Opinion Dynamics on Barabasi-Albert Networks with Heterogeneous Confidence Thresholds

The classical Hegselmann-Krause (HK) model, while widely used in opinion dynamics, relies on homogeneous assumptions that fail to capture real-world complexities like stubbornness and heterogeneity. This study extends the HK model by incorporating degree-based agent heterogeneity, classifying agents into high-, medium-, and low-degree groups. Six predefined strategies assign agents as open-, moderate-, or closed-minded based on their degree. Simulations on Barabasi-Albert (BA) networks reveal that higher average degrees reduce opinion clustering and increase consensus likelihood. Notably, strategy S3, in which high-degree groups are classified as moderately open-minded, medium-degree groups as open-minded, and low-degree groups as closed-minded, is the most effective in promoting opinion clustering and facilitating consensus formation. In contrast, strategy S4, where high-degree groups are considered closed-minded, medium-degree groups are open-minded, and low-degree groups are moderately open-minded, is the least effective in achieving consensus. Furthermore, larger networks tend to experience more opinion fragmentation than smaller ones. This study makes a significant contribution to understanding public opinion dynamics by demonstrating how degree-based strategies and network heterogeneity influence clustering behavior and consensus formation.