Let $G$ be a finite graph with $n$ vertices, $\{{v}_{1},\mathrm{\dots},{v}_{n}\}$
and $m$ edges, $\{{e}_{1},\mathrm{\dots},{e}_{m}\}$.
For each edge $e=({v}_{i},{v}_{j})$ of $G$ choose one vertex
to be the positive end and the other to be the negative end. In this way,
we assign an orientation to $G$. The
of $G$ with respect an orientation is an $n\times m$ matrix
$D=({d}_{ij})$
where

$${d}_{ij}=\{\begin{array}{cc}+1\hfill & \text{if}{v}_{i}\text{is the positive end of}{e}_{j}\hfill \\ 1\hfill & \text{if}{v}_{i}\text{is the negative end of}{e}_{j}\hfill \\ 0\hfill & \text{otherwise}.\hfill \end{array}$$ 
