Degree matrix

In the mathematical field of graph theory the degree matrix is a diagonal matrix which contains information about the degree of each vertex.

[edit] Definition

Given a graph $G = (V, E)$ with $\|V\|=n$ the degree matrix $D$ for $G$ is a $n \times n$ square matrix defined as

$d_{i,j}:=\left\{ \begin{matrix} \deg(v_i) & \mbox{if}\ i = j \\ 0 & \mbox{otherwise} \end{matrix} \right.$

Vertex labeled graph	Degree matrix
	$\begin{pmatrix} 4 & 0 & 0 & 0 & 0 & 0\\ 0 & 3 & 0 & 0 & 0 & 0\\ 0 & 0 & 2 & 0 & 0 & 0\\ 0 & 0 & 0 & 3 & 0 & 0\\ 0 & 0 & 0 & 0 & 3 & 0\\ 0 & 0 & 0 & 0 & 0 & 1\\ \end{pmatrix}$