(all neighbors are connected). In functional terms, graphs with larger clustering coefficients support rapid local sharing of information (between neighboring nodes). Therefore, we define the local efficiency of a network as the average value of the clustering coefficients for each individual node (Latora & Marchiori, 2003; Achard & Bullmore, 2007). While such regular, highly clustered networks have high local efficiency, information must pass through a large number of short-range connections to reach nodes on the opposite side of the network, so that the average minimum path length between any two nodes will be large, and thus the global efficiency of information transfer (the average rate at which messages travel between any two randomly selected nodes) will be low. Now consider the other extreme, in which all connections are random (Figure 1A – right). In such random networks, the distance between any two nodes is likely to be small, resulting in a low minimum path length and high efficiency of global information transfer. However, local clustering (and thereby local efficiency) is also low, with the result that the potential for modular information processing is limited. In between these extremes are networks with predominantly locally structured connections, but also with a few
