Adaptive rewiring in weighted networks

Human connectome studies suggest that the brain has a modular small world network structure with rich-club effect. Such structure emerges spontaneously in simple model neural networks, (e.g. coupled maps), through adaptive rewiring according to the dynamic functional connectivity. The utility of adaptive rewiring has so far exclusively been demonstrated for unweighted networks; it is anything but guaranteed to work as well for weighted networks. We investigate adaptive rewiring in weighted networks, comparing various right-skewed, symmetrical, and left-skewed fixed weight distributions. We examine how network clustering, path length, modularity, and rich club coefficients develop for weakly, intermediate and strongly coupled networks. At low coupling strength, the weight distribution, as well as episodes of functional synchrony, have a significant effect on network evolution. With increased coupling strengths, all weighted networks robustly develop architectures similar to the unweighted ones. Adaptive rewiring appears relatively ineffective in networks with (biologically implausibly) extreme right-skewed weight distributions but performed most economically in biologically plausible log-normal distributions.