We present a graph matching method that encompasses both a model of structural consistency and a model of geometrical deformations. Our method poses the graph matching problem as one of mixture modelling which is solved using the EM algorithm. The solution is then approximated as a succession of assignment problems which are solved, in a smooth way, using Softassign. Our method allows us to detect outliers in both graphs involved in the matching. Unlike the outlier rejectors such as RANSAC and Graph Transformation Matching, our method is able to refine an initial the tentative correspondence-set in a more flexible way than simply removing spurious correspondences. In the experiments, our method shows a good ratio between effectiveness and computational time compared with other methods inside and outside the graphs’ field.