  We investigate the evolution of Boolean networks subject to a selective
pressure which favors robustness against noise, as a model of evolved genetic
regulatory systems. By mapping the evolutionary process into a statistical
ensemble and minimizing its associated free energy, we find the structural
properties which emerge as the selective pressure is increased and identify a
phase transition from a random topology to a "segregated core" structure, where
a smaller and more densely connected subset of the nodes is responsible for
most of the regulation in the network. This segregated structure is very
similar qualitatively to what is found in gene regulatory networks, where only
a much smaller subset of genes --- those responsible for transcription factors
--- is responsible for global regulation. We obtain the full phase diagram of
the evolutionary process as a function of selective pressure and the average
number of inputs per node. We compare the theoretical predictions with Monte
Carlo simulations of evolved networks and with empirical data for Saccharomyces
cerevisiae and Escherichia coli.
