We consider graphs parameterized on a portion X⊂Zd×{1,...,M}k of a cylindrical subset of the lattice Zd×Zk, and perform a discrete-to-continuum dimension-reduction process for energies defined on X of quadratic type. Our only assumptions are that X be connected as a graph and periodic in the first d-directions. We show that, upon scaling of the domain and of the energies by a small parameter ɛ, the scaled energies converge to a d-dimensional limit energy. The main technical points are a dimension-reducing coarse-graining process and a discrete version of the p-connectedness approach by Zhikov.
