Extremal Dependence and Community-Structured Risk Propagation in Complex Social Information Networks

Extreme opinion propagation in social information networks often appears as a low-frequency but high-impact process, in which abnormal activity becomes synchronized across structurally related users or communities during crisis periods. Conventional correlation-based methods mainly describe average co-movement and may therefore miss dependence patterns that emerge only in the tail regime. To address this issue, this paper proposes a community-structured extremal dependence framework for social opinion propagation risk analysis. A tail pairwise dependence matrix (TPDM) is used to construct a weighted extremal dependence network, on which node-level risk scoring, community detection, and community-level intervention analyses are performed. The proposed risk score integrates degree centrality, betweenness centrality, tail exposure, and community embedding strength, while the intervention component is formulated as a minimum cut problem on the induced community graph. The framework is evaluated on a controlled synthetic social discussion network with 100 nodes. The experiment is intended as a methodological proof of concept rather than as a real-platform empirical validation. The results show that the TPDM-based network produces a structured representation with two dominant coupled communities, several peripheral singleton nodes, concentrated high-risk nodes, and one principal source–target interface in the community graph. These findings indicate that extremal dependence can provide a useful representation of candidate risk-coupling structures under the synthetic setting. However, the inferred edges should not be interpreted as causal propagation paths, and the minimum cut result should be understood as a candidate intervention interface rather than as a guarantee of complete diffusion blockage. Future work should validate the framework on real social media traces, incorporate temporal causal information, and examine robustness under multi-channel diffusion and adaptive user behavior.