A local adaptive algorithm for emerging scale-free hierarchical networks

In this work we study a growing network model with chaotic dynamical units that evolves using a local adaptive rewiring algorithm. Using numerical simulations we show that the model allows for the emergence of hierarchical networks. First, we show that the networks that emerge with the algorithm present a wide degree distribution that can be fitted by a power law function, and thus are scale-free networks. Using the LaNet-vi visualization tool we present a graphical representation that reveals a central core formed only by hubs, and also show the presence of a preferential attachment mechanism. In order to present a quantitative analysis of the hierarchical structure we analyze the clustering coefficient. In particular, we show that as the network grows the clustering becomes independent of system size, and also presents a power law decay as a function of the degree. Finally, we compare our results with a similar version of the model that has continuous non-linear phase oscillators as dynamical units. The results show that local interactions play a fundamental role in the emergence of hierarchical networks.