Propagation models are essential for modeling and simulating dynamic processes such as epidemics and information diffusion. However, existing tools struggle to scale to large-scale graphs that emerge across social networks, epidemic networks and so on, due to limited algorithmic efficiency, weak scalability, and high communication overhead. We present FS_GPlib, a unified library that enables efficient, high-fidelity propagation modeling on Web-scale graphs. FS_GPlib introduces a dual-acceleration framework: it combines micro-level synchronous message-passing updates with macro-level batched Monte Carlo simulation, leveraging high-dimensional tensor operations for parallel execution. To further enhance scalability, it supports distributed simulation via a novel target-node-based graph partitioning strategy that minimizes communication overhead while maintaining load balance. Theoretically, we show that under ideal assumptions, the runtime of simulations converges approximately to a constant. Extensive experiments demonstrate up to 35,000× speedup over standard libraries such as NDlib and execution of a full Monte Carlo simulation on a Web-scale (billion-edge) graph in 11 seconds while maintaining high simulation fidelity. FS_GPlib supports 29 propagation models—including epidemic and opinion dynamics and dynamic network models—and offers a lightweight Python API compatible with mainstream data science ecosystems. By addressing the unique challenges of modeling diffusion and cascades on the Web, FS_GPlib provides a scalable, extensible, and theoretically grounded solution for large-scale propagation analysis in epidemiology, social media analysis, and online network dynamics. Code available at: https://github.com/Allen-Ciel/FS_GPlib.

Information cocooning—amplified by algorithmic filtering—poses complex challenges for emotional dynamics in online social networks. This study explores how algorithmically reinforced information cocooning shapes information diffusion and group emotional dynamics in online social networks. We propose a viewpoint-based network evolution model that simulates structural transformations driven by user preferences. To model the hidden influence of personalized comment recommendations, we introduce the hidden comment area cocoon (H-CAC)—a novel higher-order structure that captures cocooning at the comment level. This structure is integrated into an emotion spreading model, enabling the quantification of how cocooning affects collective sentiment. By defining recommendation accuracy as a tunable parameter, we systematically evaluate its impact on emotional volatility and polarization. Extensive simulations, validated with real-world data, reveal that while cocooning reduces content diversity, it can significantly enhance emotional resilience within groups. Our findings offer a new computational lens on the dual role of cocooning and provide actionable insights for designing emotionally stable, algorithmically governed social platforms.

Synchronization is essential for the stability and coordinated operation of complex networked systems. Pinning control, which selectively controls a subset of nodes, provides a scalable solution to enhance network synchronizability. However, existing strategies face key limitations. Heuristic centrality-based methods lack a direct connection to synchronization dynamics, while spectral approaches, though effective, are computationally intensive. To address these challenges, we propose a perturbation-based optimized (PBO) strategy that dynamically evaluates each node’s spectral impact on the Laplacian matrix, achieving improved synchronizability with significantly reduced computational costs (with complexity$O(kM)$). Extensive experiments demonstrate that the proposed method outperforms traditional strategies in synchronizability, convergence rate, and pinning robustness to node failures. Notably, in all the empirical networks tested and some generated networks, PBO significantly outperforms the brute-force greedy (BFG) strategy, demonstrating its ability to avoid local optima and adapt to complex connectivity patterns. Our study establishes the theoretical relationship between network synchronizability and convergence rate, offering new insights into efficient synchronization strategies for large-scale complex networks.