Social media and online content diffusion

Social Media enables the spread of user-generated content through the interconnected network of its users [3]. As content is reshared by users and distributed by platform algorithms, it can diffuse across the network, reaching a larger online population compared to the author’s primary contacts. This diffusion capability has attracted considerable interest across various research disciplines. In marketing, studies examine the role of SM in driving word-of-mouth promotion for products [35]. Political science and communication scholars have examined the spread of fake news and rumors on SM platforms [1,36–38]. Similarly, in the health sciences, SM is a critical tool for disseminating health behaviors and gauging public opinions and health choices during events such as pandemics [15,39]. Lastly, network scientists have also focused on understanding the underlying structures that enable information and behaviors to propagate through the interconnected links of social networks on SM platforms [3,40].

Research on the diffusion phenomenon of SM typically addresses three key aspects: structural features, temporal dynamics, and content characteristics [2]. First, scholars have emphasized the importance of social network structures formed through various connections between users, such as friendships, followers, group memberships, and resharing links. Structural features like user centrality, the presence of weak ties, and the formation of clusters play a critical role in shaping the outcomes of information diffusion [3,41]. Second, research has explored the temporal dynamics of diffusion events [36,38,42–44], focusing on the speed and duration of information spread. Key findings indicate that sharing behavior often occurs in clustered bursts and that the aggregate temporal patterns of communication vary depending on factors such as the topic [45], the emotions expressed [27,46,47], or the users involved [48]. Understanding these temporal patterns is crucial for decision-makers, including business managers, law enforcement, and crisis response teams, as it enables them to respond with effective intervention. Finally, the content of SM communications, ranging from text [33] to multimedia like videos [49] and emojis [50,51], has also been analyzed to examine how different forms of information, emotions, and meaning influence recipients. These studies highlight the differential impact of content characteristics on how information spreads and resonates with audiences.

To better understand the structural and temporal dynamics of information spread on social media, researchers often use the concept of cascade trees to model the propagation process through interpersonal transmission and resharing [1,36]. In this framework, the original post is the root of a tree-like graph that expands as users reshare it. Each node represents a user, and each branch corresponds to a resharing event. For instance, a chain of retweets on X (formerly Twitter) can be visualized as a cascade tree, illustrating who retweeted whom through added nodes and connections. These models are instrumental in analyzing diffusion patterns, including virality, influence, and the identification of key spreaders.

Online propagation of emotions

Human emotions involve coordinated changes in perception, physiological responses, motivation, behavior, and feelings triggered by how individuals appraise events that matter to them [52]. Since external factors can trigger emotions in individuals, the emotional expressions in online content can act as powerful cues that stimulate users to mirror, amplify, or retransmit the emotion to others. As per the emotional contagion theory, the transfer of emotions can be automatic, unconscious and difficult to control, the primary pathways to such transfer are empathy which induces mimicry [53]. Further, research has also shown that online content can also reflect the emotions of its authors and serves as a pathway for transmitting emotions between users [21,54], even via mediums like emails and webpages [33], or through emojis [51]. This dynamic makes human collectives conducive to the emergence and propagation of emotional cascades, where the transfer of emotions spreads rapidly from a few individuals to a significant portion of a collective [21]. Such findings within online settings are significant because emotional transmission, once dependent on face-to-face cues like body language and vocal tones, has evolved to operate through computer-mediated communication and network-driven cues in online environments.

Research on the emotionality of SM content has evolved in two key directions. One foundational area is focused on the empirical evidence of emotional contagion, which differs from information diffusion. Emotional contagion occurs when content expressing a particular emotional state created by one user on SM invokes similar emotions in the recipients. For instance, Ferrara and Yang [10] show that exposure to negative (positive) content increases the likelihood of users posting negative (positive) content on Twitter. Similarly, in a large-scale Facebook experiment, Kramer et al. [19] found that emotional expressions in users’ news feeds influenced the emotions expressed in their subsequent posts. Their study also revealed that emotional exposure can impact social engagement, shaping user activity levels on the platform. Context also plays a significant role, as shown by Coviello et al. [54], who found that real-world events, such as rainfall, can predict online emotional responses. Notably, the emotions elicited by rainfall in one geographic location spread online to users in unaffected regions, highlighting the reach and influence of emotional contagion in online environments. However, asserting the underlying mechanism of contagion requires a deeper study of the latent psychological states of the users, either through recording subsequent posts or through experimental methods.

A related research stream shows that different emotions exhibit distinct diffusion or propagation patterns. For instance, a study on Weibo found that anger is more likely to spread between users than joy, whereas sadness has a weaker correlation among users [55]. Stieglitz and Dang-Xuan [8] observed that political tweets that are more emotionally charged get retweeted more frequently and at a faster pace. Similarly, analyzing thousands of rumors on Twitter, Pröllochs et al. [27] compared the diffusion rates of various emotion categories. They found that, unlike the emotions of surprise, fear, and disgust, expressions of anger, anticipation, and trust result in more reshares, reach a broader audience, and persist over a longer period. Berger and Milkman [33] also support these findings, showing that New York Times articles evoking high-arousal emotions, such as awe, anger, and anxiety, are more likely to go viral than those associated with low-arousal emotions, such as sadness.

