An extended Hegselmann-Krause model incorporating agent heterogeneity and influence propagation.

Traditional models of opinion dynamics provide a simplified framework for understanding human behavior in basic social scenarios. However, with the rise of complex communication patterns and heterogeneous social interactions in modern networks, more comprehensive and nuanced models are required. This paper proposes an extended opinion dynamics model that integrates individual heterogeneity, homophily-based influence weights, and multi-layer influence propagation mechanisms. First, we modify the classical Hegselmann-Krause (HK) model by introducing a selective influence neighborhood based on individuals' social network connections, thereby capturing the structure-dependent nature of interpersonal interactions. Second, drawing on the theory of homophily, we model the influence weights between individuals according to their opinion similarity and domain-specific attributes. Third, we incorporate a k-layer influence propagation mechanism to simulate indirect social influence through extended paths in the network. Finally, simulation experiments and validation using real-world data demonstrate that the proposed model effectively captures the dynamics of opinion evolution and enhances predictive accuracy in complex social systems.