The structure and morphology of three polymer/graphene nanocomposites have been studied using classical molecular dynamics (MD) simulations. The simulations use 10-monomer oligomeric chains of three polymers: polyethylene (PE), polystyrene (PS) and polyvinylidene fluoride (PVDF). The structure of the polymer chains at the graphene surface has been investigated and characterized by pair correlation functions (PCF), g(r), g(θ) and g(r,θ). In addition, the influence of the temperature on the graphene/polymer interactions has been analysed for each of the three polymer/graphene nanocomposite systems. The results indicate that graphene induces order in both the PE and PVDF systems by providing a nucleation site for crystallisation, steering the growth of oligomer crystals according to the orientation of the graphene sheet, whereas the PS system remains disordered in the presence of graphene. The overall results are in line with the findings in a recent quantumchemical study by some of the present authors.