Definition

The degree matrix of an undirected Graph is a Diagonal Matrix representing the sum of the weight of edges connected to each node. It is used together with the Adjacency Matrix to construct the Laplacian Matrix of a graph.

Given a graph $G$ and the corresponding Adjacency Matrix $A = (a_{ij})$ . The degree matrix is defined as $D := diag (d_{1}, d_{2}, \dots, d_{n})$ where $d_{i} := j = 1 \sum n a_{ij}$ ,