oriented incidence matrix

Let $G$ be a directed graph on $n$ vertices and $m$ edges, we define the oriented incidence matrix $B = (b_{i j})$ as follows:
$b_{i j}$ is 1 if $i$ is the source of the $j$ th edge
$b_{i j}$ is -1 if $i$ is the target of the $j$ th edge
$b_{i j} = 0$ otherwise

Example

Let $G$ be the following graph:
Pasted image 20260409095759.png|200
Its oriented incidence matrix is

B = [\begin{matrix} 1 & - 1 & - 1 & 1 & 0 & 0 \\ - 1 & 0 & 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & - 1 & - 1 & - 1 \end{matrix}]