  We reconstruct the neutrino mass matrix in flavor basis, in the case of
inverted mass hierarchy (ordering), using all available experimental data on
neutrino masses and oscillations. We analyze the dependence of the matrix
elements m_{alpha beta} on the CP violating Dirac, delta, and Majorana, rho and
sigma, phases, for different values of the absolute mass scale. We find that
the present data admit various structures of the mass matrix: (i) hierarchical
structures with a set of small (zero) elements; (ii) structures with equalities
among various groups of elements: e-row and/or mu tau-block elements, diagonal
and/or off-diagonal elements; (iii) ``democratic'' structure. We find values of
phases for which these structures are realized. The mass matrix elements can
anti-correlate with flavor: inverted partial or complete flavor alignment is
possible. For various structures of the mass matrix we identify possible
underlying symmetry. We find that the mass matrix can be reconstructed
completely only in particular cases, provided that the absolute scale of the
mass is measured. Generally, the freedom related to the Majorana phase sigma
will not be removed, thus admitting various types of mass matrix.
