Centrality measures

Centrality measures quantify how important, influential, or well-positioned a node is within a network, such as a person in a social graph, a page in a hyperlink graph, or a server in a network topology. They are a core building block of graph analytics, used whenever the question is which nodes matter most, rather than what the network looks like as a whole.

Several distinct measures answer different versions of that question: degree centrality counts a node's direct connections; betweenness centrality counts how often a node sits on the shortest path between other pairs of nodes, marking bridges and bottlenecks; closeness centrality measures how few hops separate a node from everyone else; and eigenvector-based measures, of which PageRank is the best known, weight a connection more if it comes from another well-connected node. No single measure is universally correct — they capture different notions of importance and can rank the same network very differently.

Centrality measures matter for identifying key influencers, critical infrastructure, or fraud rings, and they underpin community detection and link prediction work built on the same graph. A common pitfall is choosing degree centrality by default because it is simplest, when betweenness or eigenvector centrality often better answers the actual business question about influence or structural importance.