Traditional models for areal data assume a hierarchical structure where one of the components is the random effects that spatially correlate the areas. The conditional autoregressive (CAR) model is the most popular distribution to jointly model the prior uncertainty about these spatial random effects. One limitation of the CAR distribution is the inability of producing high correlations between neighboring areas. We propose a robust model for areal data that alleviates this problem. We represent the map by an undirected graph where the nodes are the areas and randomly-weighted edges connect nodes that are neighbors. The model is based on a multivariate Student-t distribution, spatially structured, in which the precision matrix is indirectly built assuming a multivariate distribution for the random edges. The weights’ joint distribution is a spatial multivariate Student-t that induces another t distribution for the areas’ spatial effects which inherit its capacity to accommodate outliers and heavy-tail behavior. Most important, it can produce a higher marginal correlation between the spatial effects than the CAR model overcoming one of the main limitations to this model. We fit the proposed model to analyze real cancer maps and compared its performance with several state-of-art competitors. Our proposed model provides better fitting in almost all cases.