We study the electronic transport properties of biphenyl-2,2'-dithiol molecule connected to graphene electrodes through different lateral linking groups by density functional theory and non-equilibrium Green's function. It is clearly found that the different lateral linking groups in molecular devices significantly influence the current and switching ratio. The linking groups -NH2 and -CH3 decrease the switching ratio. The linking groups -BO2, -COOH and -OH enhance the switching ratio. The characteristics of the molecular switch are analyzed by transmission spectra in the different bias and the molecular projected self-consistent Hamiltonian at zero bias. Furthermore, the observed negative differential resistance effect in devices with -NH2 and -OH in the oxidation state is explained by transmission spectra. The results suggest that the reasonable different lateral linking groups in the devices may significantly influence the current and switching ratio, displaying a potential application in future molecular circuit. (C) 2018 Elsevier B.V. All rights reserved.