Network-science related applications frequently deal with inference of spatio-temporal processes. Such inference tasks can be aided by a graph whose topology contributes to the underlying spatio-temporal dependencies. Contemporary approaches extrapolate dynamic processes relying on a fixed dynamical model, that is not adaptive to changes in the dynamics. Alleviating this limitation, the present work adopts a candidate set of graph-adaptive dynamical models with one active at any given time. Given partially observed nodal samples, a scalable Bayesian tracker is leveraged to infer the graph processes and learn the active dynamical model simultaneously in a data-driven fashion. The resulting algorithm is termed graph-adaptive interacting multiple dynamical models (Grad-IMDM). Numerical tests with synthetic and real data corroborate that the proposed Grad-IMDM is capable of tracking the graph processes and adapting to the dynamical model that best fits the data.