Stability of small-world networks of neural populations
At large scales the brain is a complex network of anatomical structures, or neural populations, with the small-world characteristics of dense local clustering between neighboring populations and a short path length between any two populations. There have been extensive studies of the structural and dynamical advantages of small-world networks over the last decade, providing a number of possible reasons for the evolution of this small-world architecture. However, there has been little work on the stability of small-world brain networks. A network model, which is a variant of the WattsStrogatz model, is used to generate random-rewire networks (RRNs). Depending on their parameters these networks can be regular, small-world, or random. Stability of small-world networks is investigated with a physiologically based model of brain electrical activity and compared with the results for regular, random, and experimentally determined cortical networks. The stability of RRNs is independent of network size; and small-world brain networks are less likely to be stable than random networks with the same number of populations and average number of connections. For this network model our results suggest that if stability is the dominant constraint on network structure then brain networks are more likely to have random rather than small-world connectivity. Thus a specific type of network architecture may be required for brain networks to be small-world and maintain marginal stability.
stability cortical networks small world network spectra