Online social media platforms enable influencers to distribute content and quickly capture audience reactions, significantly shaping their promotional strategies and advertising agreements. Understanding how sentiment dynamics and emotional contagion unfold among followers is vital for influencers and marketers, as these processes shape engagement, brand perception, and purchasing behavior. While sentiment analysis tools effectively track sentiment fluctuations, dynamical models explaining their evolution remain limited, often neglecting network structures and interactions both among blogs and between their topic-focused follower groups. In this study, we tracked influential tech-focused Weibo bloggers over six months, quantifying follower sentiment from text-mined feedback. By treating each blogger's audience as a single "macro-agent", we find that sentiment trajectories follow the principle of iterative averaging -- a foundational mechanism in many dynamical models of opinion formation, a theoretical framework at the intersection of social network analysis and dynamical systems theory. The sentiment evolution aligns closely with opinion-dynamics models, particularly modified versions of the classical French-DeGroot model that incorporate delayed perception and distinguish between expressed and private opinions. The inferred influence structures reveal interdependencies among blogs that may arise from homophily, whereby emotionally similar users subscribe to the same blogs and collectively shape the shared sentiment expressed within these communities.

Financial anomalies exhibit heterogeneous mechanisms (price shocks, liquidity freezes, contagion cascades, regime shifts), but existing detectors treat all anomalies uniformly, producing scalar scores without revealing which mechanism is failing, where risks concentrate, or how to intervene. This opacity prevents targeted regulatory responses. Three unsolved challenges persist: (1) static graph structures cannot adapt when market correlations shift during regime changes; (2) uniform detection mechanisms miss type-specific signatures across multiple temporal scales while failing to integrate individual behaviors with network contagion; (3) black-box outputs provide no actionable guidance on anomaly mechanisms or their temporal evolution. We address these via adaptive graph learning with specialized expert networks that provide built-in interpretability. Our framework captures multi-scale temporal dependencies through BiLSTM with self-attention, fuses temporal and spatial information via cross-modal attention, learns dynamic graphs through neural multi-source interpolation, adaptively balances learned dynamics with structural priors via stress-modulated fusion, routes anomalies to four mechanism-specific experts, and produces dual-level interpretable attributions. Critically, interpretability is embedded architecturally rather than applied post-hoc. On 100 US equities (2017-2024), we achieve 92.3% detection of 13 major events with 3.8-day lead time, outperforming best baseline by 30.8pp. Silicon Valley Bank case study demonstrates anomaly evolution tracking: Price-Shock expert weight rose to 0.39 (33% above baseline 0.29) during closure, peaking at 0.48 (66% above baseline) one week later, revealing automatic temporal mechanism identification without labeled supervision.

Small and Medium-sized Enterprises (SMEs) are known to play a vital role in economic growth, employment, and innovation. However, they tend to face significant challenges in accessing credit due to limited financial histories, collateral constraints, and exposure to macroeconomic shocks. These challenges make an accurate credit risk assessment by lenders crucial, particularly since SMEs frequently operate within interconnected firm networks through which default risk can propagate. This paper presents and tests a novel approach for modelling the risk of SME credit, using a unique large data set of SME loans provided by a prominent financial institution. Specifically, our approach employs Graph Neural Networks to predict SME default using multilayer network data derived from common ownership and financial transactions between firms. We show that combining this information with traditional structured data not only improves application scoring performance, but also explicitly models contagion risk between companies. Further analysis shows how the directionality and intensity of these connections influence financial risk contagion, offering a deeper understanding of the underlying processes. Our findings highlight the predictive power of network data, as well as the role of supply chain networks in exposing SMEs to correlated default risk.

An enduring challenge in contagion theory is that the pathways contagions follow through social networks exhibit emergent complexities that are difficult to predict using network structure. Here, we address this challenge by developing a causal modeling framework that (i) simulates the possible network pathways that emerge as contagions spread and (ii) identifies which edges and nodes are most impactful on diffusion across these possible pathways. This yields a surprising discovery. If people require exposure to multiple peers to adopt a contagion (a.k.a., 'complex contagions'), the pathways that emerge often only work in one direction. In fact, the more complex a contagion is, the more asymmetric its paths become. This emergent directedness problematizes canonical theories of how networks mediate contagion. Weak ties spanning network regions - widely thought to facilitate mutual influence and integration - prove to privilege the spread contagions from one community to the other. Emergent directedness also disproportionately channels complex contagions from the network periphery to the core, inverting standard centrality models. We demonstrate two practical applications. We show that emergent directedness accounts for unexplained nonlinearity in the effects of tie strength in a recent study of job diffusion over LinkedIn. Lastly, we show that network evolution is biased toward growing directed paths, but that cultural factors (e.g., triadic closure) can curtail this bias, with strategic implications for network building and behavioral interventions.

We present AgentZero++, an agent-based model that integrates cognitive, emotional, and social mechanisms to simulate decentralized collective violence in spatially distributed systems. Building on Epstein's Agent\_Zero framework, we extend the original model with eight behavioral enhancements: age-based impulse control; memory-based risk estimation; affect-cognition coupling; endogenous destructive radius; fight-or-flight dynamics; affective homophily; retaliatory damage; and multi-agent coordination. These additions allow agents to adapt based on internal states, previous experiences, and social feedback, producing emergent dynamics such as protest asymmetries, escalation cycles, and localized retaliation. Implemented in Python using the Mesa ABM framework, AgentZero++ enables modular experimentation and visualization of how micro-level cognitive heterogeneity shapes macro-level conflict patterns. Our results highlight how small variations in memory, reactivity, and affective alignment can amplify or dampen unrest through feedback loops. By explicitly modeling emotional thresholds, identity-driven behavior, and adaptive networks, this work contributes a flexible and extensible platform for analyzing affective contagion and psychologically grounded collective action.

