Fig. 3.
Basic network properties. The measures are illustrated with a simple undirected graph with 12 nodes and 23 edges. (A) Degree: the number of edges attached to a given node. The node a has a degree of 6, and the peripheral node b has the degree of 1. (B) Clustering coefficient: the extent to which nodes tend to cluster together, measuring the segregation of a network. In this example, the central node c has 6 neighbors and 15 possible connections among the 6 neighbors. These neighbors maintain 8 out of 15 possible edges. Thus, the clustering coefficient is 0.53 (8 of 15). (C) Centrality: the indicators of centrality identify the most influential nodes within a network. In a social network, it is used to identify the most influential person. In this example, node d contributes more to the centrality because all nodes on the right side pass through the node d to reach the other nodes in the left side. (D) Path length: The average of the shortest distances for all node pairs in a network. The shortest path length between the nodes f and g is three steps that pass through two intermediate nodes. (E) Modularity: one measure of the structure of networks that is designed to reflect the strength of a division of a network into modules (also called groups, clusters, or communities). In the example, the network forms two modules interconnected by the single hub node h. Reproduced with permission from Sporns O: The non-random brain: Efficiency, economy, and complex dynamics. Front Comput Neurosci 2011; 5:2.