Adjacency Matrix/Examples/Loop-Graph

Example of Adjacency Matrix

The elements on the main diagonal of the adjacency matrix for a loop-graph are not all non-zero:

$\qquad \begin{pmatrix} 0 & 1 & 0 & 0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 2 & 1 & 1 & 1 & 0 \\ 0 & 0 & 1 & 2 & 1 & 1 & 0 \\ 1 & 1 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 1 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 \\ \end{pmatrix}$

Also defined as

Some other treatments of this subject require that a loop contributes a value of $1$ to the vertex to which it is incident.