Monatomic metal (e.g. silver) structures could form preferably at graphene edges. We explore their structural and electronic properties by performing density functional theory based first-principles calculations. The results show that cohesion between metal atoms, as well as electronic coupling between metal atoms and graphene edges offer remarkable structural stability of the hybrid. We find that the outstanding mechanical properties of graphene allow tunable properties of the metal monatomic structures by straining the structure. The concept is extended to metal rings and helices that form at open ends of carbon nanotubes and edges of twisted graphene ribbons. These findings demostrate the role of graphene edges as an efficient one-dimensional template for low-dimensional metal structures that are mechanotunable.