Scanning-tunneling-microscopy observations of a reversible, tip-induced transition between triangular- and star-shaped networks of partial dislocations on the basal (0001) plane of highly oriented pyrolytic graphite are reported. The transition between network geometries results from small variations (0.14 V) in the tip-to-substrate voltage bias and is attributed to shear-induced motion of partial dislocations. The shear stress required for the transition is estimated to be 5 MPa. Dislocation motion occurs over distances of tens of nanometers on the time scale of several minutes, allowing the dynamics of the transition between the two networks to be observed in real time. Atomically resolved images near a dislocation show distortions of the atomic lattice that are consistent with glide of the surface basal plane. Analysis of the separation distance between pairs of dislocations yields a surface stacking-fault energy of 2.1-4.5 mJ/m2.