The study of how emotions spread across social media platforms emphasizes the need for theoretical frameworks to comprehensively understand emotional propagation. Building on extant research, we draw from two foundational theoretical approaches that offer distinct but complementary perspectives to guide our analysis. First, Goldenberg and Gross [21] propose studying emotional contagion through an “emotional cascade approach,” which examines how a piece of content elicits sequential reactions or reshares after it is viewed by others. We adopt this framework to analyze reshares on Twitter in the aftermath of celebrity suicides. Second, we guide our empirical analysis using the “circumplex model of affect” [31], which categorizes emotions along two bipolar dimensions: valence (positive vs. negative) and arousal (the level of physiological activation they evoke). High-arousal negative emotions include anger, fear, frustration, distress, and annoyance, whereas low-arousal negative emotions encompass misery, sadness, and boredom. On the positive valence side, high-arousal emotions include happiness and excitement, while low-arousal positive emotions include satisfaction, joy, and relaxation. The model is a structure of the affective experience of individuals where emotions at the opposite end of each dimension seldom are experienced together. Thus, sadness and joy, which lie along the dimension of valence, do not typically occur together, or sadness and anger, which lie apart on the arousal dimension, seldom will be observed together.

Previous research on the online dynamics of emotional content has shown that high arousal and negative emotions are significant drivers of virality [28,33]. However, many studies examine arousal and valence separately and often restrict their analysis to a single metric of retransmission, with the exception of a few studies [10,27,33]. For example, while an existing study finds that emotions like fear and anger [55] are more likely to be reshared on social media, it does not examine other aspects of the temporal dynamics, such as the duration or speed with which the retransmission occurs. Overall, there is limited evidence in social media research distinguishing the temporal dynamics of diffusion created by various emotions. Recent studies that challenge valence–arousal frameworks highlight the potential of focusing on discrete emotions [28,32], and there is room to extend their findings by demonstrating how discrete emotions vary in their temporal patterns of diffusion.

Self-harm and digital social influence

The third body of work informing our study pertains to suicide contagion, a phenomenon extensively studied across multiple disciplines, including health sciences, communication, and psychology. The literature widely recognizes suicide as a contagious act, with contagion occurring through proximity, demographic similarity, or the prominence of the victims. Instances of suicide contagion have been documented for at least two centuries [30,56]. Celebrity suicides, in particular, have been associated with inducing copycat behavior in the population as far back as the 18th century [24]. This effect is often facilitated by media exposure and cognitive mechanisms such as imitation and suggestion [57,58]. Research has shown that media publicity, even before the advent of digital and social media, played a significant role in triggering copycat suicides [26]. This phenomenon, commonly known as “The Werther Effect,” was first identified following the publication of Goethe’s novel “The Sorrows of Young Werther” [59], which reportedly led to a wave of suicides across Europe. Empirical evidence for this effect was later confirmed by Phillips [24], who analyzed suicides reported in newspapers in the US and UK and correlated them with subsequent increases in suicide rates within those communities.

More recent studies have demonstrated evidence of suicide contagion across different regions, including US, Europe, and East Asia [22,23,26,57]. For example, a study found that in August 2014, following the suicide of Robin Williams (celebrity actor), there was an excess of 1,841 monthly suicide cases in the US—a 10% increase over baseline rates [22]. Additionally, research on ethnic and locally clustered suicide events also suggests that individuals who are in contact with or associated with someone who has died by suicide are more likely to engage in the same act [60]. This subset of the more general realm of behavioral contagion underscores the urgency of preventive interventions, particularly in the early stages of a contagion event, when the spread can escalate rapidly. Special attention is needed for vulnerable populations, including youth and individuals with mental health conditions [61], who are more susceptible to social influence through exposure to others’ behaviors, emotions, and thoughts.

Social media expands interpersonal communication, potentially amplifying the extent of suicidal contagion. Content shared on SM following celebrity suicides often exhibits distinct emotional patterns. For instance, a study of Reddit posts following the suicide of ten celebrities found an increased expression of inward-focused content, anxiety, anger, and negative emotions [62]. Similarly, Niederkrotenthaler et al. [63] analyzed Twitter activity following the suicide of Swedish DJ Tim Bergling (Avicii), identifying several short-lived peaks of social media engagement appearing after the incident. Each wave of engagement aligned with major news revelations—initial death reports, confirmation of suicide, and disclosure of the method—highlighting how different types of information trigger distinct emotional and temporal patterns. Their analysis also revealed that tweets referencing the suicide method, though limited in volume, reached disproportionately larger audiences due to being shared by highly followed accounts. Fahey et al. [25] further examined the temporal evolution of emotions following celebrity suicides, showing that suicides of younger celebrities, women, and individuals in the entertainment industry tend to evoke stronger emotional responses. These emotional and textual dynamics are thought to be fundamental mechanisms through which exposure to suicide news and suicidal ideas occurs in digital environments, potentially triggering emotional or even behavioral contagion.

Social media also provides a valuable lens for understanding both the mental health of individuals and the mechanisms of social influence. Patterns in language, emotional tone, and engagement have been used to detect suicidal ideation and predict broader trends, including national suicide rates [62,64,65]. Distinct linguistic markers such as first-person pronouns, present-tense verbs, angry tones, and references to death are more prevalent in suicidal posts [66], revealing how online expression reflects and shapes collective responses to suicide-related events.

