Figure 1. Rich club detection and node/edge classification.

(A) Example networks, each composed of 48 nodes and 123 undirected edges, and displayed using a spring-embedding layout algorithm. Both networks contain a set of high-degree nodes (red). In the network at the top, these nodes are interconnected with a density (rich-club coefficient) of 0.711. The network below was derived by randomizing the original network, preserving all node degrees. High-degree nodes are again shown in red, and their connection density is 0.578. Comparison of the network at the top to a population of 10,000 randomized networks indicates the presence of a rich club, with p = 0.0004. Note that due to constraints imposed by the degree sequence high-degree nodes in the randomized network remain linked with an edge density that exceeds that of the network as a whole. (B) Identification of rich club nodes allows the classification of edges into rich club, feeder and local edges.