Universality, criticality and complexity of information propagation in social media

The impact of social media on information dissemination is profound, influencing societal dynamics in unprecedented ways. Examples such as the COVID-19 infodemic and the GameStop stock surge highlight the need to understand information propagation mechanisms. The propagation of information in social media exhibits similarities to natural phenomena like neuronal firing and earthquakes, characterized by bursty activity and avalanches. Macroscopic analysis reveals power-law decay in avalanche size and duration distributions (*P*(S) ~ S⁻τ and *P*(T) ~ T⁻α), suggesting critical behavior. This is supported by the theory of absorbing phase transitions and hyperscaling relations (〈S〉 ~ Tγ). However, the values of the exponents vary widely across studies, indicating uncertainty about underlying models and the existence of universality classes. A key open question is whether simple contagion (single exposure sufficient for diffusion) or complex contagion (multiple exposures needed) better describes information spread. This paper addresses these issues by performing a large-scale analysis of hashtag time series from multiple social media platforms.

Previous research on information propagation in social media has shown qualitative similarities with other natural phenomena, characterized by bursty activity patterns and avalanches. Power-law distributions of avalanche size and duration are often reported, interpreted as evidence of criticality. However, significant variability exists in the estimated values of critical exponents (τ and α) across different studies, hindering the identification of well-defined universality classes. This variability stems from various factors such as different definitions of avalanches (hashtags, reply trees, retweet chains), temporal resolution, and data sources. The debate between simple and complex contagion models remains open. Simple contagion, where a single exposure is sufficient for diffusion, forms the basis of many theoretical models, including the mean-field branching process (BP) with τ = 3/2 and α = 2. In contrast, complex contagion models, such as the linear threshold model and the Random Field Ising Model (RFIM), require multiple exposures for activation. Existing studies provide mixed evidence for either model, highlighting the need for comprehensive analysis.

This study analyzes hashtag time series from six platforms: Twitter, Telegram, Weibo, Parler, StackOverflow, and Delicious, encompassing a total of 206,972,692 time series and 905,377,009 events collected over more than 10 years. Avalanches are defined using a percolation theory-inspired approach, with temporal resolution (Δ) determined via a principled method identifying the critical point of a one-dimensional percolation model. The authors use maximum likelihood estimation to estimate the critical exponents (τ, α, and γ) from the avalanche size and duration distributions. A novel statistical technique distinguishes between simple (BP) and complex (RFIM) contagion for individual time series by comparing their likelihood and p-values. The methodology includes fitting each time series to both the BP and RFIM models, evaluating the goodness of fit through p-values (with a threshold of p = 0.1), and selecting the best-fitting model based on log-likelihood ratios. The analysis focuses on time series with at least two avalanches larger than Smin = 10 and different sizes. Aggregate and individual-level analyses are performed to assess the prevalence of simple and complex contagion dynamics.

The study reveals that information propagation in social media displays universal statistics of avalanches well described by power-law distributions, indicating near-critical behavior at the aggregate level. The estimated critical exponents (τ, α, and γ) are consistent across different platforms and are more compatible with the Random Field Ising Model (RFIM) than the Branching Process (BP), suggesting that complex contagion plays a significant role. Approximately 20% of time series are within 5% of criticality and account for 53% of all events. Individual time series analysis shows that roughly 50% are better explained by complex contagion (RFIM), while the other 50% are better explained by simple contagion (BP). However, aggregating data from only the time series attributed to complex contagion still yields power-law scaling consistent with the RFIM universality class. In contrast, aggregating data from the BP class displays a crossover from BP to RFIM scaling, indicating a mixture of both processes. Qualitative analysis suggests that conversational topics (e.g., music, TV shows) tend towards simple contagion, while politically charged or controversial topics tend towards complex contagion. The universality observed suggests underlying critical dynamics independent of platform-specific features.

The findings challenge the common assumption that simple contagion solely drives information diffusion in social media. The prevalence of complex contagion (RFIM), particularly for politically or socially charged topics, necessitates reconsideration of predictive algorithms that rely solely on temporal characteristics of the signal. The results highlight the importance of both the semantic content of hashtags and the network structure in understanding information propagation. The universality observed across diverse platforms suggests a fundamental mechanism underlying information spread, independent of individual platform designs. This universality warrants further investigation to identify the root cause and leverage it for improved prediction models.

This research demonstrates the universality and criticality of information propagation in social media, showcasing a mixture of simple and complex contagion dynamics. The prevalence of complex contagion, particularly for controversial topics, necessitates a shift in predictive algorithms. Future research should focus on identifying the underlying mechanisms responsible for this universality and developing more accurate predictive models that incorporate both semantic content and network structure.

The study relies on hashtag time series, which may not fully capture the nuances of information spread. The selection of specific platforms might limit generalizability to other social media platforms with different characteristics. The analysis focuses on macroscopic properties and may not fully reflect the heterogeneity in individual user behavior. Furthermore, the definition of avalanches and the choice of temporal resolution can impact the results.