Introduction to centrality metrics

We’ve encountered some centrality metrics in Chapter 3, where we learned about bridges and hubs. Many vertex-based centrality metrics calculate properties related to hubs—the connection of a vertex to its nearest neighbors and their nearest neighbors. Many edge-based centrality metrics calculate bridging properties, where the edges near a vertex act as connectors between different hubs.

Degree is the simplest vertex-based centrality metric, which we encountered in Chapter 5. Degree centrality is simply the number of vertices directly connected to the vertex of interest. Many Laplacian-based metrics or algorithms depend on the degree matrix within algorithm calculations. On the surface, this metric seems to capture important hub properties; a vertex with a high degree centrality will carry a lot of influence within the network (and, thus, might make a good intervention target). It also scales well to very large networks. However, one...