In this paper we present a unified graph model, called Attributed Relational Graph (ARG), for multi-modal face modeling and recognition. Based on the ARG model, the 2-D and 3-D data are included in a single model. The developed ARG model consists of nodes, edges, and mutual relations. The nodes of the graph correspond to the landmark points that are extracted by an improved Active Shape Model (ASM) technique. Then, at each node of the graph, the responses of a set of log-Gabor filters to the facial image texture and shape information (depth values) are calculated; the filter responses are used to model the local structure of the face at each node of the graph. The edges of the graph are defined based on Delaunay triangulation and a set of mutual relations between the sides of the triangles are defined. The mutual relations boost the final performance of the system. The results of face matching using the 2-D and 3-D attributes and the mutual relations are fused at the score level. A rank-one identification rate of 99% is achieved by experimenting on the University of Miami face database.