  We prove combinatorially the explicit relation between genus filtrated
$s$-loop means of the Gaussian matrix model and terms of the genus expansion of
the Kontsevich--Penner matrix model (KPMM). The latter is the generating
function for volumes of discretized (open) moduli spaces
$M_{g,s}^{\mathrm{disc}}$ given by $N_{g,s}(P_1,\dots,P_s)$ for
$(P_1,\dots,P_s)\in{\mathbb Z}_+^s$. This generating function therefore enjoys
the topological recursion, and we prove that it is simultaneously the
generating function for ancestor invariants of a cohomological field theory
thus enjoying the Givental decomposition. We use another Givental-type
decomposition obtained for this model by the second authors in 1995 in terms of
special times related to the discretisation of moduli spaces thus representing
its asymptotic expansion terms (and therefore those of the Gaussian means) as
finite sums over graphs weighted by lower-order monomials in times thus giving
another proof of (quasi)polynomiality of the discrete volumes. As an
application, we find the coefficients in the first subleading order for
${\mathcal M}_{g,1}$ in two ways: using the refined Harer--Zagier recursion and
by exploiting the above Givental-type transformation. We put forward the
conjecture that the above graph expansions can be used for probing the
reduction structure of the Delgne--Mumford compactification $\overline{\mathcal
M}_{g,s}$ of moduli spaces of punctured Riemann surfaces.
