as well as the anticipation layer.
Journal of Computational Social Science (2021) 4:531-565 Table 4 Frequency of motifs on single emotion layers and the derived layers With respect to motif durability, we found that motifs 120C and 210 occur on an average of three days only, while motif 030C only occurs on an average of 2.8 days. This is in contrast to motifs 021U and 021D that are present throughout 21 days of data-extraction (see Figs. 5,6,7,8,9,10).
The motif size (i.e., the number of edges in a motif, resp. the weight of the edges) gives information about how many messages are exchanged among the Twitter users, as well as the direction of the message flow. In general, we distinguish unidirectional and bidirectional edges. Table 5 shows the average number of unidirectional and bidirectional edges for each layer of the multiplex network. The results indicate that, with the exception of anger, the derived layers generally show a comparatively lower number of unidirectional edges compared to the single-emotion layers. The anger layer has on average the smallest number of unidirectional edges, while the highest number of unidirectional edges is found in the motifs on the sadness layer followed by the fear layer. In contrast, the number of bidirectional edges are esp. high on the derived layers (the aggregated layer, interlayer, negative layer, and positive layer). The lowest number of bidirectional edges is found on the sadness layer followed by the remaining negative single-emotion layers disgust, fear, and anger. Moreover, positive single-emotion layers exhibit on average a higher frequency of bidirectional communication.
The motifs 021U, 021D, and 030T are the largest in size (i.e. with respect to their edge count) on all layers of our multiplex network (see Figs. 11,12). However, though 021U is the largest motif on most of the layers, the edge count of 021D dominates over 021U on layers sadness, joy, and disgust. All layers show a decrease in the edge count towards the end of the data-extraction period.
To mitigate the 140-character, resp. 280-character, restriction 4 , Twitter users use self-mentioning to "link together" messages, i.e., messages that span over multiple tweets. In our emotion-exchange motifs, such behavior is represented via self-loops (i.e., tweets where a Twitter user mentions herself via @username).
Motifs that contain self-loops appear in eight of the nine events studied in this paper (no motifs with self-loops were found in the Costa Rica earthquake data-set). In total, 12.69% of all motifs identified in this study contain self-loops. These motifs occur on every layer of the multiplex network. Table 6 summarizes the shape of motifs containing self-loops on each layer of our multiplex network as well as their relative occurrence on each layer. In general, motifs containing self-loops predominantly appear as Twitter users send messages conveying mixed emotions (the aggregated layer contains 39.39% of all motifs containing self-loops, followed by the interlayer with 27.36%). Considering single-emotion layers only, self-loops are most frequently found on the layers representing fear (5.42%) and anticipation (4.56%).
In general, we found that it takes some time after the respective event occurred until the number of motifs including self-loops, i.e. self-mentioning, peaks (see Fig. 13). For the mixed emotions, the peak is found on day four, for the negative emotions on day five, while the positive emotions layers show the highest peak on day nine.

Structural similarities of emotion-annotated networks
Lastly, we report on the daily structural similarities of emotion-annotated networks by considering the distribution (frequency) of the different isomorphism classes for emotion-exchange motifs (i.e., we take into account a motif's variability expressed as the edge distribution including self-loops, and the number of occurrences of each motif). To this end, we use the arithmetic fidelity measure (see [63]) which is defined as A =  belonging to the same isomorphic class i occurring in a network M2. Over time, the motifs found in each pair of layers formed from the 12 emotion layers 5 show at least a weak structural similarity. Figures 14, 15 and 16 show the respective mean similarity score averaged over the data-extraction period (solid line) and the range (minimum and maximum score) of the respective similarity score reached at some point during the data-extraction period (blue-shaded area). On average, the inter-group similarity score for pairs of positive emotion layers exhibits the highest value ( POS-POS = 0.12 ), followed by pairs of one  The lowest similarity score is found when comparing motifs on the layers aggregated, surprise, and interlayer ( ASI = 0.05 ). When considering pairs of single-emotion layers only (i.e., excluding the derived layers), the highest similarity score averaged over the data-extraction period is found between sadness and joy SADNESS-JOY = 0.15 , while the lowest one occurs between fear and disgust FEAR-DISGUST = 0.02 as well as fear and sadness FEAR-DISGUST = 0.02.   In 74% of the emotion layer pairs, the maximum score is reached after 14 days of data extraction. Interestingly, the highest maximum similarity score is found between the layers joy and sadness where = 1 exhibits the perfect similarity with respect to their motif distribution (see Fig. 15).

