  The building blocks of a quantum theory of general relativity are expected to
be discrete structures. Loop quantum gravity is formulated using a basis of
spin networks (wave functions over oriented graphs with coloured edges), thus
realizing the aforementioned expectation. Semiclassical states should, however,
reproduce the classical smooth geometry in the appropriate limits. The question
of how to recover a continuous geometry from these discrete structures is,
therefore, relevant in this context. Following previous works by Bombelli et
al. we explore this problem from a rather general mathematical perspective
using, in particular, properties of Voronoi graphs to search for their
compatible continuous geometries. We test the previously proposed methods for
computing the curvature associated to such graphs and analyse the framework in
detail, in the light of the results obtained.
