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GraphicalModels :: directedEdgesMatrix

directedEdgesMatrix -- the matrix corresponding to the directed edges of a mixed graph

Synopsis

Description

This method returns the n × n matrix of direct causal effect indeterminates. This matrix has the parameter l(i,j) in the (i,j) position if there is a directed edge i →j, and 0 otherwise. Note that this matrix is not symmetric. The documentation of gaussianRing further describes the indeterminates l(i,j).

i1 : G = mixedGraph(digraph {{b,{c,d}},{c,{d}}},bigraph {{a,d}})

o1 = MixedGraph{Bigraph => Bigraph{a => {d}}   }
                                   d => {a}
                Digraph => Digraph{b => {c, d}}
                                   c => {d}
                                   d => {}
                Graph => Graph{}

o1 : MixedGraph
i2 : R = gaussianRing G

o2 = R

o2 : PolynomialRing
i3 : compactMatrixForm =false;
i4 : directedEdgesMatrix R

o4 = | 0  0    0     0  |
     |                  |
     | 0  0  l     l    |
     |        b,c   b,d |
     |                  |
     | 0  0    0   l    |
     |              c,d |
     |                  |
     | 0  0    0     0  |

             4       4
o4 : Matrix R  <--- R

To obtain the directed edges matrix of a digraph, it should first be embedded into a mixed graph as follows.

i5 : D = digraph{{a,b},{c,d}}

o5 = Digraph{a => {b}}
             b => {}
             c => {d}
             d => {}

o5 : Digraph
i6 : Dembedded = mixedGraph(D, bigraph{})

o6 = MixedGraph{Bigraph => Bigraph{}        }
                Digraph => Digraph{a => {b}}
                                   b => {}
                                   c => {d}
                                   d => {}
                Graph => Graph{}

o6 : MixedGraph
i7 : directedEdgesMatrix gaussianRing Dembedded

o7 = | 0  0    0     0  |
     |                  |
     | 0  0  l     l    |
     |        b,c   b,d |
     |                  |
     | 0  0    0   l    |
     |              c,d |
     |                  |
     | 0  0    0     0  |

             4       4
o7 : Matrix R  <--- R

See also

Ways to use directedEdgesMatrix :