Despite these advances, there is a need for a deeper understanding of resharing—a core mechanism that can activate contagion—since it allows us to study the bottom-up development of cascades, thereby disseminating content and emotions to a larger audience. Earlier studies analyzed aggregate-level temporal patterns of tweets and their reply networks after celebrity suicides [63], as well as the emotional trends of communications classified by the characteristics of the deceased celebrity [25]. We suggest that the underlying temporal dynamics between individual retweets, as well as the cascade-level characteristics they generate (and how cascades vary in outcomes given their authors and content) will help us gain a deeper understanding of the potential micro-level mechanisms at play.

Metrics of online propagation

The propagation (diffusion) of online content has been examined through multiple measures that collectively offer the potential to understand the underlying micro-level mechanisms. We revisit these approaches to construct a more integrated theoretical lens connecting tweet content to retransmission patterns. A primary measure is cascade size, which is widely used as a core indicator of content virality and influence. It refers to the total number of retweets (i.e., the number of nodes in a cascade) and serves as a dependent variable in many studies [8,36,67,68]. While simple and intuitive, this measure overlooks the temporal dynamics of diffusion. Del Vicario et al. [36] used cascade size to track misinformation spread, while Stieglitz and Dang-Xuan [8] applied it to compare the diffusion of emotional and non-emotional content. Juul and Ugander [71] further showed that cascade size explains much of the variance in how true and false news diffuses, even when controlling for structural and temporal differences.

Second, the lifetime of the cascade is defined as the time between the first and last event in the sequence of retweets, i.e., the time between the original tweet and the last retweet [36]. A cascade with a long lifetime implies that it has been reshared numerous times or that there have been long intervals when it was not reshared but was eventually. Overall, long lifetimes mean that the Tweet’s emotional content has remained visible to the population over a longer period [27,38]. It is also possible that cascade size and lifetime will be correlated within a population because exposure of a tweet to a larger number of users will increase the likelihood that it will continue being reshared over a longer period. Third, the time-to-Nth retweet refers to how long a cascade takes to reach a predefined growth threshold, such as the time to its 100th retweet [47]. This metric allows for comparing the diffusion speed across cascades while controlling for a baseline level of virality [8,47].

Finally, the burstiness of a cascade captures the excitability of online content. It reflects how reactions cluster in time, with many users resharing within a short span followed by periods of lower activity, indicating synchronized collective responsiveness rather than steady diffusion. In recent work, “bursts” of online activity observed in email communications suggest a self-excitement process [69]. Thus, each cascade essentially is a sequence of bursts where two cascades can have the exact same number of retweets, but one may have a greater number of bursts (irregularities) than the other. Arranging retweets within each cascade chronologically can help discern multiple retweet bursts, with each burst temporally distinguishable from adjacent bursts. The theoretical distinction between the various dependent variables in the literature provides a basis for understanding the nuances of how tweets are retransmitted differently depending on the dominant emotion they convey.

Arousal and cascade size

Cascade size, defined as the total number of users who reshare a message, is a widely used indicator for evaluating the spread of online content, particularly on social media. Prior research has shown that exposure to content containing high-arousal emotions—both positive (e.g., excitement, enthusiasm) and negative (e.g., anger, fear)—tends to generate greater mobilization and action-oriented responses, compared to low-arousal or neutral content [33,70,71]. For instance, Berger and Milkman [33] found that high-arousal emotions significantly increased the likelihood of New York Times articles being forwarded via email, an early but robust indicator of emotional virality.

On social media, this arousal-driven engagement translates directly into greater resharing probabilities, thereby increasing cascade growth. Each retweet amplifies the message’s visibility and increases its chances of further propagation by mobilizing emotionally stimulated audiences. This effect is well-documented in political messaging, where morally charged and emotionally provocative content often produces large cascades [8,72]; however, the underlying mechanism—high arousal driving user engagement and resharing—is broadly applicable across a variety of social media contexts. Even studies that do not categorize emotions using dimensional models [27,55], such as the valence–arousal framework [31], have observed similar patterns. In other words, regardless of their classification, tweets expressing high-arousal emotional states tended to produce larger cascade sizes. Thus, we propose our first hypothesis:

Hypothesis 1: Social media messages containing high-arousal emotions receive a greater number of reshares than messages containing neutral or low-arousal emotions.

Arousal and cascade lifetime

The influence of emotional arousal on cascade lifetime is not consistent across social media contexts, and we argue that the emotional structure of the topic itself fundamentally shapes this variation. For instance, in emotionally ambiguous or open-ended contexts like online rumors, Pröllochs et al. [27] found that high-arousal emotions such as anger or anticipation prolong cascade lifetime; however, fear, despite being a high-arousal emotion, was linked to shorter lifetimes. Brady et al. [72] find that the effect of anger on social transmission varies across moral topics, such as climate change vs. same-sex marriage. These mixed findings suggest that emotional arousal alone may not consistently predict cascade longevity, likely due to the topic’s capability (e.g., rumors) to invite further speculation, reinterpretation, and debate from a heterogeneous and ideologically diverse user base or, conversely, trigger avoidance in the audience.

