This paper describes an efficient algorithm for inexact graph matching. The method is purely structural, that is to say it uses only the edge or connectivity structure of the graph and does not draw on node or edge attributes. We make two contributions. Commencing from a probability distribution for matching errors, we show how the problem of graph matching can be posed as maximum likelihood estimation using the apparatus of the EM algorithm. Our second contribution is to cast the recovery of correspondence matches between the graph-nodes in a matrix framework. This allows us to efficiently recover correspondence matches using singular value decomposition. We experiment with the method on both real-world and synthetic data. Here we demonstrate that the method offers comparable performance to more computationally demanding methods.