  Networks with a prescribed power-law scaling in the spectrum of the graph
Laplacian can be generated by evolutionary optimization. The Laplacian spectrum
encodes the dynamical behavior of many important processes. Here, the networks
are evolved to exhibit subdiffusive dynamics. Under the additional constraint
of degree-regularity, the evolved networks display an abundance of symmetric
motifs arranged into loops and long linear segments. Exploiting results from
algebraic graph theory on symmetric networks, we find the underlying backbone
structures and how they contribute to the spectrum. The resulting
coarse-grained networks provide an intuitive view of how the anomalous
diffusive properties can be realized in the evolved structures.
