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Let $L$ be the Laplacian of a directed weighted graph on $n$ nodes, e.g., for $n=4$: $$ L = \left(\begin{array}{cccc} w_{1,1}+w_{1,2}+w_{1,3}+w_{1,4} & -w_{1,2} & -w_{1,3} & -w_{1,4}\\ ...