I'm having a little difficulty determining the method Gephi uses for calculating node betweenness centrality for a weighted, undirected network. As a simple example, I'm looking at a 5 node network with adjacency matrix, A, whose rows are

A=

{0,3,7,0,0}

{3,0,6,0,0}

{7,6,0,2,1}

{0,0,2,0,4}

{0,0,1,4,0}

When the nonzero entries are converted to 1, the betweenness centrality (BC) is easy to compute by hand: Node 3 has BC 8 and the rest are zero. These values are confirmed by Gephi and make sense when one draws the graph itself.

However, when I use the weighted version of the network, Gephi returns the same BC values. This seems counter intuitive to me. If the edge weights are converted to link distances by taking reciprocals, the BC values are 0,0,10,6,0, respectively. That node 4 has a nonzero BC makes sense because the shortest distance path from 3 to 5 must now pass through 4.

I should point out that my intuition is supported by using Matlab's Brain Connectivity Toolbox, which also returns 0,0,10,6,0.

## Betweenness for Weighted Network

### Re: Betweenness for Weighted Network

Hi,

The current implemented algorithm does not take edge weight into account: https://github.com/gephi/gephi/blob/mas ... tance.java

The current implemented algorithm does not take edge weight into account: https://github.com/gephi/gephi/blob/mas ... tance.java