The degree matrix is the diagonal matrix whose th diagonal entry is the degree of a vertex . For a finite simple graph, , where is its adjacency matrix. For a Weighted graph Laplacian, use the sum of incident edge weights instead of the number of incident edges.
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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.