Fig. 12
Daily motif size on layers positive, aggregated, trust, anticipation, joy, and interlayer over all natural disaster events Table 6 Presence of self-loops on each layer of the multiplex network The color of the motif indicates the highest frequency at which a self-loop was found on a specific node in each motif

Discussion
During natural disasters, Twitter users predominantly express their emotional distress via the emotions of fear and sadness. Beginning with the initial expression of intense fear and anger, the emotion of sadness along with positive emotions slowly peak as the Twitter discourse evolves over time.
Messages that express sadness and positive emotions (trust, joy) convey compassion, hope, and love for those affected by the disaster as well as gratitude for those who helped the ones affected by the disaster. Below, we provide examples of messages conveying fear and anger: -I think the constant warnings on my phone that are loud as hell freak me out more than what is gonna happen #HurricaneIrma #Irma #wegotthis -San Juan PR Mayor says she is "mad as hell over hurricane Maria response..... help us we are dying!" -I hate this crazy wind. It howls like condemned werewolf from the deepest abyss of hell #Friederike" To a certain degree, OSNs serve as a therapeutic channel for the ones affected by the disaster [15,45,46]. In this context, messages conveying sadness, unlike fear and anger, predominantly express compassion:   Messages that convey love for the ones affected by the natural disaster, messages of hope and admiration/thankfulness for those involved in the rescue efforts are found as well. Below we provide examples of messages conveying joy (love), trust, and anticipation.
-Cuba has a very special place in my heart; all my love to the island and her wonderful people #HurricaneIrma #Irma -If there was 1 good thing about #HurricaneIrma it allowed me to be here with people I've grown to love! #WageHope -Please continue to pray for our wonderful city of Montecito! We are believing for love, peace and restoration of many lives -I've love being part of the Montecito community. I send love to all the families and the amazing rescue workers -Holy God we pray for all victims of natural disaster's of Hurricane Harvey, quickly send them help, comfort them -Rescue Dogs In Mexico City's Earthquake Should Be Honored By An Award Equal To The Nobel Peace Prize. God Bless All -Good note & good prep by @Westin in #StMaarten. Staff have been amazingly professional. Now let's pray! #Irma2017 Pasupathi [49] found that negative emotions exhibit a higher intensity when they are immediately experienced as opposed to emotions that occur when just remembering the event. In our study, we analyzed tweets that have been published in real-time during and shortly after a natural disaster. For all nine events, we found a considerable decrease in the emotional intensities of fear and anger towards the end of the data-extraction period (see Fig. 3). Positive emotions, on the other hand, show a comparatively lighter decrease and remain in a confined range throughout the dataextraction period (between 0.3 and 0.8).
The emotion of sadness always peaks in its intensity during the second half of the data-extraction period and reaches a relatively high intensity towards the end of the extraction (thus, not following the trend of other negative emotions such as anger and fear). As discussed above, during natural disasters positive emotions and sadness express compassion, love, gratitude, and hope, and thus play a role in the collective coping with the emotional distress and contribute to the emotional wellbeing. Fredrickson [16] referred to this phenomenon as the undoing hypothesis (a use of positive emotions to undo the effects of negative emotions).
We also found that positive messages attract more reactions in terms of likes and message distribution (retweeting) than the negative ones. Retweeting is especially seen as a convenient mechanism to extend the audience of a particular message by increasing its visibility in the Twitter sphere. Upon studying the reasons why people repeat messages, [3] found that the retweeting mechanism is used to publicly mark oneself as a listener, to approve one's message, agree with someone, or to support and encourage social action. Examples of highly retweeted messages from out data-set read: -RT @screenname 6 : Sanctions on Iran make it difficult to donate, but here's a GoFundMe set-up to help the victims of the devastating earthquake (conveys anticipation) -RT @screenname: I'm sending peace and love and prayer to the hundreds of people who perished in the Earthquake ♥(conveys joy (love)) -RT @screenname: As we pray for those affected by #HurricaneHarvey, let us also honor all of the brave heroes and first responders. (conveys joy (love)) Positive messages that call for social action coupled with Twitter's re-tweeting mechanisms turn out to be quite effective in reaching a large number of users. For example, in our data-set, the most frequently retweeted message "RT @screenname: With the current devastation in Houston, we are pledging $0.15 for every RT this gets! Please forward this along to help!" conveys anticipation and was retweeted in total 1,154,211 times. User behavior in terms of emotional expression directly contributes to the emergence of the underlying communication network [70]. For the nine disaster events, we found that 12 out of 13 possible directed 3-subgraphs are statistically significant building blocks of the emotion-annotated networks. Among those, motifs 021U and 021D were the most frequent and the largest in size with respect to their number of edges.
Due to the nature of Twitter to predominantly serve as a channel for broadcasting short messages, the high frequency of the broadcaster motif 021D does not come as a surprise. Moreover, the message-receiver motif 021U is also typical for Twitter. Message-receiving behavior (via @-screenname) emerges during information seeking (e.g., the police was repeatedly asked for official information during the 2017 G20 Hamburg riots [33]), as a reaction to another user's tweet/public statement, or by publicly mentioning a public person (such as a politician). These findings comply with our former studies on emotion-exchange motifs that emerge on Twitter during bombing and shooting attacks [35] as well as during riot events [37].
The motifs 021C (a message cycle motif) and 030T (a transitive motif) are the next most frequently occurring motifs. Similar to 021U and 021D, the motifs 021C and 030T appear on all layers of our multiplex network. The example below shows the formation of a motif 030T ( A → B → C → A ) which expresses a one-way (negative) reaction to an episode of an event being discussed. No one's seriously complaining, no one!! Though Twitter is mainly seen as a platform for message broadcasting, we identified four common motifs that contain bidirectional edges. These motifs are 111D, 111U, 120U, and 120D. A bidirectional edge in a motif signals a two-sided communication (message exchange) between a pair of users. Such a form of a communication represents a discussion about an event, an exchange of opinions, or calls for social action. We found that motifs of the shapes 111D and 111U are not characteristic for the communication of surprise, sadness, and disgust (they either appear very rarely on one of these three layers or not at all). Their low significance profile or even absence on these layers suggests that it is more common to respond to these particular emotions with other types of emotions. This finding, however, does not entirely come as a surprise. Communication of sympathy, compassion, and comfort typically involves messages of love, hope, and support as a response to someone else's sadness [19]. In our data-sets, we also found that positive emotions (average number of messages trust = 1.4 , joy = 0.91 , anticipation = 1.4 ) are typical responses to a sad message. However, because crisis event are related to intense feelings of fear, we could also confirm that sadness is frequently responded by fear ( fear = 1.37 ). According to [18], the individuals affected by a natural disaster often search for someone to blame (e.g., for a lack of preparation or the poor construction of buildings) to regain their sense of control of the highly threatening and uncertain situation. As a consequence, we also found a high number of angry responses to sad messages ( anger = 1.38 ) as well as messages conveying disgust ( anger = 1.16 ). The exchange of anticipation, trust, as well as mixed emotions (on the derived layers of our multiplex network) is often related to the motifs 111D and 111U. Below we provide an example from our data-set for a discussion involving anger (motif 111U A ↔ B → C).
-Person B: @A @C This earthquake hit a major American ally called Kurdistan.
Kurdistan more then it did to Iran. Furthermore, these four motifs (120C, 201, 030C, and 210) do not emerge before the third day of the data-extraction period, they do not appear consistently (i.e., they have a tendency to re-appear rather than consistently appear on a daily basis), and have a relatively short life-span. Unlike the three most frequent motifs (021U, 021D, 021C), the four uncommon motifs (120C, 201, 030C, and 210) indicate a more complex social interaction-201 represents a discussion between two pairs of users; 030C, a closed message cycle; and 210 as well as 120C, a message cycle with a discussion. Our analysis showed that such social interactions (though present on Twitter) are in general not characteristic communication patterns for Twitter. These results comply with our previous findings on emotion-exchange motifs occurring during riot events [37] as well as bombing and shooting attacks [35].
Emotion-exchange motifs are a useful feature to compare the underlying structure of emotion-annotated communication networks. We found that motifs representing the communication of a single negative emotion are structurally more dissimilar than those conveying a single positive emotion. Interestingly, when negative emotionexchange motifs are compared to positive emotion-exchange motifs, they exhibit a greater similarity within the inter-valence group than in their own intra-valence group. The two emotions contributing most to high inter-valence similarity scores are joy (positive valence) and sadness (negative valence). In fact, emotion-exchange motifs on these two layers show a higher similarity score than the motifs found in any pair of negative emotion layers (such as fear and disgust, which exhibit the lowest similarity score). Semantically, messages conveying joy express love, gratitude, and hope, while sadness is associated with an expression of well-being wishes and grief over the victims of the natural disasters. In both cases, these messages are also associated with compassion. Thus, our analysis showed that the exchange of semantically related messages form comparable emotion-exchange motifs.

