A simple model of global cascades in signed networks

Negative relationships play a crucial role in the diffusion of information across social networks. To explore this phenomenon, we introduce a threshold model for information cascades in signed networks, which includes a weighted parameter α∈(−∞,1] to represent the impact of negative links, causing decay or negative influence. Using rigorous mean-field analysis, we identify the conditions that enable global cascades. Interestingly, we find that negative α results in the same cascade conditions as α=0. Furthermore, with negative α, the relationship between average degree and cascade size forms a bell-shaped curve, leading to second-order phase transitions at both low and high average degrees. These findings are consistent across random networks with Poisson and scale-free degree distributions. Overall, this research provides a theoretical framework for understanding the effects of negative connections on information diffusion in social networks, offering important insights into cascade dynamics and practical strategies for managing information dissemination in real-world contexts.