Social contagion on hypergraphs with role-differentiated higher-order interactions

Existing research on complex social contagion frequently neglects the role differentiation inherent in higher-order structures. To address this gap, we introduce a hypergraph-based contagion model that explicitly distinguishes between leader and follower roles within hyperedges (groups). The model incorporates key parameters: activation threshold, follower influence weight, and symmetric and asymmetric group sizes. We derive a self-consistency equation characterizing the cascade size and identify the critical seed sizes associated with first-order phase transitions. Our results demonstrate that increasing follower influence enhances contagion dynamics through peer reinforcement, facilitating large-scale cascades initiated by smaller initial seeds. Crucially, configurations involving smaller symmetric leader-follower group sizes reduce the critical seed size. Furthermore, distributions of leader and follower group sizes following Poisson distributions generally lower the critical seed size compared to fixed-size configurations, attributable to increased structural heterogeneity. These findings provide a basic understanding of threshold-driven contagion in role-differentiated, higher-order systems and provide an analytical framework for modeling diffusion processes in domains such as education, marketing, and political mobilization.