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.Definition
Given a graph with, the degree matrix for is a diagonal matrix defined as
where the degree of a vertex counts the number of times an edge terminates at that vertex. In an undirected graph, this means that each loop increases the degree of a vertex by two. In a directed graph, the term degree may refer either to indegree or outdegree.Example
Properties
The degree matrix of a k-regular graph has a constant diagonal of.
