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hyperGraphToSimplicialComplex -- makes a simplicial complex from a (hyper)graph

Synopsis

Description

This function produces a simplicial complex from a (hyper)graph. The facets of the simplicial complex are given by the edge set of the (hyper)graph. This function is the inverse of simplicialComplexToHyperGraph and enables users to make use of functions in the package SimplicialComplexes.

i1 : R = QQ[x_1..x_6];
 
i2 : G = graph({x_1*x_2,x_2*x_3,x_3*x_4,x_4*x_5,x_1*x_5,x_1*x_6,x_5*x_6}) --5-cycle and a triangle

o2 = Graph{"edges" => {{x , x }, {x , x }, {x , x }, {x , x }, {x , x }, {x , x }, {x , x }}}
                         1   2     2   3     3   4     1   5     4   5     1   6     5   6
           "ring" => R
           "vertices" => {x , x , x , x , x , x }
                           1   2   3   4   5   6

o2 : Graph
 
i3 : DeltaG = hyperGraphToSimplicialComplex G

o3 = simplicialComplex | x_5x_6 x_1x_6 x_4x_5 x_1x_5 x_3x_4 x_2x_3 x_1x_2 |

o3 : SimplicialComplex
 
i4 : hyperGraphDeltaG = simplicialComplexToHyperGraph DeltaG

o4 = HyperGraph{"edges" => {{x , x }, {x , x }, {x , x }, {x , x }, {x , x }, {x , x }, {x , x }}}
                              1   2     2   3     3   4     1   5     4   5     1   6     5   6
                "ring" => R
                "vertices" => {x , x , x , x , x , x }
                                1   2   3   4   5   6

o4 : HyperGraph
 
i5 : GPrime = graph(hyperGraphDeltaG)

o5 = Graph{"edges" => {{x , x }, {x , x }, {x , x }, {x , x }, {x , x }, {x , x }, {x , x }}}
                         1   2     2   3     3   4     1   5     4   5     1   6     5   6
           "ring" => R
           "vertices" => {x , x , x , x , x , x }
                           1   2   3   4   5   6

o5 : Graph
 
i6 : G === GPrime

o6 = true

See also

Ways to use hyperGraphToSimplicialComplex :

For the programmer

The object hyperGraphToSimplicialComplex is a method function.