A Multi-State Hot Topic Propagation Model Driven by Evolutionary Game and Coupling Mechanism

Hot topics in social networks play a critical role in information dissemination, commercial marketing, and policy-making. This paper investigates the dynamic evolution of cross-community propagation of hot topics and proposes an Evolutionary Game-Based Multi-State SIR Propagation Model (EBSIR), named to highlight its extension of the classical SIR framework with additional user states and evolutionary game–driven dynamics, to accurately characterize the information diffusion mechanisms across different communities and the influence of key users. Firstly, to address the complexity of measuring topic influence, we develop an influence calculation method based on Temporal Graph Neural Networks (TGNNs), which effectively captures the dynamic features of topic propagation. Considering the variability of topic lifecycles, an adaptive decay function is introduced, enabling influence to evolve synergistically with both time and network structure, thus providing a more precise representation of propagation patterns and topic attenuation. Secondly, to model the diversity of user behaviors during topic dissemination, an evolutionary game-theoretic mechanism is incorporated to drive user behavior, and a population dynamics model is employed to reveal the evolution of different user strategies. Moreover, recognizing the guiding role of core nodes in topic propagation, a node identification method combining network centrality and self-attention mechanisms is proposed to accurately identify key users who critically influence information diffusion. Finally, due to the asymmetric influence of opinion leaders on information propagation paths, the proposed EBSIR model extends the traditional SIR framework by incorporating cross-community coupling coefficients in the state transition equations, enabling more precise modeling of cross-community multi-state propagation. The experimental results based on four comparative experiments show that EBSIR consistently achieves the best performance in predicting the evolution of neutral (N) and opposing (O) user states. For example, in Topic A, the RMSE for N and O are 0.023 and 0.019, respectively. Similar improvements are observed for Topics B to D, indicating that the proposed model demonstrates superior prediction accuracy and robustness, effectively capturing the dynamic propagation patterns of hot topics and user behaviors.