Through molecular dynamics (MD) simulation, the structure and mechanical properties of matrix-free polymer nanocomposites (PNCs) constructed via polymer-grafted graphene nanosheets are studied. The dispersion of graphene sheets is characterized by the radial distribution function (RDF) between graphene sheets. We observe that a longer polymer chain length L-g leads to a relatively better dispersion state attributed to the formation of a better brick-mud structure, effectively screening the van der Waals interactions between sheets. By tuning the interaction strength epsilon(end-end) between end functional groups of grafted chains, we construct physical networks with various robustness characterized by the formation of the fractal clusters at high epsilon(end-end) values. The effects of epsilon(end-end) and L-g on the mechanical properties are examined, and the enhancement of the stress-strain behavior is observed with the increase of epsilon(end-end) and L-g. Structural evolution during deformation is quantified by calculating the orientation of the graphene sheets and their distribution, the stress decomposition, and the size of the clusters formed between end groups and their distribution. Then, we briefly study the effects of time and temperature on the self-healing behavior of these unique PNCs in the rubbery state. Lastly, the self-healing kinetics is quantitatively analyzed. In general, this work can provide some rational guidelines to design and fabricate matrix-free PNCs with both excellent mechanical and self-healing properties.