Formalizing an RDF abstract graph model to be compatible with the RDF formal semantics has remained one of the foundational problems in the Semantic Web. In this paper, we propose a new formal graph model for RDF datasets. This model allows us to express the current model-theoretic semantics in the form of a graph. We also propose the concepts of resource path and triple path as well as an algorithm for traversing the new graph. We demonstrate the feasibility of this graph model through two implementations: one is a new graph engine called GraphKE, and the other is extended from RDF-3X to show that existing systems can also benefit from this model. In order to evaluate the empirical aspect of our graph model, we choose the shortest path algorithm and implement it in the GraphKE and the RDF-3X. Our experiments on both engines for finding the shortest paths in the YAGO2S-SP dataset give decent performance in terms of execution time. The empirical results show that our graph model with well-defined semantics can be effectively implemented.