Obsidian Incidence Matrix md

# Incident Matrix

A matrix representing a graph where the rows represent [[Vertex|verticies]] and columns represent [[Graph edge|edges]]. The elements of the matric represent the number of time the edge connects to the vertex.

Example for a graph with 3 vertices and 4 edges
As a table
|       | $e_1$ | $e_2$ | $e_3$ | $e_4$ |
| ----- | ----- | ----- | ----- | ----- |
| $v_1$ | a     | b     | c     | d     |
| $v_2$ | e     | f     | g     | h     |
| $v_3$ | i     | j     | k     | l     |

As a matrix
$$\begin{pmatrix}
a & b & c & d \\
e & f & g & h \\
 i & j & k & l
\end{pmatrix}$$
For an undirected graph, $G$ is simple only if $M[i,j] \leq 1$