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• We study theoretically and numerically both commensurate and incommensurate AAH graphene lattices and realize the topological edge modes of SPPs and localization transition from extended to all-localized wavefunctions, respectively. • The graphene systems can enable flexible and efficient modulation for constructing AAH lattice, thus circumventing the drawbacks of limited modulation depths in all dielectric AAH waveguide systems. • The topological edge states and localization transitions for graphene SPPs may be utilized for developing plasmonics devices operating in deep subwavelength scale on fully flat and compact platforms. By using rational and irrational on-site modulation in graphene waveguide arrays, we construct both commensurate and incommensurate Aubry-André-Harper (AAH) models and achieve the topological edge states and localization transition for graphene surface plasmon polaritons (SPPs). We show that when the commensurate AAH graphene array is truncated, topological edge states emerge, which are immune to the random perturbation of modulation depth in each individual graphene sheet. While for an incommensurate AAH array, localization transition for SPPs modes have also been achieved when the modulation depth reaches a critical value. Our work points out that graphene waveguide array provides a promising platform for robust light transport and compact localization within a fully deep subwavelength scale. [ABSTRACT FROM AUTHOR]