Betweenness Centrality and Stress Centrality
Alex
It seems to me that according to the paper referenced in the
documentation of Betweenness Centrality:
http://www.inf.uni-konstanz.de/algo/publications/b-fabc-01.pdf
And another one by the same author:
http://www.inf.uni-konstanz.de/algo/publications/b-vspbc-08.pdf
the definition given in the documentation for Betweenness Centrality
is not quite exact.
The definition given is:
"Betweenness centrality of a node is the fraction of all shortest
paths that pass through that node."
But if you read the second paper, that should be the definition of
(Normalized) Stress Centrality. This papers point out that there have
been some confusion regarding the definition of these two measures. It
is important to note that those two measures are not interchangeable
at all, as mentioned in that paper, each measure could result not only
in different values for each node but actually in a different ranking
of the nodes according to these values.
I think that the definition should be more precise, maybe putting the
mathematical definition, since a text definition could be cumbersome,
it may be something like:
"Betweenness centrality of a node V is the sum (across all pair of
nodes) of the fractions of all the shortest paths for each pair of
nodes, that pass through that node V"
Sudarshan Iyengar
You are right. While some people use stress and betweenness centrality interchangeably, it can sometimes result in a difference of ranking. For the most accurate description of the measure, I would recommend you to take a look at brandes' paper on betweenness centrality. Simply stated, betweenness centrality of a node is the sum of the fraction of total number of shortest paths that pass through that node.
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Aric Hagberg
betweenness documentation. Can you look to make sure it is OK?
http://networkx.lanl.gov/preview/reference/generated/networkx.algorithms.centrality.betweenness.betweenness_centrality.html
(
The Sphinx produced formatting looks a little off in this preview doc
page - I'll look into that).
Aric
Alex
On Nov 17, 10:52 pm, Aric Hagberg <ahagb...@gmail.com> wrote:
> Thanks for pointing this out - I added some formulas to the
> betweenness documentation. Can you look to make sure it is OK?
>
Aric Hagberg
> I think it looks excellent, thanks for the precision.
For anyone else that finds issues or potential improvements to the
NetworkX documentation -
your feedback is much appreciated. It's hard to write careful and
correct documentation
and I'm sure there are many places where it could be improved.
You can send comments to the mailing list or open a ticket at
https://networkx.lanl.gov/trac/newticket
Aric