Optimized concentration of reduced graphene oxide (rGO) in the lube is one of the important factors for effective lubrication of solid body contacts. At sufficiently lower concentration, the lubrication is ineffective and friction/wear is dominated by base oil. In contrast, at sufficiently higher concentration, the rGO sheets aggregates in the oil and weak interlayer sliding characteristic of graphene sheets is no more active for providing lubrication. However, at optimized concentration, friction coefficient and wear is remarkably reduced to 70% and 50%, respectively, as compared to neat oil. Traditionally, such lubrication is described by graphene/graphite particle deposited in contact surfaces that provides lower shear strength of boundary tribofilm. In the present investigation, graphene/graphite tribofilm was absent and existing traditional lubrication mechanism for the reduction of friction and wear is ruled out. It is demonstrated that effective lubrication is possible, if rGO is chemically linked with PEG molecules through hydrogen bonding and PEG intercalated graphene sheets provide sufficiently lower shear strength of freely suspended composite tribofilm under the contact pressure. The work revealed that physical deposition and adsorption of the graphene sheets in the metallic contacts is not necessary for the lubrication.