Quantum interference (QI) is well recognised as a significant contributing factor to the magnitude of molecular conductance values in both single-molecule and large area junctions. Numerous structure-property relationship studies have shown that para-connected oligo(phenyleneethynylene) (OPE) based molecular wires exemplify the impact of constructive quantum interference (CQI), whilst destructive quantum interference (DQI) effects are responsible for the orders of magnitude lower conductance of analogous meta-contacted OPE derivatives, despite the somewhat shorter effective tunnelling distance. Since molecular conductance is related to the value of the transmission function, evaluated at the electrode Fermi energy, T(E-F), which in turn is influenced by the presence and relative energy of (anti)resonances, it follows that the relative single-molecule conductance of para- and meta-contacted OPE-type molecules is tuned both by the anchor group and the nature of the electrode materials used in the construction of molecular junctions (gold|molecule|gold vs. gold|molecule|graphene). It is shown here that whilst amine-contacted junctions show little influence of the electrode material on molecular conductance due to the similar electrode-molecule coupling through this anchor group to both types of electrodes, the weaker coupling between thiomethyl and ethynyl anchors and the graphene substrate electrode results in a relative enhancement of the DQI effect. This work highlights an additional parameter space to explore QI effects and establishes a new working model based on the electrode materials and anchor groups in modulating QI effects beyond the chemical structure of the molecular backbone.