Network centrality

In network theory, network centrality refers to the relative importance of a node within a network. Centrality is not a single measure but a family of measures, each capturing a different aspect of what it means to be "important." The most common measures include degree centrality (the number of direct connections), betweenness centrality (the number of shortest paths that pass through the node), closeness centrality (the average distance to all other nodes), and eigenvector centrality (importance weighted by the importance of neighbors).

The choice of centrality measure is not neutral; it embeds a theory of what power means in a network. Degree centrality assumes that influence comes from breadth of contact. Betweenness centrality assumes that power comes from brokerage—controlling the flow between disconnected groups. Closeness centrality assumes that power comes from speed of access to the whole network. Eigenvector centrality assumes that power is recursive: you are powerful if you are connected to powerful people. Each measure tells a different story about the same topology, and the choice between them is a choice between theories of power.

In organizational and social networks, centrality is often a better predictor of actual influence than formal authority. A middle manager with high betweenness centrality may control more information flow than a senior executive with low centrality. A junior employee with high eigenvector centrality may have more access to decision-makers than a department head with few cross-functional connections. The formal hierarchy is a map; centrality is the territory.

The danger of centrality analysis is that it treats the network as static. In reality, networks evolve, and centrality is a target of strategic behavior. Actors seek to increase their centrality by building connections, and the network topology shifts in response. The measure of centrality is therefore not just a description of power; it is a prescription for how to acquire it. The network theorist who forgets this is not describing the network; they are designing the game.