betweennessCentrality

betweennessCentrality(filename)
Writes the betweenness centrality of each individual node to a text file. The file contains the centralities written in order of the node number.

Parameters

filename: String
Name of the file to which the betweenness centralities will be written

Notes

If n is the number of nodes in the network and \mathcal{D}_{jk} is the set of all shortest path between node j and node k, the betweenness centrality of node i is:

\frac{1}{n (n-1)} \sum_{j,k} \frac{ \left\lvert \left\{ D \in \mathcal{D}_{jk} \middle | i \in D \right\} \right\rvert}{ \left\lvert \mathcal{D}_{jk} \right\rvert }

The normalisation is such that the betweenness centrality is always in the interval \left[ 0, 1 \right]. The distance between two nodes is defined as described in meanPathLength.

Example (python-conedy)

import conedy as co

N = co.network()

i = N.cycle(20, 1, co.node(), co.weightedEdge())

N.addEdge(i + 1, i + 7, co.weightedEdge(1.0))
N.addEdge(i + 7, i + 1, co.weightedEdge(2.0))
N.addEdge(i + 1, i +11, co.weightedEdge(3.0))
N.addEdge(i +11, i + 1, co.weightedEdge(4.0))

N.betweennessCentrality("output/betweennessCentrality.py.out")

Example (conedy)

network N;

int i = N.cycle(20, 1, kuramoto());

N.addEdge(i+ 1, i+ 7, weightedEdge(1.0));
N.addEdge(i+ 7, i+ 1, weightedEdge(2.0));
N.addEdge(i+ 1, i+11, weightedEdge(3.0));
N.addEdge(i+11, i+ 1, weightedEdge(4.0));

N.betweennessCentrality( "output/betweennessCentrality.co.out" );

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