GRAPH Course
Incidence matrix
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.