Individual skill
s4h-network-centrality
Identifies which nodes in a network have the most influence, reach, or control. Use when asked 'who are the key players', 'who should we target', 'where is the bottleneck', 'who connects everyone', 'who would we lose most if they left', or when mapping influence in an organisation, market, or social network.
skills/s4h-network-centrality/SKILL.md
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# 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.
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## 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.