  We consider the correction $\Delta\sigma_\mathrm{ee}$ due to
electron-electron interaction to the conductivity of a weakly disordered metal
(Al'tshuler-Aronov correction). The correction is related to the spectral
determinant of the Laplace operator. The case of a large square metallic
network is considered. The variation of $\Delta\sigma_\mathrm{ee}(L_T)$ as a
function of the thermal length $L_T$ is found very similar to the variation of
the weak localization $\Delta\sigma_\mathrm{WL}(L_\phi)$ as a function of the
phase coherence length. Our result for $\Delta\sigma_\mathrm{ee}$ interpolates
between the known 1d and 2d results, but the interaction parameter entering the
expression of $\Delta\sigma_\mathrm{ee}$ keeps a 1d behaviour. Quite
surprisingly, the result is very close to the 2d logarithmic behaviour already
for $L_T\sim{a}/2$, where $a$ is the lattice parameter.
