negativeUndirectedLaplacian -- Computes the negative of the Laplacian matrix of an undirected graph associated with a Reaction Network.

Synopsis

• Usage:

  L = negativeUndirectedLaplacian N

• Inputs:
  • N, an instance of the type ReactionNetwork, a chemical reaction network.
• Outputs:
  • L, a matrix, the negative of the unweighted, undirected Laplacian matrix of N.

Description

i1 : N = reactionNetwork "A <--> B"

o1 = A-->B
     B-->A

o1 : ReactionNetwork

i2 : L = negativeUndirectedLaplacian N

o2 = | -1 1  |
     | 1  -1 |

              2       2
o2 : Matrix ZZ  <-- ZZ

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 = negativeUndirectedLaplacian N

o4 = | -1 1  0  0  0  0  |
     | 1  -2 1  0  0  0  |
     | 0  1  -1 0  0  0  |
     | 0  0  0  -1 1  0  |
     | 0  0  0  1  -2 1  |
     | 0  0  0  0  1  -1 |

              6       6
o4 : Matrix ZZ  <-- ZZ

See also

• negativeLaplacian -- Computes the negative of the Laplacian matrix of a Reaction Network.
• negativeWeightedLaplacian -- Computes the negative of the weighted Laplacian matrix of a Reaction Network.
• stoichiometricMatrix -- Computes the stoichiometric matrix of a Reaction Network.