In this paper, we propose an original framework for three dimensional face representation and matching for identification purposes. Basic traits of a face are encoded by extracting curves of salient ridges and ravines from the surface of a dense mesh. A compact graph representation is then extracted from these curves through an original modeling technique capable to quantitatively measure spatial relationships between curves in a three dimensional space. In this way, face recognition is obtained by matching 3D graph representations of faces. Experimental results on a 3D face database show that the proposed solution attains high recognition accuracy and is quite robust to facial expression and pose changes.