Some behaviors, ideas or technologies spread and become persistent in society, whereas others vanish. This paper analyzes the role of social influence in determining such distinct collective outcomes. Agents are assumed to acquire information from others through a certain sampling process that generates an influence network and use simple rules to decide whether to adopt or not depending on the observed sample. The diffusion threshold (i.e., the spreading rate above which the behavior becomes persistent in the population) and the endemic state (i.e., the fraction of adopters in the stationary state of the dynamics) are characterized as a function of the primitives of the model. The results highlight the importance of the correlation between visibility and connectivity (or degree) for diffusion purposes.
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