Betweenness Centrality
Betweenness Centrality (Freeman's Geodesic Betweenness) · Also known as: Freeman betweenness, BC, geodesic betweenness, shortest-path betweenness
Betweenness centrality, formalized by Linton C. Freeman in 1977, measures how often a node lies on the shortest path connecting every other pair of nodes in a network. High-betweenness nodes act as bridges or brokers: removing them fragments the network into disconnected components more severely than removing any other nodes.
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When to use it
Use betweenness centrality when your research question is about brokerage, gatekeeping, or bridge nodes — actors whose removal would disrupt information flow or network cohesion. It is appropriate for undirected and directed graphs, and for weighted graphs where edge weights represent distance or cost. It is especially valuable in communication networks, citation networks, collaboration graphs, and supply chains. Do not use it as the sole centrality measure when brokerage is not the theoretical focus: degree centrality is simpler and sufficient for pure connectivity questions, and eigenvector or PageRank centrality better captures prestige propagation. Avoid it for very large sparse networks without an efficient implementation, as naive computation is O(V^2 E).
Strengths & limitations
- Captures structural brokerage and bridge roles that degree and eigenvector centrality miss entirely.
- Applicable to directed, undirected, weighted, and unweighted networks with the same formula.
- Normalized score enables meaningful comparison of nodes within one network and across networks of different sizes.
- Brandes algorithm makes computation tractable for networks with millions of nodes when implemented in optimized libraries such as NetworkX or igraph.
- Well-grounded theoretical interpretation: high-betweenness nodes are empirically associated with information control, power, and structural holes in organizational and social research.
- Computationally expensive on very dense networks even with Brandes algorithm; approximation algorithms may be needed for web-scale graphs.
- Assumes actors use shortest paths, which may be unrealistic in networks where flows traverse longer routes (e.g., random walks in electrical networks).
- Sensitive to missing or noisy edges: even a few unobserved ties can dramatically shift betweenness rankings.
- Gives equal weight to all shortest paths even when edge capacities or relationship strengths differ substantially.
Frequently asked
How does betweenness centrality differ from degree centrality?
Degree centrality counts direct connections; a hub with many ties scores high. Betweenness centrality counts how often a node lies on shortest paths between others; a bridge connecting two sparse clusters scores high even with few direct ties. The two measures capture orthogonal aspects of structural importance.
Should I use normalized or raw betweenness scores?
Use normalized scores whenever you compare nodes across networks of different sizes or present results to readers unfamiliar with your network's scale. Raw scores are acceptable only for comparisons within a single fixed network where the denominator is constant.
How do I handle weighted edges?
Set edge weights to represent distance or cost, not similarity. Most implementations (NetworkX, igraph) accept a weight parameter interpreted as distance; if your weights represent strength or similarity, invert them (e.g., weight = 1/similarity) before computing betweenness.
Is betweenness centrality meaningful for disconnected networks?
For disconnected graphs, shortest paths between nodes in different components are undefined (infinite). Most software treats those pairs as contributing zero to the sum, which can deflate scores. Either analyze each connected component separately or use a variant such as stress centrality with an explicit treatment of disconnected pairs.
My network has millions of nodes — can I still compute betweenness centrality?
Exact computation with Brandes algorithm is O(VE) and may be too slow. Use randomized approximations (e.g., sampling k source nodes) available in NetworkX (betweenness_centrality with k parameter) or graph libraries like graph-tool, which provide confidence intervals on the approximated scores.
Sources
- Freeman, L. C. (1977). A set of measures of centrality based on betweenness. Sociometry, 40(1), 35–41. DOI: 10.2307/3033543 ↗
- Brandes, U. (2001). A faster algorithm for betweenness centrality. Journal of Mathematical Sociology, 25(2), 163–177. DOI: 10.1080/0022250X.2001.9990249 ↗
How to cite this page
ScholarGate. (2026, June 3). Betweenness Centrality (Freeman's Geodesic Betweenness). ScholarGate. https://scholargate.app/en/network-analysis/betweenness-centrality
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- Closeness CentralityNetwork analysis↔ compare
- Degree CentralityNetwork analysis↔ compare
- Eigenvector CentralityNetwork analysis↔ compare
- Modularity AnalysisNetwork analysis↔ compare
- PageRankNetwork analysis↔ compare
- Social Network AnalysisNetwork analysis↔ compare