By contrast, celebrity suicides are emotionally unambiguous, tragic, and time-bounded events. They typically elicit rapid and high-arousal emotional responses such as grief, shock, and outrage, particularly from users with parasocial ties or cultural attachments to the celebrity. However, these emotionally engaged audiences tend to be affectively homogeneous—they share similar emotional states and interpretations—at least towards such tragedies. This emotional homogeneity fosters synchronized emotional reactivity, where users collectively engage in a brief but intense expression of emotion. While this initial surge drives early resharing, it saturates the finite pool of engaged users. Therefore, their emotional energy is exhausted, and no new interpretive frames emerge to sustain discussion, unlike rumors [27], which may invite retrospection.

Research in emotional contagion supports this pattern: homogeneous groups are more likely to experience strong but short-lived amplification as their emotional responses converge and saturate quickly [21,36,73]. Once this initial group has reshared the content, often within hours, the pool of emotionally susceptible users contracts rapidly. Combined with algorithmic prioritization of recency and a lack of ongoing narrative development, this leads to a steep drop-off in visibility and engagement. As a result, even though high-arousal emotional content spreads quickly, it tends to follow a burst–decay trajectory characterized by rapid saturation and a shorter cascade lifetime overall [63,74].

Therefore, while high-arousal emotions enhance the initial probability of resharing, we propose that in emotionally constrained contexts like celebrity suicides, such emotions lead to shorter, not longer, cascade lifetimes.

Hypothesis 2: Social media messages containing high-arousal emotions are reshared for a shorter period than messages containing neutral or low-arousal emotions.

Valence and cascade lifetime

The relationship between emotional valence —particularly negative emotions— and cascade lifetime remains theoretically underdeveloped and empirically inconsistent. While substantial literature confirms that negative content increases engagement and resharing probability [8,10,43], this does not imply that such content persists longer. Unlike virality or reach, cascade’s lifetime reflects how long a message remains actively reshared in a network. In theory, a stronger emotional reaction to negative content could either shorten lifetime by driving a rapid saturation of engaged users or extend it by sustaining ongoing relevance and engagement across a broader user base.

Importantly, the empirical context can moderate how valence influences cascade dynamics. In ambiguous or ideologically contested contexts such as rumors and moral debates, negative emotions like anger can prolong cascade lifetimes by fueling speculation, reinterpretation, and ideological conflict [27,72]. In contrast, in unambiguous and tragic events like celebrity suicides, emotional responses are highly synchronized among affectively homogeneous communities that share grief, sadness, or shock. Research in emotional contagion and network homophily suggests that such alignment leads to strong but short-lived amplification, as the pool of emotionally susceptible users is quickly saturated [21,73]. Burnap et al. [47] observed similar dynamics following the Woolwich terrorist attack, where negative posts spiked and declined within a short window, indicating a brief lifespan. Moreover, algorithmic exposure mechanisms compound this trajectory. Once a burst of resharing subsides, content loses visibility due to recency decay and reduced engagement, making it less likely to reach new users.

Furthermore, negativity not only attracts attention but can also repel it. When content provokes fear, moral discomfort, or emotional overload, it may cause users to disengage, limiting the number of resharers, i.e., people willing to reshare it. According to the Extended Parallel Process Model [75], when individuals perceive a threat as emotionally overwhelming and believe they lack the efficacy to respond effectively, they may engage in fear control responses, such as emotional withdrawal or disengagement, to protect themselves. These responses further reduce the susceptible pool of audiences who could reshare.

In sum, while negative emotions may enhance initial resharing, they can also trigger withdrawal, network saturation, and algorithmic suppression, especially in emotionally unambiguous, tragic events. These processes collectively contribute to shorter cascade lifetimes. Hence, we propose:

Hypothesis 3: Social media messages containing negative-valence emotions are reshared for a shorter period than messages containing neutral or positive-valence emotions.

Arousal and resharing speed

Resharing speed refers to how quickly an original message typically propagate across social media once posted. Prior studies confirm that sentiment can accelerate this process. Stieglitz and Dang-Xuan [8] modeled speed as the time lag between an original tweet and its first retweet, showing that emotionally expressive tweets spread faster than neutral ones. Tsugawa and Ohsaki [43] measured speed as the time required for tweets to reach specific cascade sizes (e.g., 10, 100, or 1,000 retweets) and found that negative tweets tended to travel more quickly than positive or neutral ones when diffusion volume was high. Together, these findings highlight that resharing speed captures the collective responsiveness to a message, with emotionally charged content prompting more frequent and synchronized reactions.

High-arousal emotions are especially effective at increasing resharing speed due to multiple reinforcing factors. First, Prior research argues that high arousal enhances action tendencies and mobilizes individuals toward expressive behaviors such as resharing [71]. Such emotions heighten urgency, prompting users to react in closer temporal proximity, which at the collective level produces faster and more synchronized cascades. Empirical evidence supports this logic: Fan et al. [76] show that anger, a high-arousal negative emotion, diffuses more rapidly than joy because it prefers weaker ties, which enables it to penetrate more widely across the network (engaging more audience promptly), and produces shorter retweet intervals, which reduces delays between consecutive reshares. Together, these findings suggest that arousal acts as a catalyst for resharing speed, shaping not only whether content spreads but also how quickly a collective responds.

