Breaking the symmetry of social influence in information cascades

In modern interconnected societies, social influence often exhibits asymmetry, a crucial factor governing the dynamics of information cascades. Building upon the Watts threshold model, we propose a two-layer network framework to characterize this asymmetry: influence propagates via a primary layer with weight 1−α and a complementary layer with weight α, where α∈[0,0.5]. Overlapping edges, occurring with probability η∈[0,1], carry full influence weight 1. By systematically tuning η and α, we analyze how asymmetric social interaction shapes cascade dynamics on random networks. Our analysis shows that the cascade boundary in the (η,α) plane exhibits a step-like profile, with the critical overlap ηc displaying nonmonotonic dependence on α. Moreover, increasing η drives the cascade size from continuous growth to discontinuous transitions, even under strong asymmetry (small α). These results highlight the dual role of asymmetric influence: it can either facilitate or suppress large-scale cascades depending on the interplay between structural overlap and weight distribution. Our work provides actionable insights for designing influence strategies in multi-channel communication systems.