# laplacianMatrix -- Returns the laplacian matrix of a graph

## Synopsis

• Usage:
L = laplacianMatrix G
• Inputs:
• G, an instance of the type Graph,
• Outputs:
• L, , the laplacian matrix of graph G

## Description

The laplacian matrix of a graph is the adjacency matrix of the graph subtracted from the degree matrix of the graph.

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