  Central depression of nucleonic density, i.e., a reduction of density in the
nuclear interior, has been attributed to many factors. E.g., bubble structures
in superheavy (SH) nuclei are believed to be due to the electrostatic
repulsion. In light nuclei, the mechanism has been discussed in terms of shell
effects associated with occupations of s-orbits. The objective of this work is
to reveal mechanisms behind the formation of central depression in nucleonic
densities in light and heavy nuclei. We introduce several measures of the
internal nucleonic density. Through the statistical analysis, we study the
information content of these measures with respect to nuclear matter
properties. We apply nuclear density functional theory with Skyrme functionals.
Using the statistical tools of linear least square regression, we inspect
correlations between various measures of central depression and model
parameters, including nuclear matter properties. We study bivariate
correlations with selected quantities as well as multiple correlations with
groups of parameters. Detailed correlation analysis is carried out for
$^{34}$Si for which a bubble structure has been reported recently, $^{48}$Ca,
and N=82, 126, and 184 isotonic chains. We show that the central depression in
medium-mass nuclei is very sensitive to shell effects, whereas for SH systems
it is firmly driven by the electrostatic repulsion. An appreciable semi-bubble
structure in proton density is predicted for $^{294}$Og, which is currently the
heaviest nucleus known experimentally. Our correlation analysis reveals that
the central density indicators in nuclei below $^{208}$Pb carry little
information on parameters of nuclear matter; they are predominantly driven by
shell structure. On the other hand, in the SH nuclei there exists a clear
relationship between the central nucleonic density and symmetry energy.
