We present here some applications of the Minimum Message Length (MML) principle to spatially correlated data. Discrete valued Markov Random Fields are used to model spatial correlation. The models for spatial correlation used here are a generalisation of the model used in (Wallace 1998) [14] for unsupervised classification of spatially correlated data (such as image segmentation). We discuss how our work can be applied to that type of unsupervised classification. We now make the following three new contributions. First, the rectangular grid used in (Wallace 1998) [14] is generalised to an arbitrary graph of arbitrary edge distances. Secondly, we refine (Wallace 1998) [14] slightly by including a discarded message length term important to small data sets and to a simpler problem presented here. Finally, we show how the Minimum Message Length (MML) principle can be used to test for the presence of spatial correlation and how it can be used to choose between models of varying complexity to infer details of the nature of the spatial correlation.