Continuous growth of social polarization for scale-free networks

Understanding how local interactions generate social polarization is a central challenge in the study of collective dynamics. Prior work has established that homophily and social balance can trigger a first-order phase transition to polarization in homogeneous small-world networks. However, real-world social networks are structurally heterogeneous, featuring power-law degree distributions dominated by a few highly connected hubs. In this study, we investigate how this structural heterogeneity affects polarization dynamics by introducing the co-evolutionary opinion model on scale-free networks generated via a modified Holme-Kim model. We find that, in contrast to the discontinuous transition in small-world networks, social polarization for scale-free networks grows continuously with increasing connectivity, emerging earlier but reaching a lower magnitude. Individual-level analysis reveals that polarization is a hierarchical process concentrated among large-degree hubs, while most peripheral nodes remain weakly polarized. Counterfactual experiments demonstrate that neutralizing only the top 5% of large-degree nodes is sufficient to suppress system-wide polarization to the random baseline. Our findings reveal that network topology fundamentally alters the nature of polarization transitions and suggest that targeted interventions on influential nodes may be more effective than broad-based approaches for managing social polarization in heterogeneous societies.