Degree matrix
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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 [G=(V,E)] with [\|V\|=n] the degree matrix [D] for [G] is a [n \times n] square matrix defined as
- [d_:=\left\ \deg(v_i) & \mbox\ i = j \\0 & \mbox\end\right.]
Examples
The degree matrix for the following vertex labeled graph
- [\begin4 & 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.]
- The degree matrix of a k-regular graph has a constant diagonal of [k]
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