Re: [igraph] Eigenpairs of sparse graphs

[Tamas Nepusz]

Hi,

> I need to compute some extremal eigenvalues/eigenvectors of
> adjacency and Laplacian matrices for very large and sparse graphs.
> (to large for the matrices to be represented in their dense form  
> anyway).
>
> Given the graphs, how can I achieve this task with igraph?
igraph includes an interface to the ARPACK library suitable for  
solving large scale eigenvalue problems. See the following page in the  
documentation for details:

http://cneurocvs.rmki.kfki.hu/igraph/doc/html/ch19s01.html

So you should import your graph somehow into igraph (using the C core  
directly), initialize an igraph_arpack_options_t data structure, set  
its options appropriately for your specific problem, implement an  
igraph_arpack_function_t function that multiplies a given vector with  
your matrix (chances are that you'll have to use an adjacency list  
representation of your graph, see http://cneurocvs.rmki.kfki.hu/igraph/doc/html/igraph-Adjlists.html) 
, and finally call igraph_arpack_rssolve if your matrix is symmetric,  
igraph_arpack_rnsolve otherwise.

If you need examples, check the code for PageRank calculation or  
eigenvector centrality in centrality.c in the igraph source code.

I hope this helps.

Regards,
--
T.