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Identifies which nodes in a network have the most influence, reach, or control using degree, betweenness, closeness, and eigenvector centrality. Use for mapping influence in organizations, markets, or social networks.
npx claudepluginhub human-avatar/skills-for-humanityHow this skill is triggered — by the user, by Claude, or both
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/skills-for-humanity:s4h-network-centralityThe summary Claude sees in its skill listing — used to decide when to auto-load this skill
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 c...
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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.
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.
Framing check: Confirm the network definition and the question before continuing. State what you've identified in one sentence, then use AskUserQuestion:
Step 2: Enumerate the Nodes and Edges List all known nodes. For each pair, identify whether an edge exists and its weight or frequency if relevant. If working from description rather than data, reason from available information — who interacts with whom, who reports to whom, who collaborates, who is referenced.
Step 3: Calculate Centrality by Type
For each node, assess across four dimensions:
Before narrowing: Show the full centrality picture first. Use AskUserQuestion:
Step 4: Identify Structural Features Flag nodes with unusual profiles:
Step 5: Apply to the Question Translate structural findings into actionable answers for the original question. Different questions call for different centrality types: targeting for influence → eigenvector and degree; identifying single points of failure → betweenness; seeding information efficiently → closeness.
Before proceeding, use the AskUserQuestion tool. State your interpretation of the network and the question in 1–2 sentences, then ask:
Proceed based on their selection. If the user reframes, incorporate the correction before running any analysis.
Network Definition [Nodes, edges, direction, time horizon, question being answered]
Centrality Rankings
| Node | Degree | Betweenness | Closeness | Eigenvector | Overall Assessment |
|---|---|---|---|---|---|
Structural Features [Cut points, isolates, anomalous profiles, and what each means]
Answer to the Original Question [Direct application of centrality findings to the specific question — who to target, protect, connect, or disconnect]
Caveats [Where the analysis is limited by missing edges, assumed relationships, or a changing network structure]
Centrality analysis assumes the network is reasonably stable and that the edges you've mapped reflect real relationships. In dynamic networks — where ties form and dissolve quickly — centrality scores can be misleading snapshots. Pair with /s4h-network-contagion when the goal is to model spread, since centrality tells you who matters but not how something moves through the network. Pair with /s4h-social-power-mapping when the network is organizational and the edges are influence or authority rather than communication.
The most important structural insight is often not the top-ranked node — it is the node with surprisingly high betweenness relative to its degree. These "hidden brokers" are frequently invisible to conventional analysis because they are not the loudest, most senior, or most connected — they just happen to sit on the only path between two otherwise-disconnected parts of the network.
After delivering this output, use AskUserQuestion to offer the next move:
/s4h-network-contagion — Model how something spreads through this network, using the identified hubs and brokers as seed points or bottlenecks/s4h-network-weak-ties — Identify the structural holes in this network and the bridging connections that span them/s4h-social-power-mapping — Translate the structural centrality findings into an organizational power map