In view of the influence that topological defects have on the thermal and electrical properties of graphene, and given the pivotal role that such properties play in potential applications of graphene as a building block for nano-electronic components, models of graphene behavior that allow for the consideration of such defects are of the essence. In the present work, we have obtained an atomic force-constant model from the AIREBO potential (Adaptive Intermolecular Reactive Empirical Bond-Order), of Stuart et al. , that accounts for interatomic interactions up to fourth neighbors. We present explicit expressions of the potential derivatives as well as the force-constant values. We have verified that the force-constant model is invariant under the crystal symmetries and that the phonondispersion curves of the corresponding dynamic model are in good agreement with those obtained by other authors. In addition, we have verified that the thirdand fourth-neighbor interactions affect neither the displacement field in the vicinity of dislocation cores nor the corresponding formation energies predicted by the theory of discrete dislocations of Ariza and Ortiz .