These properties are captured in the characteristic path length and average clustering coefficient of networks (Figure 3C). Given a network in which all nodes can reach one another, at least one shortest path exists between all nodes, and one can calculate the characteristic path length as the average shortest path on the network, measuring how easily information can travel between distant nodes. The (local) clustering coefficient of a node is the ratio of edges present between the neighbors of a node (a node with 3 edges has 3 neighbors, see Figure 3) to the number of edges possible between neighbors of a node. This coefficient takes values between 0 and 1, where low coefficients indicate that few neighbors of a node are themselves neighbors, and high coefficients indicate that a node is embedded in a richly connected local environment. Thus, random graphs are characterized by low path lengths and low clustering coefficients, whereas lattices have high path lengths and high clustering coefficients.
