Network: Centrality

In almost every network — social, organizational, digital, biological — a small number of nodes exert disproportionate influence. They are not necessarily the most visible or the most senior. They are the most structurally positioned. Albert-László Barabási's research on scale-free networks established that real-world networks follow power-law degree distributions: a few hubs have vastly more connections than average, while most nodes have very few. These hubs emerge through preferential attachment — new nodes connect to already-well-connected nodes — which means structural inequality in networks is self-reinforcing.

Centrality analysis unpacks what "important" means in a specific network. There are four distinct types of centrality, and they identify different kinds of importance. A node can be a hub (high degree), a broker (high betweenness), an efficient spreader (high closeness), or influential because it is connected to other influential nodes (high eigenvector). These often coincide — but when they diverge, the divergence is analytically rich.

The key implication: targeting or protecting the most central nodes has outsized effect. Removing a high-betweenness broker can fragment a network; reaching a high-eigenvector hub can cascade influence throughout it.

Your Process

Step 1: Define the Network Name the nodes (what entities?) and the edges (what relationship?). Be precise about direction — is the relationship directional (A influences B but not vice versa) or undirected (mutual connection)? Name the time horizon and state what question you are trying to answer with centrality analysis.