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Feb 7, 2016 at 21:46 comment added MSardelich @Michele maybe it went unnoticed but Professor Chris Godsil is one of the authors of the book you mentioned ;-)
Aug 3, 2015 at 14:22 comment added Chris Godsil I am not sure that it needs a reference. You could make the observation that the weighted Laplacian is $B\Delta B^T$, and its rank is equal to the rank of $B$. (And then appeal to the unweighted case.)
Aug 3, 2015 at 13:42 comment added James This works, thank you. I am looking for a reference including the proof for weighted graphs, to cite it in a paper. The closest one that I could find is 'Algebraic graph theory' by R. Royle, Springer 2001, but it includes the proof for non-weighted graphs only. Do you know a reference containing the proof in the weighted case?
Aug 2, 2015 at 13:42 history answered Chris Godsil CC BY-SA 3.0