Limitations
This study comes with certain limitations. For one, though we systematically monitored Twitter and picked carefully chosen hashtags and search terms for our data collection, Twitter's Search API comes with a restriction regarding the availability of tweets one can fetch (i.e., not all tweets are indexed and made available via Twitter's public API). Thus, we cannot exclude the possibility that we missed relevant tweets due to this API restriction.
Furthermore, bots play a significant role on Twitter. According to [65], as much as 15% of all Twitter accounts can be attributed to automated bot accounts. Such accounts, apart from serving as mere chat bots, may also be designed to disseminate a large volume of spam, influence one's opinion, and can mimic a human-like behavior making them difficult to distinguish from human users (see, e.g., [10,13,34]). Though in this study we did not distinguish between human and bot accounts, the involvement of bot accounts might impact the formation of communication patterns (see [37]). In our future work, we plan to further examine the role of bots on the formation of structural network patterns and in specific on the emergence of emotion-exchange motifs.
Due to the complexity of human emotions, limited information about the context in which an emotion was experienced, and the tendency of people to differently interpret the same emotion, identifying emotions is a challenging task (see also [28]). In order to detect emotions in our data-sets, we relied on our emotion detection algorithm and existing emotion-word lexicons. In our prior work, we tested for the appropriateness of publicly available emotion-word dictionaries (see [32]) and chose the one with the best performance to mitigate errors and incompleteness in our studies. Furthermore, we enhanced the emotion detection procedure via a set of heuristics (e.g., amplifiers, maximizers, downtoners, negation, emojis) that considerably increased the accuracy of the approach. However, since even human raters (e.g., from different cultural backgrounds) sometimes disagree on the emotional valence of written texts, we cannot rule out the possibility that some of the tweets have been mislabeled. This especially happens for ironic or sarcastic messages.
Finally, our motif detection procedure relies on the exact enumeration of all 3 subgraphs in a particular network. This procedure is computationally very demanding (see also "Methods"). As previously noted in [62], networks derived from realworld OSNs are complex and lead to computational challenges.

