  We study the importance of local structural properties in networks which have
been evolved for a power-law scaling in their Laplacian spectrum. To this end,
the degree distribution, two-point degree correlations, and degree-dependent
clustering are extracted from the evolved networks and used to construct random
networks with the prescribed distributions. In the analysis of these
reconstructed networks it turns out that the degree distribution alone is not
sufficient to generate the spectral scaling and the degree-dependent clustering
has only an indirect influence. The two-point correlations are found to be the
dominant characteristic for the power-law scaling over a broader eigenvalue
range.
