Evolvability of optimal networks

It has been recently shown [Donetti et al. 2005] that the optimal topology for complex networks, in the sense of maximal synchronizability (or equivalently, minimal first passage time for random walkers, optimal information flow, etc) has a highly structured and homogeneous architecture. However, such a type of highly homogeneous networks appears rarely either in Nature or in man-made systems, where much more heterogeneous topologies are favored. Here, we explore the reason for this by studying evolutionary (and co-evolutionary) dynamical mechanisms shaping the final network structure. We shall discuss how real networks evolve, arriving at a trade-off between efficiency (not optimality) and evolutionary accessibility.

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