Local clustering

The last structural measure presented in this chapter is a little different from the ones seen so far. Betweenness, eigenvector, and closeness centrality all characterize a node by its relation to other nodes in the network. The measure presented in this section concerns the relationships between a node's neighbors, rather than those of the node itself. It is often useful to consider whether a node's neighbors tend to be connected to each other. In a social network, this question translates to asking whether the friend of a friend is also your friend, a property known as transitivity [to mathematicians who enjoy polysyllabic words]. The result of such relationships are triangles: three nodes, all mutually connected. The tendency for such triangles to arise is called clustering. When strong clustering is present, it often suggests robustness, and redundancy...