# negativeLaplacian -- Computes the negative of the Laplacian matrix of a Reaction Network.

## Synopsis

• Usage:
L = negativeLaplacian N
• Inputs:
• Outputs:
• L, , the negative of the unweighted Laplacian matrix of N.

## Description

Computes the negative of the (unweighted) Laplacian matrix of the directed graph associated with a Reaction Network.

 i1 : N = reactionNetwork "A <--> B" o1 = A-->B B-->A o1 : ReactionNetwork i2 : L = negativeLaplacian N o2 = | -1 1 | | 1 -1 | 2 2 o2 : Matrix ZZ <--- ZZ

A bigger example:

 i3 : N = oneSiteModificationA() o3 = S_0+E-->X X-->S_0+E X-->E+S_1 S_1+F-->Y Y-->S_1+F Y-->S_0+F o3 : ReactionNetwork i4 : L = negativeLaplacian N o4 = | -1 1 0 0 0 0 | | 1 -2 1 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 -1 1 0 | | 0 0 0 1 -2 1 | | 0 0 0 0 0 0 | 6 6 o4 : Matrix ZZ <--- ZZ

## Ways to use negativeLaplacian :

• "negativeLaplacian(ReactionNetwork)"

## For the programmer

The object negativeLaplacian is .