The dynamics of higher-order contagion on structurally diverse networks

Modern individuals typically participate in multiple distinct social groups, characterizing the structural diversity of their social environment. Empirical observations suggest that individuals are more likely to adopt new ideas when these ideas are validated by multiple distinct groups. Our work shifts the focus from traditional, individual-based higher-order interactions to a novel group-based mechanism, which is determined by the structure of the entire group surrounding a node. We define the structural diversity coefficient based on the number of connected components in the node’s neighborhood, and propose a novel social contagion model that incorporates higher-order effect based on structural diversity. We develop both homogeneous mean-field method and dynamic message passing approach to analyze key dynamical properties and extensive numerical simulations validate the accuracy of the theoretical analyses. The results demonstrate that the introduction of group-based higher-order effect converts the system’s phase transition from continuous to discontinuous. Strengthening higher-order effect leaves the forward threshold unchanged while lowering the backward threshold. Moreover, when only higher-order effect is present, the system exhibits bistability and first-order transition with respect to the higher-order interaction strength, whereas the system exhibits no forward threshold. Our work generalizes the concept of higher-order networks to propose a unified framework for understanding group-based higher-order structures and their associated dynamics.