How Homophily Affects Communication in Networks

We examine how three different communication processes operating through social networks are affected by homophily – the tendency of individuals to associate with others similar to themselves. We show that homophily has no effect in settings where messages reach their destinations by shortest paths; only connection density matters. In contrast, homophily substantially slows learning based on repeated updating from neighbors ’ information and Markovian random walks such as the Google random surfer model. This is true independently of connectivity: indeed, if homophily increases, random walks and learning are slowed down even if overall link density in the network is also increased. We also derive novel results on graph spectra and convergence times both in finite-sample and asymptotic settings, and relating random networks to their resulting spectra. We illustrate the applicability of the model by comparing the theoretical conclusions to computations based on high school friendship networks from the Adolescent Health dataset.