Given some number of nodes and edges, classic network models could create networks of two extremes: a regular graph in which all nodes had similar numbers of edges and connected with their nearest neighbors in a lattice-like structure, and a random graph, in which nodes had similar numbers of edges, but edges were distributed randomly throughout the graph. In a lattice, few edges were needed to communicate between nearby nodes, but many edges would be crossed to communicate with distant portions of the network. In a random graph, information could reach distant nodes using a small number of edges, but reaching nearby nodes required many more edges than on a regular lattice. Thus, regular graphs were locally efficient but globally inefficient, and random graphs were efficient for global but not local interactions.
