In the recent density functional-based calculations, it was found that the conductivity of naphthalene molecular wires can be modulated by altering the linking position of the molecule to the electrode ͓D. Walter, D. Neuhauser, and R. Baer, Chem. Phys. 299, 139 ͑2004͔͒. A quantum interference model was proposed to interpret the observation. In this paper, we further studied the conductance of a series of conjugated molecules containing aromatic rings using density functional theory combined with nonequilibrium Green's function method. For polyacene systems with different terminal connections, the conductivity is dependent on the substitution position of anchoring groups even with similar electron transport distance. The conductance of trans-substitution can be ten times or more as large as that of the cis-substitution. However, for the biphenyl system with different intramolecular connections, adding more connections between two benzene rings does not change the junction conductance. All these results indicate that the junction conductance is strongly dependent on the particular electron transport pathway. The alternating double-single linkage is the most probable one, since others are impeded by the single bonds.