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

[Gábor Csárdi]

Tamas,

actually I have the file and could reproduce the error. I will send
you the file if you want to work on this. I will not have any time
this week, at least not until the weekend. :(

Best,
G.

On Wed, Jun 10, 2009 at 12:50 PM, Tamas Nepusz<address@hidden> wrote:
> Hi Yong,
>
> I'm 99.9% convinced that such large values cannot be right. Even the
> maximal betweenness centrality in a line graph of 10000 nodes is only
> 24995000 (i.e., 4999*5000). Can you send me the source code and the
> graph you are working with (or any other graph that produces erroneously
> high betweenness values)?
>
> --
> Tamas
>
>
> On Wed, Jun 10, 2009 at 12:43:19PM +0200, Yong Zou wrote:
>> Hi Tamas,
>>
>> Could you please help me to understand those extremely big values for
>> the betweenness centrality?
>> 58743768046350440071168.000000 for a network of 10000 nodes.
>>
>> Thank you very much.
>> Yong
>>
>> On Thu, May 28, 2009 at 1:38 PM, Yong Zou<address@hidden> wrote:
>> > Thanks Tamas,
>> >
>> > Now it is clear for those floating values. But what about the very big
>> > or even negative values, then?
>> >
>> > Best,
>> > Yong
>> >
>> > On Thu, May 28, 2009 at 1:33 PM, Tamas Nepusz <address@hidden> wrote:
>> >>> 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
>> >>
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>> >>
>> >
>>
>>
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-- 
Gabor Csardi <address@hidden>     UNIL DGM