A computational study of homophily and diffusion of common knowledge on social networks based on a model of Facebook

In this paper, we introduce homophily to a game-theoretic model of collective action (e.g., protests) on Facebook and study the effect of homophily in individuals’ willingness to participate in collective action, i.e., their thresholds, on the emergence and spread of collective action. We use three different networks (a real Facebook network, an Erdős–Rényi random graph, and a scale-free network) and conduct computational experiments to study contagion dynamics (the size and the speed of diffusion) with respect to the level of homophily. We provide a series of parametric results on the time to achieve a specified contagion spread, on the spread of contagion at different times, and the probability of cascades. We demonstrate that these behaviors are highly nonlinear and nonmonotonic in homophily. Networks with randomly assigned thresholds result in both smaller and slower diffusion compared to the networks characterized by homophily and heterophily.