Graphene-based two-dimensional materials have attracted an increasing attention these last years. Among them, the system formed by molecular adsorption on, aim of modifying the conductivity of graphene and make it semiconducting, is of particular interest. We use here hierarchical first-principles simulations to investigate the energetic and electronic properties of an electron-donor, melamine, and an acceptor, NaphtaleneTetraCarboxylic DiImide (NTCDI), and the assembly of their complexes on graphene surface. In particular, the van der Waals-corrected density functional theory (DFT) method is used to compute the interaction and adsorption energies during assembly. The effect of dispersion interactions on both geometries and energies is investigated. Depending on the surface coverage and the molecular organization, there is a significant local deformation of the graphene surface. Self-assembly is driven by the competition between hydrogen bonds in the building blocks and their adsorption on the surface. The dispersion contribution accounts significantly in both intermolecular and adsorption energies. The electron transfer mechanism and density of states (DOS) calculations show the electron-donor and acceptor characters of melamine and NTCDI, respectively. Molecular adsorption affects differently the energy levels around the Fermi level differently, leading to band gap opening. These results provide information about the new materials obtained by controlling molecular assembly on graphene.