Diffusions of innovations on deterministic topologies

In this paper, we are interested in modeling diffusion of innovations on social networks. We focus on a scenario where innovation emerges at a small number of nodes in the society, and each individual needs certain portion of his neighbors (thresholds) to adopt the innovation before he does so. We analyze the dynamics of the diffusion process under deterministic topologies and threshold values. We show that the diffusion process depends on both the topology and threshold values through so called coherent sets. We investigate several interesting topologies, and utilize coherent set argument to determine the behavior of the process on these topologies.