Second, in the context of celebrity suicides, these dynamics are amplified. Unlike rumors or ongoing news, celebrity suicides are sudden, dramatic, and episodic, producing cascades that are intense but short-lived [25,63]. High-arousal emotions in this setting are expected to increase speed by reinforcing homogeneity of reaction, as grief and shock are present in the context (widely shared) and foster emotional mimicry, leading individuals to align with one another and respond in more simultaneous and concurrent ways [53]. Third, platform algorithms further compound this process by promoting content that gains traction quickly, creating feedback loops where early surges in resharing accelerate subsequent exposure [21]. As a result, high-arousal content triggers broad resonance, which manifests as reshares occurring in closer adjacency to one another, due to the combined effects of individual mobilization, collective synchronization, and algorithmic amplification.

Hypothesis 4: Social media messages containing high-arousal emotions are reshared more quickly than messages containing neutral or low-arousal emotions.

Arousal and resharing burstiness

Burstiness describes a temporal pattern of engagement characterized by short, intense flurries of activity followed by periods of minimal or no engagement. This phenomenon has been observed in various human communication systems, such as email and instant messaging, which points to the uneven micro-level tendencies of users to allocate attention, memory, and action resources [77]. In social media, burstiness reflects the clustering of retweets within narrow time windows, producing spikes in engagement that are not evenly distributed across a cascade’s lifetime.

Building on prior research, we expect high-arousal emotions to be strongly associated with bursty patterns of resharing. As we noted previously, these emotions stimulate rapid mobilization [71], activating intense reactions within emotionally aligned user groups, particularly in the wake of emotionally unambiguous events like celebrity suicides. Additionally, Social media collectives are inherently clustered, with users embedded in tightly knit communities [78]. High-arousal content is more likely to activate each of these emotionally synchronized members within these clusters. Once a cluster is triggered, users’ emotional alignment and social proximity lead to rapid, localized sharing, causing short-lived spikes in activity. Previous studies have shown that highly emotional and negative content creates brief but intense engagement spikes [9,47]. This pattern of rapid intra-cluster saturation, followed by temporary breaks before engagement spreads to other clusters, creates a cascade characterized by multiple bursts rather than sustained, uniform activity.

In contrast, low-arousal emotions are less likely to activate various clusters and spread rapidly across them. Hence, they diffuse more slowly and evenly, resulting in flatter or less pronounced engagement patterns. The emotional salience of high-arousal messages, combined with the topology of clustered networks, thus contributes to temporal irregularity in resharing behavior. Therefore, we propose:

Hypothesis 5: Social media messages containing high-arousal emotions show more bursty resharing patterns than messages containing neutral or low-arousal emotions.

Further, while we attempt to extend prior insights to the current empirical context, a contrasting theoretical approach to understanding emotional content is that theoretical frameworks (such as valence-arousal) are relatively less predictive of the virality of emotional content than models that separately examine discrete emotions [28,32]. We will discuss these issues in the implications.

Data collection

To examine the temporal dynamics and emotional composition of public responses to celebrity suicides, we identified four incidents that occurred between 2012 and 2013 and analyzed the related activity on Twitter (recently renamed X in July 2023). The analysis covered both original tweets and retweets generated in the aftermath of each event. We employed a combination of textual, temporal, and network features derived from the tweets and user activities to characterize communication patterns following the incidents. The selected celebrities, listed in Table 1, represent prominent figures from television, cinema, and sports. For ease of reference, their names are abbreviated as DC, JS, LTY, and TS. The procedure for identifying these cases and collecting the corresponding data is detailed in S1 Appendix.

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Table 1. Demographics and general characteristics of suicide events.

https://doi.org/10.1371/journal.pone.0336134.t001

The dataset comprises all posts shared on Twitter within 21 days following each suicide. This timeframe is consistent with prior research indicating that the population-level influence of celebrity suicides typically diminishes within two to three weeks [64]. The 21-day window thus provides a conservative and standardized observation period, given the daily activity counts in our data. Each entry in the dataset represents either an original tweet or a retweet, totaling approximately 1.1 million posts. In this structure, every tweet constitutes a distinct observation, and each of its retweets is recorded as an additional observation. For example, if tweet A is retweeted three times (rA1, rA2, rA3), the resulting cascade includes four posts: one original and three reshares.

Each post in the dataset includes three sets of variables: content variables (word count, dominant emotion, and words-per-sentence) which reflect the linguistic characteristics of the tweet; temporal variables (the time between the original tweet and last retweet and the time difference between subsequent retweets) pointing to the conversational features of the posts; and structural variables (follower/friend count, exposure, retweet count) exhibit how the network of users is formed around every single post on the platform. A descriptive guide table of the tweet variables is provided in S1 Appendix (S1 Table 2).

Identifying resharing cascades

Following earlier studies on online social media [1,36,79], we employ the notion of a “cascade” as the series of reshares (retweets) occurring for a single tweet. Therefore, if a tweet is retweeted n times, a cascade of size n + 1 is generated, with its lifetime being the timespan between the last retweet and the original tweet.

