For a wide range of applications of graphene suspensions, a thorough understanding of their rheological properties is crucial. We probe the microstructure of dense suspensions of micron-sized, few-layer, defect-free graphene platelets by measuring their viscoelastic properties at various concentrations up to 39 mg ml(-1). We propose a model to relate the yield strain to the mesh size of the microstructure as a function of volume fraction ϕ. From the yield stress measurements we infer the typical bond energy (≈20 kBT) and ϕ dependence of the bond number density. These results allow us to express the steady shear viscosity for Peclet number Pe < 10 in terms of the platelet dimensions, bond energy and ϕ using a relaxation ansatz.