Centrality is a way of measuring how important a particular point (called a node) is within a network. It comes from graph theory and network analysis, where researchers map relationships as webs of connections, then ask: which nodes matter most? A person in a social network, a webpage on the internet, a protein in a biological pathway, or a city in a transportation grid can all be ranked by centrality. The concept is flexible because “important” means different things depending on context, so several distinct types of centrality exist, each capturing a different dimension of influence.
The Core Idea Behind Centrality
Any network can be drawn as a set of dots (nodes) connected by lines (edges). Centrality assigns a score to each node based on its position in that structure. A node with high centrality is prominent: it may have the most connections, sit on the most efficient paths, or link otherwise disconnected groups together. In social networks, centrality often reflects power, prestige, or visibility. In infrastructure networks, it can reveal bottlenecks. In biology, it highlights essential components of a system.
Because no single number captures every kind of importance, researchers developed multiple centrality measures. The four most widely used are degree centrality, closeness centrality, betweenness centrality, and eigenvector centrality. Each answers a slightly different question about what makes a node matter.
Degree Centrality: Who Has the Most Connections?
Degree centrality is the simplest measure. It counts the number of direct connections a node has. A person in a social network who knows 200 people has a higher degree centrality than someone who knows 15. The logic is straightforward: the better connected you are, the more important you are likely to be.
In directed networks, where relationships have a direction (think of Twitter followers versus people you follow), degree centrality splits into two versions. In-degree counts how many connections point toward you, while out-degree counts how many point away from you. A Twitter account with millions of followers but following only a handful of people has very high in-degree and low out-degree. To compare nodes across networks of different sizes, degree centrality is often standardized by dividing a node’s connection count by the maximum possible connections (the total number of other nodes in the network).
Closeness Centrality: Who Can Reach Everyone Fastest?
Closeness centrality measures how quickly a node can reach every other node in the network. It is calculated as the inverse of a node’s average shortest distance to all other nodes. If you are only one or two steps away from everyone else, your closeness centrality is high. If you are tucked away in a corner of the network and it takes many hops to reach most people, your score is low.
This measure is especially useful when you care about the speed of information flow. In a company’s internal communication network, for example, the person with the highest closeness centrality is the one who could spread a message to the entire organization in the fewest steps. The formula inverts the average distance so that higher scores correspond to more central positions, which makes it more intuitive to interpret.
Betweenness Centrality: Who Controls the Flow?
Betweenness centrality captures something the other measures miss: brokerage. It counts how often a node falls on the shortest path between two other nodes. A node with high betweenness acts as a bridge, connecting parts of the network that would otherwise be poorly linked or completely disconnected.
This is the measure that identifies gatekeepers and bottlenecks. Someone might have relatively few direct connections (low degree centrality) yet still score high on betweenness because they are the only link between two large groups. Sociologist Ronald Burt described these positions as “structural holes,” gaps in a network that certain individuals span. The people who fill those holes gain strategic advantages: access to novel information, control over what flows between groups, and the ability to broker resources. In practical terms, if you removed a high-betweenness node, communication between clusters in the network would slow dramatically or break down entirely.
Eigenvector Centrality: Who Knows the Right People?
Eigenvector centrality goes beyond counting connections. It weights each connection by the importance of the node on the other end. Being linked to five highly connected, influential nodes matters more than being linked to five isolated ones. The idea is intuitive: it considers not just how many people you know, but who you know.
A useful analogy is Facebook. A person with 300 friends who are mostly casual acquaintances would score lower on eigenvector centrality than someone with 300 friends who are all prominent public figures. Google’s original PageRank algorithm is a close relative of eigenvector centrality, ranking web pages higher when they receive links from other high-ranking pages. Scores are computed iteratively: each node’s centrality depends on the centrality of its neighbors, and the calculation cycles through the network until the values stabilize.
How Centrality Is Used in Practice
Disease Outbreaks and Public Health
Centrality plays a direct role in understanding how infectious diseases spread. During outbreaks, public health researchers map contact networks and use degree, betweenness, and closeness centrality to identify superspreaders, the individuals or locations through which a pathogen is most likely to travel. This was particularly relevant during COVID-19, where transmission was highly uneven and superspreader events drove much of the spread. Identifying bridging connections between communities (the links between distinct social groups or geographic regions) turned out to be critical for designing targeted interventions rather than relying on blanket restrictions.
High-centrality locations also matter. Densely populated markets and transportation hubs act as bottleneck points in transmission networks, similar to high-betweenness nodes in a social graph.
Brain Connectivity
Neuroscientists use centrality to map the brain’s wiring. Regions that function as high-centrality hubs tend to cluster in areas responsible for higher-order thinking: the medial parietal cortex, frontal regions, the basal ganglia, and the thalamus. These hubs sit at the intersection of multiple brain networks and play an integrative role, pulling together information from different systems to support complex cognition like language and abstract thought. The default-mode network and executive control networks, both involved in a wide range of cognitive tasks, contain many of these hub regions.
Mental Health and Social Networks
A person’s centrality in their social network appears to have measurable effects on well-being. Research on patients with mental health conditions found that those with higher in-degree and eigenvector centrality in an online support community experienced greater reductions in distress, better satisfaction of basic life needs, and more improvement in symptoms compared to less central members. The finding suggests that being well-connected to other well-connected people in a supportive environment is associated with better recovery outcomes, not just having connections, but having connections that themselves are embedded in the network.
Choosing the Right Centrality Measure
No single centrality metric is universally “best.” The right choice depends on what you want to know. If you care about raw popularity or activity, degree centrality is the starting point. If you want to find the most efficient spreader of information, closeness centrality is more relevant. If you need to locate the nodes whose removal would most disrupt communication, betweenness centrality is the answer. And if influence flows through chains of important contacts, eigenvector centrality captures that dynamic.
In practice, analysts often compute several centrality measures on the same network and compare them. A node that ranks high on multiple measures is almost certainly critical to the network’s function. A node that ranks high on only one, say high betweenness but low degree, reveals a more specialized and sometimes more strategically interesting role. Software tools like Gephi, NetworkX (Python), igraph (R), and UCINET make it straightforward to calculate all of these metrics, even on networks with thousands or millions of nodes.