Diffusion in small worlds with homophily and social reinforcement: A theoretical model

We introduce homophily in a percolation model of word-of-mouth diffusion in social networks by reorganizing the nodes according to similarity in preferences for adoption of an innovation. Such preferences are described by a “minimum utility requirement” for an agent to adopt. We show that homophily removes the non-linear relation between preferences and diffusion in the standard percolation model with a high diffusion regime (“hit”) and a low diffusion regime (“flop”). Instead, in a model with perfect homophily, the final diffusion scales linearly with individual preferences: all agents who are willing to adopt, do adopt the innovation. We also investigate the combined effect of homophily and social reinforcement in diffusion. Results indicate that social reinforcement renders clustered networks more efficient in terms of diffusion size for network with strong homophily, while the opposite is true for networks without homophily. The simple structure of our model allows to disentangle the effect of social influence, homophily and the network structure on diffusion. However, the controllability of the theoretical structure comes at the expenses of the realism of the model. For this, we discuss possible extensions and empirical applications.