Hi,
> How do you define the edge weights in the randomized graph?
Right now, I am taking the edge weights of the original network and doing
sampling with replacement.
Thank you for the advice on how to correlate edge weights with network
structure, I was really stuck.
Your suggestions on estimating the statistical significance of node betweenness
centrality is interesting.
> 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 got your point. My graphs are "biological", generated from a set of
biological experimental data and database information, so each node corresponds
to a gene, so I would say that node ID in my case not an arbitrary property and
has meaning behind it. What I was thinking initially was to compare betweenness
centrality of nodes in "real" network with that of "randomized" ones and say
something like compared to random networks the betweenness centrality of some
nodes are statistically significant, so the properties of these nodes should be
analyzed further.
Thank you for your comments and suggestions,
Sudeep
________________________________
From: Tamás Nepusz <[email protected]>
To: Help for igraph users <[email protected]>
Sent: Sunday, 10 February 2013 8:27 PM
Subject: Re: [igraph] random weighted graphs
> 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.
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