 Degree matrix

The degree matrix is the diagonal matrix whose $i$th diagonal entry is the degree of a vertex $i$. For a finite simple graph, $d_i={\sum }_j{A}_{ij}$, where $A$ is its adjacency matrix. For a Weighted graph Laplacian, use the sum of incident edge weights instead of the number of incident edges.

In the context of graph theory, the degree matrix is a square diagonal matrix that is used to represent the degrees of the vertices in a graph. Specifically, for a simple undirected graph \( G \) with \( n \) vertices, the degree matrix \( D \) is defined as follows: 1. The matrix \( D \) is of size \( n \times n \). 2. The diagonal entries of \( D \) are the degrees of the corresponding vertices in the graph.