Directed Betweenness Centrality
Directed Betweenness Centrality (Freeman's Betweenness on Directed Graphs) · Also known as: directed BC, digraph betweenness, asymmetric betweenness centrality, directed Freeman betweenness
Directed Betweenness Centrality extends Freeman's classic betweenness measure to directed graphs, quantifying how often a node lies on the shortest directed paths between all other pairs of nodes. It identifies gatekeepers, brokers, and bottlenecks in asymmetric flows such as information cascades, citation networks, and organizational hierarchies.
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When to use it
Use directed betweenness centrality when edges in your network carry an inherent direction and asymmetric flow matters — for example citation networks, directed trade, retweet chains, regulatory hierarchies, or neural connectivity. It correctly identifies brokers and bottlenecks that undirected betweenness would miss or misrank. Do NOT use it on undirected networks where edge direction is an artifact (use standard betweenness centrality instead), on networks with fewer than about 20 nodes where the measure is unstable, or when you need to capture influence propagation along many paths rather than just shortest paths (consider PageRank or Katz centrality instead).
Strengths & limitations
- Correctly captures asymmetric brokerage and gateway roles that undirected betweenness conflates.
- Identifies nodes whose removal would most disrupt directed information or resource flows.
- Normalized scores are directly comparable across networks of different sizes.
- Efficient computation via Brandes' algorithm scales to networks with millions of nodes.
- Applicable across diverse domains: citation, organizational, web, biological, and financial networks.
- Distinguishes in-betweenness from out-betweenness when the direction of brokerage matters.
- Relies solely on shortest paths; longer but influential directed paths are ignored.
- Computationally heavier than degree or closeness centrality on very large dense digraphs.
- Sensitive to missing or incorrectly coded edge directions, which can drastically alter rankings.
- On sparse directed networks with few paths, many nodes score zero, reducing discriminability.
Frequently asked
How does directed betweenness differ from undirected betweenness?
In an undirected network, the path from A to B and from B to A are identical, so betweenness sums over unordered pairs. In a directed network, these are separate paths that may not exist or may have different lengths, so directed betweenness sums over ordered pairs and strictly respects edge direction.
Can I compare directed betweenness scores across different networks?
Only if you use normalized scores and the networks have comparable densities. Raw scores grow with network size, so normalization by (n-1)(n-2) is necessary. Even then, structural differences (density, diameter) affect the scale, so cross-network comparisons require caution.
What software computes directed betweenness centrality?
NetworkX (Python), igraph (R/Python), and Gephi all support directed betweenness using Brandes' algorithm. Ensure your graph object is defined as a directed graph (DiGraph in NetworkX) before calling the betweenness function.
What should I do if many nodes have betweenness zero?
Zero scores typically indicate a sparse or fragmented digraph where few paths exist. Check for disconnected components and consider whether your network definition (edge inclusion criteria) is appropriate. You may also examine in-degree and out-degree distributions to understand the network's connectivity structure.
Is directed betweenness the best measure for finding influential nodes in a directed network?
It depends on what 'influential' means. Betweenness identifies brokers on shortest paths; PageRank captures prestige through recursive endorsement; in-degree highlights recipients of many directed ties. Use directed betweenness when you specifically care about who controls directed flows or information bottlenecks.
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). Directed Betweenness Centrality (Freeman's Betweenness on Directed Graphs). ScholarGate. https://scholargate.app/en/network-analysis/directed-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.
- Betweenness CentralityNetwork analysis↔ compare
- Directed Closeness CentralityNetwork analysis↔ compare
- Directed Eigenvector CentralityNetwork analysis↔ compare
- Directed PageRankNetwork analysis↔ compare
- Directed Social Network AnalysisNetwork analysis↔ compare