Zigzag- and armchair-edged hexagonal graphenes are sandwiched between two Au electrodes to construct molecular nanodevices, and the effects of the orderly and locally doped with B, N, and BN for such graphene nanoflakes are considered, respectively. Based on the first-principles method, the electronic transport properties of these devices are investigated systematically. Our calculated results show that the using of B and BN to dope armchair-edged hexagonal graphenes can modulate the electronic transport properties significantly. Intrinsic and doped zigzag-hexagonal graphenes presents a semiconductoring behavior, and when it is doped with N and BN, there appears a negative differential resistance (NDR) phenomenon, especially for N-doping, and a very obvious NDR can be observed in zigzag-edged hexagonal grapheme: this might be important for developing molecular switches. The underlying causes for these findings are clearly elucidated by the transmission features and the doping-induced changes in electronic properties of a hexagonal graphene.