Re: [igraph] Degree-preserving rewiring of a large graph

[Tamás Nepusz]

Hi,

> I am using igraph in R, and need a clarification about the rewire()
> function. The parameter niter is the number of times the algorithm will
> choose two arbitrary edges and shuffle them?
Yes; more precisely, niter is the number of times the algorithm will *try* to 
choose two random edges and shuffle them. This means that the iteration counter 
is increased even if the random selection happened to have yielded a pair which 
cannot be rewired sensibly because it would have created multiple edges 
somewhere.

> I am working with a graph of ~150K edges - if my understanding of niter
> is correct, how many iterations would be recommended to obtain a
> reasonably rewired graph?
If you want to rewire your graph, I would suggest at least 10 times the number 
of your edges -- however, I’m pretty sure that there are more rigorous results 
in the literature. For instance, this deck of slides states that you need at 
least m/2 * ln(1/epsilon) steps where m is the number of edges and epsilon is 
some kind of tolerance value (although I did not find any definition for 
epsilon in the slides):

http://www.graphanalysis.org/SIAM-CSE13/05_Pinar.pdf

A pretty arbitrary choice of epsilon = 10^-6 would yield ~7 times the number of 
edges.

> My current problem is to compute the probability of observing each
> particular edge in a random graph with the same degree sequence.
In this case, you don’t really need rewiring; you can use the 
degree.sequence.game() function which generates graphs for you with a 
prescribed degree distribution. If you want to avoid loop and multiple edges, 
make sure to use method=“vl” or method=“simple.no.multiple”. method=“vl” is 
probably better as it is said to sample the space of all possible graphs with a 
prescribed degree sequence uniformly.

T.