Re: [igraph] test network topology

[Tamas Nepusz]

> 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

> 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
>
>
>
>
>
>
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> Colin Garroway (PhD candidate)
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