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

[Yong Zou]

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
>>
>> _______________________________________________
>> igraph-help mailing list
>> address@hidden
>> http://lists.nongnu.org/mailman/listinfo/igraph-help
>>
>