Following the four suicide events (DC, LTY, JS, TS), 91,868 distinct cascades were created on Twitter in the time window of 21 days after each suicide date. These were identified by tweets that were retweeted at least once. The distribution of cascade size in terms of the number of retweets is right-skewed, as expected, for online user-generated content. Sixty-seven percent of the cascades consist of one original tweet and one retweet, thus having a size of two, and only 8% involve more than five retweets. We list the summary statistics of cascade variables in Table 2. Author statistics in this table refer to the original author alone and not the retweeters in that cascade.

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Table 2. Summary statistics of cascade variables.

https://doi.org/10.1371/journal.pone.0336134.t002

When users retweet (reshare) a tweet, it becomes visible to the followers of the user who retweeted it. This sets off a chain reaction, allowing a new set of users to read and engage with the content. If a user from this second set decides to retweet, the tweet then becomes visible to their followers, and the process continues. This iterative resharing process forms a cascade graph illustrating the order and relationships among the users involved in the retweeting sequence.

However, while we have the retweet time stamp and the user ID of the retweeter, data on which specific retweet instance was read and reshared by the user is unavailable. For example, if user Y retweets a tweet from user X, and then user Z retweets the retweet from user Y (because Y viewed Z’s retweet as Z’s follower or by any other means), our data records two retweet instances, each representing a pair of the original author and the final retweeter: (X, Y) and (X, Z). Thus, our data does not include information on which intermediate actor (Y), if any, resulted in Z resharing the original tweet (that is, the contagion chain X-Y-Z). Despite this limitation, we can create a time series of retweets within each cascade by recording the temporal footprint of each node in the cascade graph (where each node represents a retweet instance). Thus, although the sequence order cannot capture the exact relationships among users, it remains a valuable approach for studying contagion dynamics. This methodology has been previously employed in research to analyze temporal sequences of human actions and communications, providing insights into group and individual behavior under various conditions, such as excitement and stress [80–82].

Emotion detection

To quantify the emotional content of a tweet, we extracted emotion scores for each cascade using the DistilRoBERTa model, a type of Bidirectional Encoder Representations from Transformers (BERT) model [34]. Specifically, we use a fine-tuned DistilRoBERTa-base checkpoint, trained on datasets such as Twitter and Reddit, to identify six basic emotions (anger, disgust, fear, joy, sadness, surprise) and neutral content [83]. The performance of this type of language model on natural language processing tasks has been reported to be on par with that of humans and is well-suited for detecting emotions in our dataset [84]. The architecture of this model is similar to BERT, which uses a deep neural network model and self-attention mechanism with compression such that the resulting model is more efficient and smaller. The model can recognize multiple emotions for each tweet and assign probability scores for each associated emotion, with the probability scores adding up to one. Each tweet was then characterized by a dominant emotion identified through the highest probability score. For example, a message identified as having an anger score of 30% and a sadness score of 70% would then be categorized as having the dominant emotion of sadness.

Model validation was performed on a random subset of 1000 tweets from our dataset that was annotated by Prolific users for the basic emotion types (sadness, neutral, surprise, anger, joy, disgust, and fear) to ensure that the model is relatively accurate in identifying the dominant emotion. Using human annotations as ground truth, the DistilRoBERTa model achieved a weighted average for precision, recall, and F1 scores of 0.45, 0.29, and 0.35, respectively. Accuracy scores for individual emotional categories mostly outperform results obtained from weighted random guessing. Details of the validation and the results of the validation are provided in S2 Appendix.

Our analysis of the cascades’ dominant emotion indicates that 40% of cascades signal the dominant emotion of fear, followed by 33% of sadness, 11% being neutral, and the remaining 12% indicating either surprise, anger, joy, or disgust as their dominant emotion. Fig 1a displays the composition and frequency of these negative emotions in the cascades of each suicide event. Looking beyond the dominant emotional label, we also analyzed the mean probability score of each emotion within the four suicide events. Our findings on the intensity of emotions (Fig 1b) indicate that fear and sadness are generally more pronounced compared to other emotions and that the intensity of emotions also varies with regard to each event, indicating how users tend to express a different composition of emotions under different conditions. For example, the cascades in LTY and JS events exhibit more emotional content and less neutrality, which can be attributed to their popularity and the public’s general perception. Lee Thompson Young (LTY) is the youngest of these four celebrities. Therefore, the composition of his fan base and the fact that people are more affected by the death of a young person may explain why the intensity of fear and sadness is highest in the aftermath of that event [25].

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Fig 1. (a, left) Frequency and (b, right) intensity of emotions in the cascades.

https://doi.org/10.1371/journal.pone.0336134.g001

Table 3 lists the count of cascades labeled with each dominant emotion. This categorization shows that fear and sadness are the most predominant emotions in cascades, followed by surprise, anger, joy, and disgust. S1 Table 3 (S1 Appendix) shows sample tweets from each category with their emotion scores.

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Table 3. Percentage of cascades in each event labeled with each dominant emotion.

https://doi.org/10.1371/journal.pone.0336134.t003

Operationalizing propagation metrics

Cascade Size: Consistent with prior work [1], we define cascade size as the number of retweets plus one, capturing all nodes in the cascade, including the original tweet.

Cascade Lifetime: Following prior work [27,36], we compute cascade lifetime as the duration between the first and last tweet. It is important to note that while our data contains retweets up to 21 days after the event, it is unlikely that this truncated window would result in us missing any activity (i.e., retweets) related to the event. This is because social media activity around shocking events, including on Twitter, drops to negligible levels after 2–3 weeks [63]. As summarized in Table 4, cascade lifetimes in our dataset range from 0 to 28,600 minutes (roughly 20 days), with a mean of 218 minutes (3.6 hours).

