# degreeMatrix -- Returns the degree matrix of a graph

## Synopsis

• Usage:
D = degreeMatrix G
• Inputs:
• G, an instance of the type Graph
• Outputs:
• D, , The degree matrix of graph G

## Description

The degree matrix is the n by n diagonal matrix (where n is the number of vertices in the vertex set of the graph G) indexed by the vertices of G where A_(u,u) is the degree of vertex u. The degree of a vertex u is the number of edges such that {u,v} is an edge for any v also in the vertex set. This matrix is always diagonal.

 i1 : G = graph({1,2,3,4,5},{{1,2},{2,3},{3,4},{3,5},{4,5}}); i2 : degreeMatrix G o2 = | 1 0 0 0 0 | | 0 2 0 0 0 | | 0 0 3 0 0 | | 0 0 0 2 0 | | 0 0 0 0 2 | 5 5 o2 : Matrix ZZ <--- ZZ