Degree matrix - Definition and Overview

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

Definition

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

<math>d_{i,j}:=\left\{

\begin{matrix} \deg(v_i) & \mbox{if}\ i = j \\ 0 & \mbox{otherwise} \end{matrix} \right. <math>

Examples

• the diagonal matrix of a k-regular graph has a constant diagonal of <math>k<math>