The nature of chemical bonding in caged cycloalkanes CnXn, CnFn-center dot, (n = 4, 8, 20; X = H, F), and C10X16, C10F16-center dot, (X = H, F) has been investigated using topological analysis of the ELF function, electron density, and the Laplacian of electron density at density functional theory (DFT) level. The bonding analysis performed for the perfluorinated radical anion of dodecahedrane (C20F20-center dot), bestowing an additional electron, shows an unexpected local maximum of the ELF inside the carbon cage. The presence of such an attractor confirms the sigma stellation concept presented by Irikura (J. Phys. Chem. A 2008, 112, 983) and essential change of the electron localization inside the cage. The basin belongs to the rare asynaptic type, V(asyn), and its mean electron population is 0.26 (0.36e). The value of the integrated spin density, 0.13e, shows that both spin-up and spin-down electrons reside in the vicinity of the cage center. A similar attractor has been found for perfluorinated radical anion of adamantane (C10F16-center dot). However, the saturation of the basis set suggests that such an attractor may be an artifact. For both caged perfluorinated tetrahedrane and cubane (CnFn-center dot, n = 4, 8), no valence attractors are present inside the cage. Unpaired electron density is concentrated mainly on the C-C bonding basins. The results obtained in this study are complementary to those based on the molecular orbital theory presented by Irikura.