A single-crystal graphene sheet includes a polycyclic aromatic molecule wherein a plurality of carbon atoms are covalently bound to each other, the single-crystal graphene sheet comprising between about 1 layer to about 300 layers; and wherein a peak ratio of a Raman D band intensity to a Raman G band intensity is equal to or less than 0.2. Also described is a method for preparing a single-crystal graphene sheet, the method includes forming a catalyst layer, which includes a single-crystal graphitizing metal catalyst sheet; disposing a carbonaceous material on the catalyst layer; and heat-treating the catalyst layer and the carbonaceous material in at least one of an inert atmosphere and a reducing atmosphere. Also described is a transparent electrode including a single-crystal graphene sheet.