Diffusion and cascading behavior in random networks

► We analyze the spread of new behaviors in social networks modeled by random graphs. ► When the network is sparse, the contagion is limited by its low global connectivity. ► When it is dense, the contagion is limited by the stability of the high-degree nodes. ► Our results explain the robust-yet-fragile nature of social networks. ► We show existence of equilibria with co-existent conventions.