Degree matrix

In the mathematical field of graph theory the degree matrix is a diagonal matrix which contains information about the degree of each vertex—that is, the number of edges attached to each vertex. It is used together with the adjacency matrix to construct the Laplacian matrix of a graph.

Given a graph ${\displaystyle G=(V,E)}$ with ${\displaystyle |V|=n}$, the degree matrix ${\displaystyle D}$ for ${\displaystyle G}$ is a ${\displaystyle n\times n}$ diagonal matrix defined as

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