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Table 4. Summary of propagation measures: structural and temporal.

https://doi.org/10.1371/journal.pone.0336134.t004

Time to Nth ReTweet: Based on existing measures [8,47], we first identify tweets that received at least five retweets (8,812 cascades) and then calculate the time taken to reach the fifth retweet; The time-to-fifth retweet ranges between 7 seconds to over 14 days, distinguishing between influential tweets that either gained traction rapidly or over an extended period.

Median Delay: We propose median delay as another measure of retransmission speed, defined as the median amount of time elapsed between each two consecutive retweets within a cascade. This measure has not been used in prior studies, but the median delay can reveal another beneficial aspect of the temporal dynamics of a cascade. A cascade with a slight median delay indicates a fast sequence of resharing, which may happen because of the social network structure in which the authors and retweeters are a part or because of the rapid influence it has on the audience who reshare (adopt) the content, or both. Either way, median delay, being less biased than the average delay, can appropriately capture the dynamics of tweet retransmission. Our measure improves upon the previous measure of time-to-Nth retweets since, by definition, we may be excluding many tweets from the analysis. The summary statistics in Table 4 show that the median delay, as defined in our data, can range from zero (usually smaller cascades that receive rapid reshares) to over a million seconds (again, small cascades that took a long time to get reshared). On average, cascades in the JS suicide event demonstrated smaller ranges of median delay, showing that content related to this event was reshared faster compared to the others.

Burstiness: In our context, this can manifest as a (temporal) sequence of retweets within each cascade, where subsets of retweets are posted rapidly within short intervals of time. Intuitively, the greater the intensity of an emotion, or if the emotions fall within a specific category of valence or arousal [31], the more likely reactions to them will be clustered in time. To assess the degree of burstiness of a cascade, we employ the coefficient of variation (CV), calculated as the ratio of the standard deviation to the mean of inter-retweet delays (σ/μ) as the most straightforward measure of irregularity [85]. A CV value exceeding one implies that events are more clustered or irregularly spaced than a random process. In contrast, a CV value below one indicates a more uniform spacing of events.

The characteristics of the retweet cascade data and the details of the outcome variables are represented in Fig 2. Table 4 presents the descriptive statistics for all the above propagation outcomes. We use these five measures to run a series of analyses, which are presented in Table 5 (Size and Log Lifetime), Table 6 (Median Delay and Time-to-fifth RT), and Table 7 (Burstiness).

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Table 5. Regression results on the lifetime and size of cascades.

https://doi.org/10.1371/journal.pone.0336134.t005

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Table 6. Regression results on the median delay and time-to-fifth RT of cascades.

https://doi.org/10.1371/journal.pone.0336134.t006

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Table 7. Regression results on the burstiness of cascades (coefficient of variation).

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Fig 2. Cascades’ temporal structure and data generation process.

https://doi.org/10.1371/journal.pone.0336134.g002

Regression model

The common model specification for all these regressions is as follows. Each regression model examines the propagation measure as the dependent variable (DV) (at the cascade level, log-transformed where necessary to account for the distribution’s skewness), as a function of several independent variables (Table 2), which include the tweet’s emotional content, linguistic features, and the original author characteristics (popularity and activity). The transformations of specific propagation measures yielded an approximately normal distribution of the variables. Since the emotion of a tweet is defined only by the dominant emotion, for each cascade, only one of the six dummy independent variables is coded as ‘1’, else ‘0’. Thus, estimation is conducted with Neutral as the base emotion (See Table 3). The controls in the model include friends count, status count, favorites count, word count, hashtags, and fixed effects for each celebrity (Eq 1).

(Eq 1)

Since each observation represents a distinct cascade resulting from a specific tweet, the coefficient estimates from the above regression will indicate how the emotional content within each tweet (the independent variables) is correlated with the various propagation metrics (the dependent variable). The results will thus indicate the role of various emotions contained within tweets in triggering resharing in distinct ways, depending on which metric(s) it strongly correlates with.

Cascade size

The average cascade size is 5.36 (SD = 40.2), indicating substantial variation in diffusion patterns. To address the over-dispersed nature of the count data, we employed a negative binomial regression model [86] and, for comparison, fitted a Poisson model to the independent variables. As cascades expand and reach wider audiences, the likelihood of additional reshares increases, suggesting that the dynamics of large cascades differ meaningfully from those of small ones. Accordingly, we analyzed two subsets of data: (1) the full sample of 91,868 cascades, where a single retweet corresponds to a cascade size of 2 (including the original tweet), and (2) cascades with three or more posts (size ≥ 3), totaling 30,637 observations. The regression results for cascade size across these subsets are reported in Table 5. We acknowledge that sampling on the dependent variable may limit generalizability. The size threshold was set to improve construct validity by focusing on cascades that show meaningful network diffusion beyond isolated or incidental reshares. This approach helps reduce noise from the large number of trivial cascades that dominate the distribution.

