Hi Satrajit,
I believe the current implementation is equivalent to the first several 
equations in this document:
  http://www.math.ucsd.edu/~fan/research/cb/ch1.pdf
It may be that there are several ways to define a laplacian; I'm not an 
expert on the subject.  Gael might be able to weigh in - I think he 
contributed the current Laplacian implementation.

FYI, I'm working on some related things in a current scipy PR:  
https://github.com/scipy/scipy/pull/119 (unfortunately it's been sitting 
idle for the last month or so - I hope to be able to finish and merge it 
some time soon).
   Jake

Satrajit Ghosh wrote:
> i've opened an issue on computing graph laplacians at:
>
> https://github.com/scikit-learn/scikit-learn/issues/811
>
> any thoughts would be much welcome.
>
> cheers,
>
> satra
>
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