To determine if our characteristic path length findings were robust and reliable, we computed the efficiency of functional brain networks. It has been previously reported that efficiency as a graph metric (1) is not susceptible to disconnected nodes, (2) is applicable to unweighted as well as weighted graphs, and (3) is a more meaningful measure of parallel information processing than path length [50]. Efficiency of a graph (E global−net) [100] is the inverse of the harmonic mean of the minimum path length between each pair of nodes, L ij, and was computed as,(1)To evaluate the network for its global efficiency of parallel information processing, we compared the global efficiency of the network (E global−net) with corresponding values (E global−ran) obtained and averaged across 1,000 random networks with the same number of nodes and degree distribution. A network with small-world properties is characterized by a global efficiency value that is lower than the random network: E global (E global−net/E global−ran)<1.
