The electron localization function (ELF) has been separated in its sigma and pi components. The topological analysis of the new ELFσ and ELFπ functions has been used to quantify the concept of resonance. The highest bifurcation values of these functions describe in a correct way the aromaticity of classical ring molecules and some new aromatic compounds as B6CO6, Al42−, and N5−. In the case of Al42−, an important σ delocalization contribution has been found, which is in agreement with previous interpretation.