Analysis of Opinion Evolution Based on Hegselmann–Krause Model with Historical Opinion

In realistic social networks, individuals are influenced not only by current interactions, but also by recent historical opinions, prior experience, and external guidance. However, historical dependence and its decaying effect remain insufficiently studied in bounded-confidence opinion dynamics. To address this issue, this paper proposes an extended Hegselmann–Krause (HK) model in which each individual updates its opinion according to four information sources: the current opinion, historical opinions, neighbors’ opinions, and a target opinion. The historical-opinion term is modeled as a weighted average of recent historical opinions, and its influence is regulated by an attenuation rate to capture memory decay over time. Simulation experiments are conducted to examine the effects of confidence thresholds, attenuation rates, weighting coefficients, and network topology on opinion evolution. The results show that low confidence thresholds tend to generate fragmented clusters, moderate thresholds facilitate opinion integration, and excessively high thresholds may lead to rapid homogenization. The attenuation rate regulates the balance between historical dependence and adaptability to new information, while different weighting configurations produce distinct evolution patterns. In addition, comparisons across ER random, WS small-world, and BA scale-free networks show that network topology significantly affects convergence speed and final opinion distributions. Finally, simulations on a real-world review-network topology derived from the Epinions dataset illustrate the applicability of the proposed model in an e-commerce-related setting. These findings extend the HK framework from a memory-aware perspective.