Summary: 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 \(M_{g, s}^{\text{disc}}\) given by \(N_{g, s}(P_1, \ldots, P_s)\) for \((P_1, \ldots, P_s) \in \mathbb{Z}_+^s\). 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 J. Ambjørn et al. [Nucl. Phys., B 404, No. 1–2, 127–172 (1995; Zbl 1043.81636); erratum ibid. 449, No. 3, 681 (1995)] in terms of special times related to the discretization 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: by 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 Deligne-Mumford compactification \(\overline{\mathcal{M}}_{g, s}\) of moduli spaces of punctured Riemann surfaces.