The dependency of network function on topology is most easily appreciated by considering a now-classic series of simple abstract models introduced by Watts and Strogatz (1998). Let us imagine that each node is continually exchanging information with the nodes with which it is connected (i.e. its neighbors), and that this exchange takes place at a constant rate. Consider first a regular ring network, a circular arrangement of nodes in which each node is connected by a line or edge to each of its four nearest neighbors (Figure 1A - left). This network is highly clustered, or cliquish, in that for any given node, any pair of its neighbors is likely to be connected to one another. This notion can be quantified by the clustering coefficient of a node, which ranges from 0 (none of the neighbors are connected) to 1 (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
