A perturbative solution to the linear influence/network autocorrelation model under network dynamics

Known by many names and arising in many settings, the forced linear diffusion model is central to the modeling of power and influence within social networks (while also serving as the mechanistic justification for the widely used spatial/network autocorrelation models). The standard equilibrium solution to the diffusion model depends on strict timescale separation between network dynamics and attribute dynamics, such that the diffusion network can be considered fixed with respect to the diffusion process. Here, we consider a relaxation of this assumption, in which the network changes only slowly relative to the diffusion dynamics. In this case, we show that one can obtain a perturbative solution to the diffusion model, which depends on knowledge of past states in only a minimal way.