Centrality Analysis — Degree, Betweenness, Eigenvector
Also known as: Merkeziyet Analizi (Degree, Betweenness, Eigenvector), node centrality, centrality measures, graph centrality
Centrality analysis is a family of network-analytic measures, formalized by Freeman (1979), that quantifies the structural importance of individual nodes within a graph. Each centrality index captures a distinct mechanism of influence: degree centrality reflects direct connectivity, betweenness centrality identifies nodes that broker information flow, closeness centrality captures proximity to all others, and eigenvector centrality (along with PageRank) rewards connection to highly connected neighbors.
Key highlights
- Each index captures a distinct mechanism of structural importance, giving a multidimensional portrait of the network.
- No distributional assumptions are required; the method works on any graph regardless of variable type.
- Degree and eigenvector centrality scale efficiently to very large graphs; degree centrality is computed in O(V+E).
- Widely supported across disciplines — from sociology and biology to computer science — making results broadly communicable.
Intuition
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How it works
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When to use it
Centrality analysis applies whenever relational data can be represented as a graph and the question concerns which nodes are structurally most important. It is used in social network analysis, bibliometrics, biology, transportation, and information systems research. No normality assumption is required, and the method is suitable for cross-sectional and longitudinal network data. The network should be connected, or components should be analysed separately, so that path-based measures such as betweenness and closeness are well-defined. At least 10 nodes are needed for scores to be interpretable, and at least 20 for centrality rankings to be statistically meaningful. Weighted networks require a theoretically grounded weight definition before centrality is computed.
Strengths & limitations
- Each index captures a distinct mechanism of structural importance, giving a multidimensional portrait of the network.
- No distributional assumptions are required; the method works on any graph regardless of variable type.
- Degree and eigenvector centrality scale efficiently to very large graphs; degree centrality is computed in O(V+E).
- Widely supported across disciplines — from sociology and biology to computer science — making results broadly communicable.
- Betweenness centrality has computational complexity O(VE), making it expensive on very large networks.
- Path-based measures (betweenness, closeness) are undefined or require special treatment in disconnected graphs.
- Centrality scores are sensitive to the choice of edge-weight definition in weighted networks; a poorly chosen weight distorts every index.
- With fewer than 20 nodes the measures lack statistical power and should be treated as exploratory descriptions rather than inferential results.
Common pitfalls
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Applications
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Frequently asked
Which centrality measure should I use?
The choice depends on your substantive question. Use degree centrality to identify nodes with the most direct connections. Use betweenness centrality to find brokers who control information flow between parts of the network. Use closeness centrality to identify nodes that can reach all others quickly. Use eigenvector centrality or PageRank when the prestige of a node's neighbors matters as much as their number. Reporting two or three complementary indices and comparing the rankings is usually more informative than relying on a single measure.
Can centrality analysis be applied to directed networks?
Yes. In a directed network, in-degree and out-degree are computed and interpreted separately: in-degree reflects how often a node is chosen or cited by others, while out-degree reflects how many others it reaches or references. Betweenness and closeness also have directed variants. Eigenvector centrality on directed graphs typically uses the dominant left or right eigenvector depending on whether prestige flows to or from a node.
What is the minimum network size needed for meaningful results?
The statwise registry specifies a minimum of 10 nodes for any centrality computation, and meaningful statistical interpretation requires at least 20. Below 20 nodes the ranking of a handful of nodes does not generalise, and descriptive network statistics are the more honest choice.
How do I handle a disconnected graph?
Path-based measures — betweenness and closeness — are undefined between nodes in different components. The standard approach is to analyse each connected component separately, or to restrict closeness to reachable nodes and normalize accordingly. Degree and eigenvector centrality do not require connectivity and can be computed on the full graph.
Sources
- 1.Freeman, L.C. (1979). Centrality in Social Networks: Conceptual Clarification. Social Networks, 1(3), 215-239.
- 2.Borgatti, S.P. (2005). Centrality and Network Flow. Social Networks, 27(1), 55-71.
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Cite this page
ScholarGate. (2026, June 1). Centrality Analysis. ScholarGate. https://scholargate.app/network-analysis/centrality-analysis