How close to optimal are small world properties of human brain networks

A number of studies have reported small-world properties in human brain networks. Recently Barmpoutis et al. [2] have shown that there exist networks with optimal small-world structure, in the sense that they optimize all small-world attributes compared to other networks of given order and size. We wished to evaluate how close human brain network properties are compared to the properties of optimal small-world networks. We have constructed weighted functional human brain networks based on functional magnetic resonance imaging (fMRI) data and MNI anatomical parcellation of brain. These weighted networks were further thresholded in order to obtain a set of simple undirected graphs. In the obtained graphs we computed small-world characteristics and compared them to the characteristics of comparable optimal small-world networks.