Hierarchy (β) is a measure of the relationship between the clustering coefficient and number of nodes in the network. Networks with higher hierarchy values are characterized by high degree nodes, which exhibit low clustering, and vice versa. These hierarchical networks contain small densely connected clusters; these clusters combine to form large less-interconnected clusters, which combine again to form larger lesser-interconnected clusters [51]. We examined β values obtained for the functional brain networks constructed by thresholding (threshold values ranged from 0.01 to 0.99 with an increment of 0.01) the wavelet correlation matrix at scale 3 (0.01–0.05 Hz). As shown in Figure 2A, the β values for both groups, when controlled for the degree of the network, were significantly higher (−7.5<β<2.5) than β values obtained from random networks (p<0.01). Furthermore, β values in the young-adult group were significantly higher than in the child group (p<0.001, Kolmogorov-Smirnov Test). The mean β value for the two groups, obtained by thresholding the correlation matrices such that the network has on average K′ ( = 48) edges per node, which is equivalent to a network cost of 0.54, was significantly higher in young-adults than in children (p<0.01), as shown in Figure 2B.
