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## Re: [igraph] test network topology

 From: Tamas Nepusz Subject: Re: [igraph] test network topology Date: Fri, 9 May 2008 16:23:21 +0200

I generated 1000 random graphs with similar characteristics to my empirical graph. I then calculated the the transitivity and shortest path length for each random graph.
I think I would have done the same. The random graphs would have had the same degree distribution as my original graph (see the rewiring functionality of igraph or the degree sequence game. the latter one does not prevent multiedges and loops, but the graph can be simplified afterwards). Scale-free-ness can also be assessed by the so-called s-measure of Li et al, see the following paper:
```http://arxiv.org/abs/cond-mat/0501169

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I took my graph to have small world characteristics if the empirical transitivity was greater than some proportion of the transitivity values of the random graphs (greater than 95% of random transitivity??) and the shortest path for the empirical and random graphs were similar.
Another possibility is to calculate the mean and the variance of transitivity and shortest path measures for random graphs and then compare them to the empirical graph. (E.g., if the characteristic path length of the empirical graph is, say, two standard deviations smaller than the mean characteristic path length of the corresponding random networks under the assumption of normality (which does not hold IMHO, but it is a useful approximation))
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T.

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What do you think?  Make any sense?

Colin

Hello List,

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I have a methodological question for you: suppose you have an empiric network and you want to see which theoretical model (random graph or small world) is more close to it, what igraph functions will you combine? I know how to simulate in igraph random graphs and small world graphs with similar characteristic than the empirical network (number of nodes, links, mean degree), but what could be the right "test" at the end?
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thank you,
Simone

dott. Simone Gabbriellini - PhD Student
Department of Social Sciences
University of Pisa

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Colin Garroway (PhD candidate)
Wildlife Research and Development Section
Ontario Ministry of Natural Resources
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