Graph filters are fundamental for extracting and processing signals defined over irregular domains. Most graph filters in the literature are linear, and are usually based on polynomials of the graph shift matrix. Autoregressive Moving Average (ARMA) graph filters are a generalization of polynomial filters, but are still linear. In this work, we propose a nonlinear graph filter that is an extension of the order one ARMA graph filter, to give the Median Autoregressive Graph Filter (MAF). The proposed MAF has a similar localization property to the linear counterpart, and can be implemented in a distributive manner. Though strictly nonlinear, the MAF has some linear-like properties, which will be formally proven in this work. Application of the proposed MAF to the denoising of real-world sensor network datasets will be presented. Comparisons with the linear counterpart will also be made.