  We demonstrate that free graphene sheet edges can curl back on
themselves,reconstructing as nanotubes. This results in lower formation
energies than any other non-functionalised edge structure reported to date in
the literature. We determine the critical tube size and formation barrier and
compare with density functional simulations of other edge terminations
including a new reconstructed Klein edge. Simulated high resolution electron
microscopy images show why such rolled edges may be difficult to detect. Rolled
zigzag edges serve as metallic conduction channels, separated from the
neighbouring bulk graphene by a chain of insulating sp$^3$-carbon atoms, and
introduce Van Hove singularities into the graphene density of states.
