incidence matrix

Let $G$ be a graph with $n$ vertices and $m$ edges. The incidence matrix of $G$ is the $n \times m$ matrix $C = (c_{i j})$ such that
$c_{i j} = 1$ if the $i$ th vertex is incident to the $j$ th edge (ie. that it is an endpoint of $j$ ), 0 otherwise.

Example

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

C = [\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}]