centrality

Centrality is a set of metrics used in network analysis to quantify the importance or influence of a node within a network. The concept is applicable across domains, including social networks, transportation, biology, and information systems, and helps identify actors or components that are pivotal for connectivity or flow. Centrality depends on the network’s structure and on how distances or connections are measured.

Common centrality measures include: degree centrality—the number of direct connections a node has (with in-degree and out-degree for directed networks); closeness centrality—the inverse of the average shortest-path distance to all other nodes; betweenness centrality—the fraction of shortest paths between all node pairs that pass through the node; eigenvector centrality—based on the idea that connections to highly connected nodes contribute more to centrality; PageRank, a related measure using a damping factor that models a random walker; Katz centrality, which attenuates the influence of distant nodes. There are other measures as well, such as HITS, which distinguishes hubs and authorities.

Interpretation and caveats: Different measures capture different notions of importance, and the choice of measure depends on the research question and network type. Centrality scores are relative and can be sensitive to network sampling, weighting, direction, and temporal changes. In practical use, centrality helps prioritize interventions, resources, or further study, but should be considered alongside other network and domain information.