In pristine graphene ribbons, disruption of the aromatic bond network results in depopulation of covalent orbitals and tends to elongate the edge, with an effective force of fe ∼ 2 eV/Å (larger for armchair edges than for zigzag edges, according to calculations). This force can have quite striking macroscopic manifestations in the case of narrow ribbons, as it favors their spontaneous twisting, resulting in the parallel edges forming a double helix, resembling DNA, with a pitch t of about 15–20 lattice parameters. Through atomistic simulations, we investigate how the torsion τ ∼ 1/λt decreases with the width of the ribbon, and observe its bifurcation: the twist of wider ribbons abruptly vanishes and instead the corrugation localizes near the edges. The length-scale (λe) of the emerging sinusoidal “frill†at the edge is fully determined by the intrinsic parameters of graphene, namely its bending stiffness D=1.5 eV and the edge force fe with λe ∼D/fe. Analysis reveals other warping configurations and suggests their sensitivity to the chemical passivation of the edges, leading to possible applications in sensors.