
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). Scalefreeness can also be assessed by the socalled smeasure of Li et al, see the following paper:
http://arxiv.org/abs/condmat/0501169
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))
 T.
What do you think? Make any sense? Colin 2008/5/9 simone gabbriellini <address@hidden>: Hello List,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?thank you, Simone dott. Simone Gabbriellini  PhD Student Department of Social Sciences University of Pisa address@hidden _______________________________________________ igraphhelp mailing list address@hidden http://lists.nongnu.org/mailman/listinfo/igraphhelp  Colin Garroway (PhD candidate) Wildlife Research and Development Section Ontario Ministry of Natural Resources c/o Trent University DNA Building 2140 East Bank Drive Peterborough, ON, K9J 7B8 Canada Phone: 7057551535 _______________________________________________ igraphhelp mailing list address@hidden http://lists.nongnu.org/mailman/listinfo/igraphhelp
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