Adaptive rewiring in chaotic networks renders small-world connectivity with consistent clusters

Coupled map networks evolve from sparsely connected random graphs to small-world networks according to a simple adaptive rewiring algorithm. This evolution is known to occur for networks of a constant number of units and connections, and system parameters, including uniform connection strength, if the maps are chaotic. The present study investigates the consistency of the generated structures. Evolution to small-world networks is shown to occur over a wide range of network sizes above a certain threshold. The distribution of the connections reveals hierarchical structures for larger networks. In spite of high variability in the number of connections of each unit, for a given network size the number of clusters evolving shows a remarkable uniformity