| The functionality of many empirical networks is provided by dynamical processes based on the network structure. Evolving networks commonly change their structure due to the resulting dynamical behavior. A deeper understanding of the interplay between the network topology and the dynamical behavior should therefore provide valuable insight into the structure-function relationship of networked systems. We propose a simple evolutionary optimization scheme in which the "fitness" of a network is determined by the eigenvalue spectrum of the time evolution operator of the dynamical process. As basic example we consider the graph Laplacian, the relevant operator for many fundamental processes such as diffusion or synchronization, and show that our algorithm successfully evolves networks into states with a given desired behavior. |
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