Due to the great interest that biochemical sensors constructed from graphene nanostructures have raised recently, in this work we analyse in detail the electronic factors responsible for the large affinity of biomolecular units for graphene surfaces using ab initio quantum chemical tools based on density functional theory. Both finite and periodic graphene structures have been employed in our study. Whereas the former allows the analysis of the different energy components contributing to the interaction energy separately, the periodic structure provides a more realistic calculation of the total adsorption energy in an extended graphene surface and serves to validate the results obtained using the finite model. In addition, qualitative relations between interaction energy and electron polarization upon adsorption have been established using the finite model. In this work, we have analysed thermodynamically stable adsorption complexes formed by glycine, melamine, pyronin cation, porphine, tetrabenzoporphine and phthalocyanine with a 2D structure of ninety six carbons and periodic structures formed by cells of fifty and seventy two carbons. Differences in the electrostatic, Pauli repulsion, induction and dispersion energies among aromatic and non-aromatic molecules, charged and non-charged molecules and H-π and stacking interactions have been thoroughly analysed in this work.