Theoretical calculations (B3LYP/6-311++G**) were performed on a series of formally hypervalent compounds, showing linear three-center geometries. The bonding nature was analyzed by the electron density , r(r), and electron-localization function (ELF) topologies, including calculations of the AIM charges and NMR chemical shifts (GIAO method). In addition, a quantitative analysis was also performed of the localization and delocalization indexes, obtained from the electron-pair density in conjunction with the definition of an atom in a molecule. Furthermore, the populations and fluctuations in the ELF basins were also evaluated. The compounds studied presented linear (1-15), T-shaped (6-9) and bipyramidal structures (10-15). The topological analysis gave the overall properties of the different bonds in a highly ionic character, the bipyramidal compounds (10-15) having similar geometrical and electronic behaviour for the axial/equatorial bonds. These compounds did not present electron delocalization between the two axial fluorine atoms. Therefore, no 3c-4e bond scheme appeared in the bonding definition. The T-shaped structures presented different geometrical as well as electronic behaviour between axial/equatorial bonds with small amount of electron delocalization between axial atoms, and consequently a small contribution for the 3c-4e model. However, the geometrical parameters of the linear structures 1-5 showed larger differences compared with their parent compounds, yielding a net electron delocalization compatible with the 3c-4e bond model