Re: [igraph] random weighted graphs

[sudeep s]

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 <address@hidden>
To: Help for igraph users <address@hidden>
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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