The paper studies transition phenomena in information cascades observed along a diffusion process over some graph. We introduce the Laplace Hazard matrix and show that its spectral radius fully characterizes the dynamics of the contagion both in terms of influence and of explosion time. Using this concept, we prove tight non-asymptotic bounds for the influence of a set of nodes, and we also provide an in-depth analysis of the critical time after which the contagion becomes super-critical. Our contributions include formal definitions and tight lower bounds of critical explosion time. We illustrate the relevance of our theoretical results through several examples of information cascades used in epidemiology and viral marketing models. Finally, we provide a series of numerical experiments for various types of networks which confirm the tightness of the theoretical bounds.

The ability of humans to detect and respond to others' emotions is fundamental to understanding social behavior. Here, agents are instantiated with emotion classifiers of varying accuracy to study the impact of perceptual accuracy on emergent emotional and spatial behavior. Agents are visually represented with face photos from the KDEF database and endowed with one of three classifiers trained on the JAFFE (poor), CK+ (medium), or KDEF (high) datasets. Agents communicate locally on a 2D toroidal lattice, perceiving neighbors' emotional state based on their classifier and responding with movement toward perceived positive emotions and away from perceived negative emotions. Note that the agents respond to perceived, instead of ground-truth, emotions, introducing systematic misperception and frustration. A battery of experiments is carried out on homogeneous and heterogeneous populations and scenarios with repeated emotional shocks. Results show that low-accuracy classifiers on the part of the agent reliably result in diminished trust, emotional disintegration into sadness, and disordered social organization. By contrast, the agent that develops high accuracy develops hardy emotional clusters and resilience to emotional disruptions. Even in emotionally neutral scenarios, misperception is enough to generate segregation and disintegration of cohesion. These findings underscore the fact that biases or imprecision in emotion recognition may significantly warp social processes and disrupt emotional integration.

A common assumption in the literature on information diffusion is that populations are homogeneous regarding individuals' information acquisition and propagation process: Individuals update their informed and actively communicating state either through imitation (simple contagion) or peer influence (complex contagion). Here, we study the impact of the mixing and placement of individuals with different update processes on how information cascades in social networks. We consider Simple Spreaders, which take information from a random neighbor and communicate it, and Threshold-based Spreaders, which require a threshold number of active neighbors to change their state to active communication. Even though, in a population made exclusively of Simple Spreaders, information reaches all elements of any (connected) network, we show that, when Simple and Threshold-based Spreaders coexist and occupy random positions in a social network, the number of Simple Spreaders systematically amplifies the cascades only in degree heterogeneous networks (exponential and scale-free). In random and modular structures, this cascading effect originated by Simple Spreaders only exists above a critical mass of these individuals. In contrast, when Threshold-based Spreaders are assorted preferentially in the nodes with a higher degree, the cascading effect of Simple Spreaders vanishes, and the spread of information is drastically impaired. Overall, the study highlights the significance of the strategic placement of different roles in networked structures, with Simple Spreaders driving widespread cascades in heterogeneous networks and Threshold-based Spreaders playing a critical regulatory role in information spread with a tunable effect based on the threshold value. These effects have consequences to our understanding of social phenomena, such as the spread of innovations in heterogeneous social systems with the presence of eager (Simple Spreaders) versus averse (Threshold-based Spreaders) adopters, but also to information warfare on social media where Simple Spreaders can be seen as embedded agents (e.g., bots) used to amplify the virality of ill-intended content and, oppositely, Threshold-based Spreaders as an essential self-regulatory element of social systems operating as information filters.

We introduce a mathematical model that combines the concepts of complex contagion with payoff-biased imitation, to describe how social behaviors spread through a population. Traditional models of social learning by imitation are based on simple contagion -- where an individual may imitate a more successful neighbor following a single interaction. Our framework generalizes this process to incorporate complex contagion, which requires multiple exposures before an individual considers adopting a different behavior. We formulate this as a discrete time and state stochastic process in a finite population, and we derive its continuum limit as an ordinary differential equation that generalizes the replicator equation, the most widely used dynamical model in evolutionary game theory. When applied to linear frequency-dependent games, our social learning with complex contagion produces qualitatively different outcomes than traditional imitation dynamics: it can shift the Prisoner's Dilemma from a unique all-defector equilibrium to either a stable mixture of cooperators and defectors in the population, or a bistable system; it changes the Snowdrift game from a single to a bistable equilibrium; and it can alter the Coordination game from bistability at the boundaries to two internal equilibria. The long-term outcome depends on the balance between the complexity of the contagion process and the strength of selection that biases imitation towards more successful types. Our analysis intercalates the fields of evolutionary game theory with complex contagions, and it provides a synthetic framework that describes more realistic forms of behavioral change in social systems.

Network scientists often use complex dynamic processes to describe network contagions, but tools for fitting contagion models typically assume simple dynamics. Here, we address this gap by developing a nonparametric method to reconstruct a network and dynamics from a series of node states, using a model that breaks the dichotomy between simple pairwise and complex neighborhood-based contagions. We then show that a network is more easily reconstructed when observed through the lens of complex contagions if it is dense or the dynamic saturates, and that simple contagions are better otherwise.