Effects of topology on network evolution

The ubiquity of scale-free topology in nature raises the question of whether this particular network design confers an evolutionary advantage1. A series of studies has identified key principles controlling the growth and the dynamics of scale-free networks2,3,4. Here, we use neuron-based networks of boolean components as a framework for modelling a large class of dynamical behaviours in both natural and artificial systems5,6,7. Applying a training algorithm, we characterize how networks with distinct topologies evolve towards a pre-established target function through a process of random mutations and selection8,9,10. We find that homogeneous random networks and scale-free networks exhibit drastically different evolutionary paths. Whereas homogeneous random networks accumulate neutral mutations and evolve by sparse punctuated steps11,12, scale-free networks evolve rapidly and continuously. Remarkably, this latter property is robust to variations of the degree exponent. In contrast, homogeneous random networks require a specific tuning of their connectivity to optimize their ability to evolve. These results highlight an organizing principle that governs the evolution of complex networks and that can improve the design of engineered systems.