  We study metanetworks arising in genotype and phenotype spaces, in the
context of a model population of Boolean graphs evolved under selection for
short dynamical attractors. We define the adjacency matrix of a graph as its
genotype, which gets mutated in the course of evolution, while its phenotype is
its set of dynamical attractors. Metanetworks in the genotype and phenotype
spaces are formed, respectively, by genetic proximity and by phenotypic
similarity, the latter weighted by the sizes of the basins of attraction of the
shared attractors. We find that populations of evolved networks form giant
clusters in genotype space, have Poissonian degree distributions but exhibit
hierarchically organized $\kappa$-core decompositions. Nevertheless, at large
scales, they form tree-like expander graphs. Random populations of Boolean
graphs are typically so far removed from each other genetically that they
cannot form a metanetwork. In phenotype space, the metanetworks of evolved
populations are super robust both under the elimination of weak connections and
random removal of nodes.
