Laplacian, Spectral graph theory -- Supra-Laplacian matrix
The basic Laplacian matrix (combinatorial Laplacian matrix) is defined as:
$$ L = D - A $$
or
$$ L_{i,j}:= \begin{cases} \deg(v_i) & \mbox{if}\ i = j \\ -1 & \mbox{if}\ i \neq j\ \mbox{and}\ v_i \mbox{ is adjacent to } v_j \\ 0 & \mbox{otherwise} \end{cases} $$
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