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Degree matrix - Definition and Overview |
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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>
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