  In this paper, we investigate the Moore-Penrose inversion of a simple
connected graph. We analyze qualitative, statistical, and extreme properties of
spectral indices of signable pseudo-invertible graphs. We introduce and analyze
a wide class of signable pseudo-invertible simple connected graphs. It is a
generalization of the classical concept of positively integrally invertible
graphs due to Godsil. We present several constructions of signable
pseudo-invertible graphs. We also discuss statistical properties of various
spectral indices of the class of signable pseudo-invertible graphs.
