I've calculated betweenness for each node in a network of approximately
100,000 nodes and one million edges. For almost all nodes, betweenness
values range from 0 to 9,149.8877, in gradual increments. However, the
highest nine values are as follows:: 3 nodes have the value of 10,000, 5
nodes have a betweenness of 20,000, and one node has a value of 40,000.
These nodes do have relatively high out- and in- degree but there is nothing
else unusual about them.
I calculated these values in graph-tool about a year ago.
Is this normal for the calculation of betweenness (i.e. values >= 10,0000 go
up in increments of 10,0000), or has something gone wrong?
I'm not sure what kind of answer you are expecting, since
it's impossible to say anything without knowing your network, and what
your expectations were. Why would an increment of around 10000 be wrong
for your network?
You can easily test for yourself that the betweenness values for many
networks do not increment by that amount.
Sorry if I was not clear - there are over 100,000 nodes in my network which
have betweenness values like 0, 0.238135, 16.401913, 150.58386, 8716.5635,
up to 9149.8877, and then right at the end of the distribution there are 9
nodes with betweenness values of EXACTLY 10k, 10k, 10k, 20k,20k, 20k,20k,
20k,40k.
This seems bizarre to me - it is not the fact that these betweenness values
are very high, but rather that the intervals increment by exactly 10k each
time.
So I thought this must be a bug.
As it appears that it is not a bug that is known, I'll investigate further.