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We represent face images by a set of triangular labeled graphs, each containing information on the appearance and geometry of a 3-tuple of face feature points. Our method automatically learns a model set and builds a graph space for each individual. A two-stage method for fast matching is developed, where in the first stage a Maximum a Posterior solution based on PCA factorization is used to efficiently prune the search space and select very few candidate model sets, and in the second stage a nearest neighborhood classifier is used to find the closest model graphs to the query image graphs. Finally, the probe image is assigned to the trained individual with the maximum number of references. Our proposed technique achieves perfect results on the ORL face set and an accuracy rate of 97.7% on the FERET face set, which shows the superiority of the proposed technique over all considered state-of-the-art methods (Elastic Bunch Graph Matching, LDA+PCA, Bayesian Intra/Extra-personal Classifier, Boosted Haar Classifier).