Documentation / Algorithms

Betweenness Centrality

Compute the betweenness centrality of each vertex of a given graph.

The betweenness centrality counts how many shortest paths between each pair of nodes of the graph pass by a node. It does it for all nodes of the graph.

Betweenness Centrality

The above graph shows the betweenness centrality applied to a grid graph, where color indicates centrality, green is lower centrality and red is maximal centrality.


This algorithm, by default, stores the centrality values for each edge inside the Cb attribute. You can change this attribute name at construction time.

This algorithm does not accept multi-graphs (p-graphs with p>1) yet.

This algorithm does not take into account edge direction yet.

By default the weight attribute name is weight, you can activate the weights using setWeighted(). You can change the weight attribute name using the dedicated constructor or the setWeightAttributeName(String) method. This method implicitly enable weights in the computation. Use setUnweighted() to disable weights.

The result of the computation is stored on each node inside the Cb attribute. You can change the name of this attribute using the dedicated constructor or the setCentralityAttributeName(String) method.

As the computing of centrality can take a lot of time, you can provide a progress callback to get notified each time the algorithm finished processing a node (however the centrality values are usable only when the algorithm finished). See the registerProgressIndicator(Progress) method.

Betweenness Centrality 2


By default the algorithm performs on a graph considered as not weighted with complexity O(nm). You can specify that the graph edges contain weights in which case the algorithm complexity is O(nm + n^2 log n).


Here is an example of use:

Graph graph = new SingleGraph("Betweenness Test");

//    E----D  AB=1, BC=5, CD=3, DE=2, BE=6, EA=4  
//   /|    |  Cb(A)=4
//  / |    |  Cb(B)=2
// A  |    |  Cb(C)=0
//  \ |    |  Cb(D)=2
//   \|    |  Cb(E)=4
//    B----C

Node A = graph.addNode("A");
Node B = graph.addNode("B");
Node E = graph.addNode("E");
Node C = graph.addNode("C");
Node D = graph.addNode("D");

graph.addEdge("AB", "A", "B");
graph.addEdge("BE", "B", "E");
graph.addEdge("BC", "B", "C");
graph.addEdge("ED", "E", "D");
graph.addEdge("CD", "C", "D");
graph.addEdge("AE", "A", "E");

BetweennessCentrality bcb = new BetweennessCentrality();
bcb.setWeight(A, B, 1);
bcb.setWeight(B, E, 6);
bcb.setWeight(B, C, 5);
bcb.setWeight(E, D, 2);
bcb.setWeight(C, D, 3);
bcb.setWeight(A, E, 4);

System.out.println("A="+ A.getAttribute("Cb"));
System.out.println("B="+ B.getAttribute("Cb"));
System.out.println("C="+ C.getAttribute("Cb"));
System.out.println("D="+ D.getAttribute("Cb"));
System.out.println("E="+ E.getAttribute("Cb"));


This is based on the algorithm described in “A Faster Algorithm for Betweenness Centrality”, Ulrik Brandes, Journal of Mathematical Sociology, 2001:

  • A Faster Algorithm for Betweenness Centrality,
  • Ulrik Brandes,
  • Journal of Mathematical Sociology 25:2,
  • 2001,
  • pp. 163 - 177,
  • DOI: 10.1080/0022250X.2001.9990249

And in “On variants of shortest-path betweenness centrality and their generic computation” , of the same author, 2008:

  • On variants of shortest-path betweenness centrality and their generic computation,
  • Ulrik Brandes,
  • Social Networks 30:2,
  • pp. 136 - 145,
  • 2008,
  • issn 0378-8733,
  • DOI: 10.1016/j.socnet.2007.11.001