In this work, a new polymeric structure was designed consisting of a nanometric sheet of graphene (G) and a polymethylmethacrylate (PMMA) repeat unit, which was designated as PMMA-G. Three degrees of polymerization of PMMA-G were considered: monomer (PMMA-G1), dimer (PMMA-G2), and trimer (PMMA-G3). The effect of incorporating a nanometric sheet of graphene into the molecular structure of PMMA on the modification of some of its main optical, magnetic, and electrical properties was investigated. Currently, the study presented here is of great relevance since various areas of technology require new materials with specific properties for the development of new devices. The results of our study reveal that the dielectric constant of PMMA is reduced when graphene is incorporated. However, a percentage increase of 14.48% in the refractive index of PMMA when graphene is inserted to form the nanocomposite is observed. It is found that the absolute value of molar magnetic susceptibility of PMMA increases considerably when reinforced with graphene. Finally, when reinforcing PMMA with graphene to obtain the PMMA-G nanocomposite, the electrical resistivity increases by almost an order of magnitude. We used computational tools under Materials Studio (MS) software. We built a PMMA molecule with three degrees of polymerization, graphene sheet, and polymethylmethacrylate-graphene composite (PMMA-G) was built also with three degrees of polymerization using a concentration of 50% graphene over the PMMA polymer. For each structure, we used computational code DMol3 of MS, which is based on the Density Functional Theory, and the geometry optimization process was carried out to obtain the most stable structures. Finally, using the connectivity indices method together with topological properties of the molecular structures, implemented in Synthia computational code of MS software, we calculated the dielectric constant, magnetic susceptibility, refractive index, and electrical resistivity, for pure PMMA and PMMA-G structures for their three degrees of polymerization. The results were analyzed, and the changes in these properties were discussed in terms of the effect of an electric and magnetic field on the molecular structures of PMMA-G with respect to PMMA.