A divacancy (DV) is one of the most abundant and most important defects in irradiated graphene, which modifies electronic and chemical properties of graphene. In this paper, we present ab initio calculations to study the dynamics and stability of DVs in graphene. Divacancies in graphene have various reconstructed structures, such as triple pentagon-triple heptagon (555-777) and pentagon-octagon-pentagon (5-8-5) patterns. A direct observation of the structural transformations between these reconstructions was recorded in transmission electron microscope images reported by Girit in ScienceSCIEAS0036-807510.1126/science.1166999 323, 1705 (2009). We clarify the atomic structures of DVs observed in the experiment and investigate the atomic processes and energetics for the observed dynamical motions in great detail. It is found that a series of Stone-Wales-type transformations are responsible for the migration and structural transformations of DVs and that a pentagon-heptagon-heptagon-pentagon (5-7-7-5) defect appearing as an intermediate structure during the dynamical process plays an important role in the transformations of DVs.