> I am graduating from PUC Minas Brazil and my work theme of completion is on 
> the R language, specifically on the package IGRAPH. I wonder if you can help 
> me understand how R calculates the centrality of edges in the function below:
The calculation is not implemented in R; it is implemented in C and R just 
calls the compiled C code. As far as I know, the implementation is based on the 
following algorithm:

Ulrik Brandes: A Faster Algorithm for Betweenness Centrality. Journal of 
Mathematical Sociology 25(2):163-177, 2001.
http://www.inf.uni-konstanz.de/algo/publications/b-fabc-01.pdf

The paper focuses on the betweenness scores of the nodes, but the same idea can 
be used to calculate the betweenness scores of the edges as well.

-- 
T.
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