Zealots and Preachers: A Heterogeneous Node–Edge Diffusion Model on Networks

Abstract

We introduce the Zealot–Preacher model, a generalized diffusion framework on networks with simultaneous heterogeneity at the node and edge levels. Standard diffusion models typically assume homogeneous susceptibility across nodes and homogeneous transmission strength across edges. We relax both assumptions by assigning to each node a latent receptiveness parameter and to each edge a latent conductiveness parameter governing influence propagation. The framework accommodates both binary contagion and continuous consensus dynamics and nests standard homogeneous diffusion as a special case. We characterize the resulting weighted consensus process and show that low-receptiveness nodes disproportionately influence long-run network outcomes. To estimate the model in large networks, we develop a hierarchical latent-variable approach in which receptiveness and conductiveness follow Beta distributions, with hyperparameters estimated by maximum likelihood and individual effects recovered through Bayesian updating. An application to U.S. interlocking director networks shows that diffusion of board gender diversity is constrained primarily by widespread node-level resistance rather than by the absence of conductive transmission channels. Female shared directors exhibit higher average conductiveness than male shared directors, suggesting gendered heterogeneity in diffusion channels.