undirectedEdgesMatrix -- matrix corresponding to the edges of an undirected graph

Synopsis

Usage:

undirectedEdgesMatrix(R)
Inputs:
- R, a ring, which should be created with gaussianRing created with a graph or an instance of the type MixedGraph
Outputs:
- a matrix, the n x n symmetric concentration matrix of an undirected gaussian graphical model.

Description

This symmetric matrix has entries $k_{(i,i)}$ along the diagonal and entry $k_{(i,j)}$ in the $(i,j)$ position if there is an edge between i and j, and a zero otherwise. The documentation of gaussianRing further describes the indeterminates $k_{(i,j)}$.

i1 : G = graph({{a,b},{b,c},{c,d},{a,d}})

o1 = Graph{a => {b, d}}
           b => {a, c}
           c => {b, d}
           d => {a, c}

o1 : Graph

i2 : R = gaussianRing G

o2 = R

o2 : PolynomialRing

i3 : compactMatrixForm =false;

i4 : K = undirectedEdgesMatrix(R)

o4 = |  k     k       0   k     |
     |   a,a   a,b         a,d  |
     |                          |
     |  k     k     k       0   |
     |   a,b   b,b   b,c        |
     |                          |
     |    0   k     k     k     |
     |         b,c   c,c   c,d  |
     |                          |
     |  k       0   k     k     |
     |   a,d         c,d   d,d  |

             4      4
o4 : Matrix R  <-- R

For mixed graphs with other types of edges, the size of the matrix coincides with the number of elements in compU, which depends on the vertex partition built in partitionLMG.

i5 : G = mixedGraph(digraph {{1,3},{2,4}},bigraph {{3,4}},graph {{1,2}});

i6 : R = gaussianRing G;

i7 : K = undirectedEdgesMatrix(R)

o7 = |  k     k     |
     |   1,1   1,2  |
     |              |
     |  k     k     |
     |   1,2   2,2  |

             2      2
o7 : Matrix R  <-- R

Ways to use undirectedEdgesMatrix :

undirectedEdgesMatrix(Ring)

For the programmer

The object undirectedEdgesMatrix is a method function.

undirectedEdgesMatrix -- matrix corresponding to the edges of an undirected graph

Synopsis

Description

See also

Ways to use undirectedEdgesMatrix :

For the programmer