Re: [igraph] random weighted graphs

[Tamás Nepusz]

> I tried using rewire.edges from R igraph 0.6 package, but  found out that the 
> generated random graphs had almost the same edge weights as that of my 
> original  graph.
How do you define the edge weights in the randomized graph?

> So, if  someone could point out how to estimate if there is a correlation 
> between network structure and weights, that would be of great help.
Try to correlate some simple structural quantities with the edge weights. For 
instance, calculate the correlation between the edge weight and, say, the total 
degree of the endpoints of that edge. If you find that there is a positive 
correlation, then this means that edges with higher weight tend to appear more 
likely between vertices with high degrees. You can then decide whether this is 
a structural property that you wish to preserve in your randomized networks or 
not.

> Additionally, is there a better method to estimate the statistical 
> significance of node betweenness centrality of weighted graphs ?
It wasn't clear to me whether you are planning to compare the betweenness 
centrality score of node i in the "real" network with the betweenness 
centrality scores of node i in the "randomized" networks. I think it does not 
make sense to compare node i with node i only because the ID of a node is just 
an arbitrary property that has nothing to do with the betweenness score 
whatsoever. I would probably do the following:

1. Generate lots of randomized networks using degree.sequence.game instead of 
using rewire.edges because it is hard to determine how many iterations you need 
in rewire.edges to get sufficiently "far away" from the initial configuration. 
On the other hand, degree.sequence.game starts "from scratch".

2. Estimate the _distribution_ of betweenness scores by pooling all the 
betweenness values from all the nodes of all the randomized networks, and then 
compare this distribution with the observed betweenness scores from your real 
network.

-- 
T.