Determining the Adjacency Matrix for a Model

What Is an Adjacency Matrix?

An adjacency matrix is a square matrix that provides information on reactants and products of reactions in a model. It lets you easily determine:

• The reactants and products in a specific reaction in a model

• The reactions that a specific species is part of, and whether the species is a reactant or product in that reaction

An adjacency matrix is an N-by-N matrix, where N equals the total number of species and reactions in a model. Each row corresponds to a species or reaction, and each column corresponds to a species or reaction.

The matrix indicates which species and reactions are involved as reactants and products:

• Reactants are represented in the matrix with a 1 at the appropriate location (row of species, column of reaction). Reactants appear above the diagonal.

• Products are represented in the matrix with a 1 at the appropriate location (row of reaction, column of species). Products appear below the diagonal.

• All other locations in the matrix contain a 0.

For example, if a model object contains one reaction equal to A + B -> C and the Name property of the reaction is R1, the adjacency matrix is:

       A    B    C   R1
  A    0    0    0   1
  B    0    0    0   1
  C    0    0    0   0
  R1   0    0    1   0

Retrieving an Adjacency Matrix for a Model

Retrieve an adjacency matrix for a model by passing the model object as an input argument to the getadjacencymatrix method.

1. Read in m1, a model object, using sbmlimport:

   m1 = sbmlimport('lotka.xml');

2. Get the adjacency matrix for m1:

   [M, Headings] = getadjacencymatrix(m1)
   
   M =
   
      (5,1)        1
      (5,2)        1
      (6,3)        1
      (7,4)        1
      (1,5)        1
      (2,5)        1
      (2,6)        1
      (3,6)        1
      (3,7)        1
   
   
   Headings = 
   
       'x'
       'y1'
       'y2'
       'z'
       'Reaction1'
       'Reaction2'
       'Reaction3'

3. Convert the adjacency matrix from a sparse matrix to a full matrix to more easily see the relationships between species and reactions:

   M_full = full(M)

   M_full =
   
        0     0     0     0     1     0     0
        0     0     0     0     1     1     0
        0     0     0     0     0     1     1
        0     0     0     0     0     0     0
        1     1     0     0     0     0     0
        0     0     1     0     0     0     0
        0     0     0     1     0     0     0