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igraph / xdata-igraph

xdata igraph, has been merged into igraph/igraph
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ASE on the Laplacian #41

Closed gaborcsardi closed 10 years ago

gaborcsardi commented 10 years ago

Daniel:

I would like to be able to embed the graph laplacian either normalized or non-normalized. Possible options include D-A, I-D^{-1/2}AD^{-1/2}, D^{-1/2}AD^{-1/2}. There are other versions such as the regularized version Karl Rohe came up with.

From #38.

gaborcsardi commented 10 years ago

Maybe this should be called laplacian.spectral.embedding or lse then?

dpmcsuss commented 10 years ago

Yes, lse is fine, with options to indicate which of the various versions we want.

gaborcsardi commented 10 years ago

What is the definition you want for the Laplacian of a directed graph? Most definitions do not make much sense, maybe this is the best: F. Chung, Laplacians and the Cheeger inequality for directed graphs, Annals of Combinatorics 9 (2005), pp. 1-19

gaborcsardi commented 10 years ago

Actually docs are missing.... and the directed case, too.

dpmcsuss commented 10 years ago

Sorry for ignoring this earlier. Again it might be good to have a couple options. The version in Chung is symmetric which seems strange for a directed graph.

I think http://arxiv.org/pdf/1204.2296v1.pdf Eq (2.3) would be my preference for the default.