Emotions demonstrate a variety of effects on cascade size (Table 5, Models 2 & 4). Prior studies have typically examined emotions as just positive and negative, but we note that there are nuances amongst negative emotions. Except for surprise and disgust, the emotions of fear, sadness, anger, and joy reduce the size of cascades compared to the baseline of neutral emotion. Disgust has a positive effect on size in Model 4. Among the control variables, word count positively influences cascade size, and hashtags do not have any significant effect. The dummy variables for celebrity indicate significant effects on cascade size (LTY > DC > JS > TS). The popularity of original authors (# Auth. Followers) has a positive effect on size, whereas their friendliness (i.e., the number of people they follow: # Auth. Friends) decreases cascade size. The verified status of the authors on Twitter (Auth. Verified) positively influences cascade size. Finally, the activity level of the original authors, including the total number of tweets they posted in their account’s lifetime (# Auth. Tweets), is negatively related to cascade size. In contrast, the total number of tweets they liked (# Auth. Likes) increases the cascade size. Interestingly, not only emotions but also the author’s characteristics, including their follower count and activity levels, affect the virality of their content distinctly.

Cascade lifetime

The size of the cascades is intuitively correlated with their lifetime (), suggesting that content that persists longer usually receives more retweets, too. There are two overall observations about the coefficients. First, similar to cascade size, there is a significant contextual difference between the four suicide events, indicating that the celebrity in question influences the longevity of cascades. Second, with some exceptions, the coefficients for control variables are remarkably similar in size and significance across the two metrics of Cascade Size and Lifetime – but not the coefficients for the emotion categories. Emotions exhibit a diverse and nuanced set of effects. The cascades where the dominant emotion is either anger, fear, or surprise lead to a reduced lifetime compared to those containing disgust and the positive emotion of joy, which extend the cascade.

The coefficients for control variables are similar to those observed for Cascade size except for Hashtag, which is significant here (Table 5, Models 6 & 8). Thus, hashtags have a positive effect on the lifetime of the cascades, suggesting that algorithmic hashtag-based recommendations can contribute to the diffusion by extending the cascades’ lifetime [45] by maintaining the visibility of the tweets for a longer period of time. Furthermore, more prominent authors, i.e., those with a larger pool of followers (# Auth. Followers), generate cascades with longer lifetimes (Model 6, ) whereas a greater number of friends of the tweeted author is associated with a reduced lifetime (Model 6, ).

Median delay

Next, as a measure of cascade speed [82], we examined the median inter-retweet delay in the temporal sequence by which cascades were reshared. A lower median delay represents a high cadence of retweets within each cascade. Larger delays in retweeting suggest lower intensity with which the tweet corners attention from the users, a lower cadence. We drop all tweets with less than five retweets for our analysis to focus on highly contagious cascades with rich information in their resharing pattern. As before, this leaves us with 8,812 observations (cascades). The results of the analysis are presented in Table 6 (Models 1 & 2).

Our results suggest that the emotions of joy and fear make tweets get retweeted slower by increasing the median delay, as seen in the models above (Table 6, Model 2). The resulting sequence of Twitter activity would be relatively dispersed, with separate incidents of events (retweets) taking place at longer intervals of time. Meanwhile, the emotions of anger (Model 2, β = −0.139, p = 0.019, CI = 0.059), disgust (Model 2, β = −0.301, p = 0.00, CI = 0.069), and surprise (Model 2, β = −0.184, p = 0.00, CI = 0.079) increase the resharing speed, controlling for all contextual, linguistic, and network-related factors.

We also observe that the authors’ activity level positively influences the speed of future reshares. Furthermore, popular users with higher follower count create cascades with faster resharing rates (Model 2, β = −0.086, p = 0.045, CI = 0.043). As expected, this fast and long-lasting effect makes emotions and ideas viral and more potent in influencing additional users. Unlike cascade lifetime, here the effect of author friendliness (number of users they follow, # Auth. Friends) is also slightly positive towards cascade speed by decreasing the median delay (Model 2, β = −0.009, p = 0.068, CI = 0.005), which means that although they create shorter living cascades, their content can still generate slightly faster responses by the audience.

Time to 5^th Retweet (Time5RT)

Like the median delay, this measure also accounts for the speed at which cascades grow. The effects of anger and disgust remain positive and significant, but joy has a negative effect. The results (Table 6, Model 4) also show that fear, which used to be ineffective towards median delay, can increase Time5RT (Model 4, β = 0.210, p = 0.016, CI = 0.086) and thus slow the resharing speed. Furthermore, the effects of author characteristics (popularity and activity) are similar to the effects they have on median delay, except for author activity (# Auth Tweets), which does not show any significant effect on Time5RT. The nuanced difference across the coefficients for these two measures (median-delay vis-a-vis Time5RT) could be clarified by the non-uniform distribution of the temporal process through which these retweets occur, such as bursts of activity in brief time spans.

Cascade burstiness

Here, the results (Table 7, Model 2) show that the emotions of anger (Model 2, β = 0.117, p = 0.004, CI = 0.04) and disgust (Model 2, β = 0.609, p = 0.031, CI = 0.282) generate bursty and clustered temporal sequences of retweets: whereas tweets containing fear (Model 2, β = −0.226, p = 0.003, CI = 0.075), and joy (Model 2, β = −0.206, p = 0.000, CI = 0.031) generate less bursty patterns.