Analysis of tipping points in social networks for diffusion of innovations

Tipping point phenomena (events that had rarely observed becomes suddenly common) for diffusion of innovations have received huge attention from academia and industry [4, 6, 12]. Understanding tipping point phenomena has numerous applications including viral marketing and minimizing the spread of contamination. Depending on the characteristics of the information and social network structures, the information either cascades globally or terminates quickly. For example, sometimes new technologies become widespread over the network (a global cascade), but in some cases they simply disappear in a short time. In this work, we identify conditions for the occurrence of tipping points for general classes of network structures and provide a novel proof for its correctness. Various models of information spreading have been studied. These models are established based on the common assumption that the neighbors play significant roles for the spread of information. The SIR (Susceptible-Infected-Recover) model is one of those popular models applied to the cases when accepting the information requires low costs, such as the epidemics of contagious diseases [1, 2, 8]. Under the SIR model, some sufficient conditions for a global cascade have been studied [2, 3, 9]. On the other hand, for the diffusion of new technologies or innovations which requires relatively high costs to adopters, the linear threshold model is widely used [7, 12, 13]. However, general conditions for a global cascade under the linear threshold model are known for restricted cases. In the linear threshold model, individuals make their decisions based on the decisions of their …