[SciPy-User] Graph connect components and sparse matrices
Zachary Pincus
zachary.pincus@yale....
Wed Nov 18 08:03:18 CST 2009
Hi Gaël,
> Any idea how I could squeeze the information out of the sparse linear
> algebra that we carry around with scipy? I thought about using
> arpack to
> get the largest eigen vectors of the transition matrix, but that was a
> stupid idea, as (AFAIK) it will not partition my graph in connect
> components, but only tell me how many connect components I have.
From this useful tutorial on spectral clustering:
http://www.kyb.tuebingen.mpg.de/bs/people/ule/publications/publication_downloads/Luxburg07_tutorial.pdf
> Thus, the matrix L has as many eigenvalues 0 as there are connected
> components, and
> the corresponding eigenvectors are the indicator vectors of the
> connected components.
(where L is the graph laplacian).
Zach
On Nov 18, 2009, at 8:46 AM, Gael Varoquaux wrote:
> Hi there,
>
> I would like to list the connect components of a graph (or a sparse
> matrix, same thing). I know of course of the bread-first traversal, as
> implemented eg in networkX, to find the connect components. However, I
> have a feeling that sparse linear algebra must be performing such
> searches, to decompose sparse matrices in blocks. I'd love to piggy
> back
> on such implementations, rather than code and maintain a C or cython
> version of breadth-first graph traversal.
>
> Any idea how I could squeeze the information out of the sparse linear
> algebra that we carry around with scipy? I thought about using
> arpack to
> get the largest eigen vectors of the transition matrix, but that was a
> stupid idea, as (AFAIK) it will not partition my graph in connect
> components, but only tell me how many connect components I have.
>
> Gaël
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