# Incidence matrix ¶

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This may also be called Matrice d’incidence. It's mainly used in directed graphs as an amelioration of the adjacency matrix because we lost some information.

This is a matrix vertex by vertex too, and the values are -1, 0, or 1. If we are at row=A, col=B

• -1: an arc is leaving A ($A \to B$)
• 1: an arc is entering A ($B \to A$)
• 0: no arc ($A \to B$ or $B \to A$)

If you can pick either -1 or 1, pick the one you want.

## Example ¶

The incidence matrix for

is

$\displaylines{ \hspace{0.7cm}\begin{array}{} a&b&c&d&h&i \end{array} \ \ \ \\ \begin{array}{} a\\b\\c\\d\\h\\i \end{array} \begin{pmatrix} 0 & 1 & -1 & 1 & 0 & 0 \\ 1 & 0 & 0 & 1 & 1 & 0 \\ 1 & 0 & 0 & -1 & 0 & 1 \\ -1 & -1 & 1 & 0 & 1 & 0 \\ 0 & -1 & 0 & -1 & 0 & 1 \\ 0 & 0 & -1 & 0 & 1 & 0 \\ \end{pmatrix} }$

Note: if you remove all the minus (-) before the ones then you got the adjacency matrix for the undirected graph.