Re: [igraph] betweenness centrality -- negative and floating values?

[Tamas Nepusz]

> Ok, I can understand the floating values for the BC then because of
> this weight of 1/k. It also means that the more shortest paths between
> A and B, the less weight will be counted.
>
> However from the original definition for BC,
> http://en.wikipedia.org/wiki/Centrality, this sounds to be different
> for me.
No, it isn't. The formula on that Wikipedia page has the number of  
shortest paths between s and t in the denumerator, so if there is more  
than a single shortest path between s and t, the vertices  
participating in those paths will receive a contribution of 1/k due to  
this path, where k is \sigma_{s,t} - the number of shortest paths  
between s and t.

> I'm quite confused by this now. The values should be
> normalized to the interval [0 1]?
It can be normalized if you wish, but igraph doesn't do that by  
default. As it says on the Wikipedia page you mentioned, "This may be  
normalised by dividing through the number of pairs of vertices not  
including v, which is (n − 1)(n − 2) / 2.". So if you want to get  
values between 0 and 1, divide the betweenness centrality values by  
(n-1)(n-2)/2.

--
Tamas