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ReactionNetworks :: negativeUndirectedLaplacian

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

Synopsis

Description

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

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

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 = 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

Ways to use negativeUndirectedLaplacian :

For the programmer

The object negativeUndirectedLaplacian is a method function.