Conclusion
In this paper, we analyzed over 16 million tweets sent from 6.1 million different Twitter accounts that have been sent during nine natural disasters. In particular, we analyzed the structural communication patterns (emotion-exchange motifs) that emerge as Twitter users directly exchange emotional messages. Our findings show that emotional messages receive considerably more attention in terms of likes compared to neutral ones. For each of the nine events, we found that the affected individuals predominantly experience fear and sadness as a natural disaster strikes. Moreover, in the immediate aftermath of a disaster event, Twitter users especially convey disgust and anger, as well as a range of positive emotions that serve as an antidote against the disruptive effects of the experienced negative emotions. These findings about the general emotional tone during natural disasters comply with other related scientific contributions.
Our approach to studying emotional responses during crisis events especially uses the novel concept of emotion-exchange motifs-small network structures that are statistically representative for the communication of specific emotions. To the best of our knowledge, this interdisciplinary approach is the first to combine network motifs with the study of human emotions. In particular, we found that individuals affected by a natural disaster tend to frequently broadcast unidirectional messages conveying fear, sadness, and disgust, while positive emotions, such as joy, trust, and anticipation inspire online conversations. Moreover, online conversations involving positive emotions show a relatively high number of bidirectional messages of the same (positive) emotional tone. On the other hand, for messages conveying sadness and disgust the low presence of emotion-exchange motifs containing bidirectional edges (111U) revealed that sadness and disgust (unlike fear and anger) are typically responded to by other types of emotions. For example, sadness is frequently found in messages of compassion and is responded to by joy/love, while disgust is connected to a high response rate of angry messages.
In addition, the emotion-exchange motifs found in our data-set reveal that the communication of positive emotions forms a unique and distinct set of motifs (cyclic subgraph 030C) that do not appear as Twitter users exchange negative emotions. In contrast, a mixture of different emotions in a conversation leads to more complex structures (120C, 201, 210) where all three users participating in an emotionexchange motif take an active role with respect to their message-sending behavior and exhibit a clear local hierarchy with respect to the choice of a conversational partner.
Finally, we used emotion-exchange motifs to examine the structural similarities of different emotion-annotated networks. In this context, we showed that the intra-valence networks (e.g., sadness and fear) exhibit a lower similarity score than inter-valence networks (e.g., joy and sadness). In fact, emotion-exchange motifs representing the communication of sadness and joy showed the highest similarity score, even reaching a perfect (maximum) similarity score at some point during the data-extraction period. We attribute this finding to the semantics of the messages conveyed as people communicate the two emotions. Supported by findings from the related work and empirical evidence found in our data-sets, the emotions of joy and sadness are commonly used to express the feelings of compassion, gratitude, and hope.
Based on our improved understanding of the statistically significant and recurring communication patterns that emerge during natural disasters, our future research will further investigate whether the identified emotion-exchange motifs are universal across different types of crisis events (such as riots, terror, and shooting attacks) and examine whether during negative events certain emotion-exchange motifs are characteristic for the communication of specific emotions. Furthermore, to gain a more in-depth understanding of the communication structures that emerge as people exchange emotions, we plan to further investigate the concept of temporal emotionexchange motifs.
Author contributions Both authors contributed to the study conception and design. Data extraction was carried out by both authors, data pre-processing by MS, and data analysis by EK. Both authors read and approved the final manuscript.
Funding Open access funding provided by Vienna University of Economics and Business (WU). Not applicable.

Data availability
The network data are freely available for download from our website: https ://nm.wu. ac.at/nm/strem beck/data/natur al_disas ters.zip.

Compliance with ethical standards
Conflict of interest The authors declare that they have no conflict of interest.