RulePlot[WolframModel[{{1,2,3,4}}{{1,4,6},{2,5,4},{3,6,5}}]]
Out[]=
HypergraphPlot@WolframModel[{{1,2,3}}{{6,1,4},{2,4,5},{6,3,5}},{{1,2,3}},3,"FinalState"]
Out[]=
Table[RandomSample/@{{6,1,4},{2,4,5},{6,3,5}},6]
In[]:=
Out[]=
DeleteDuplicates[Table[RandomSample/@{{6,1,4},{2,4,5},{6,3,5}},6]]
In[]:=
Out[]=
HypergraphPlot@WolframModel[{{1,2,3}}#,{{1,2,3}},3,"FinalState"]&/@%
In[]:=
Out[]=
HypergraphPlot@WolframModel[{{1,2,3}}#,{{1,2,3}},3,"FinalState"]&/@%
In[]:=
Out[]=
DeleteDuplicates[{{{6,4,1},{2,5,4},{5,6,3}},{{6,1,4},{5,2,4},{6,3,5}},{{6,4,1},{4,5,2},{5,3,6}},{{1,6,4},{4,2,5},{3,6,5}},{{4,1,6},{5,2,4},{5,3,6}},{{6,1,4},{2,4,5},{6,3,5}}}]
In[]:=
Out[]=
{{6,1,4},{2,4,5},{6,3,5}}
GridGraph[{2,2,2}]
In[]:=
Out[]=
EdgeList[%]
In[]:=
{12,13,15,24,26,34,37,48,56,57,68,78}
Out[]=
List@@@%
In[]:=
{{1,2},{1,3},{1,5},{2,4},{2,6},{3,4},{3,7},{4,8},{5,6},{5,7},{6,8},{7,8}}
Out[]=
Rest/@TableVertexOutComponent
,i,1,{i,8}
In[]:=
{{2,3,5},{1,4,6},{1,4,7},{2,3,8},{1,6,7},{2,5,8},{3,5,8},{4,6,7}}
Out[]=
HypergraphPlot/@WolframModel[{{1,2,3}}->{{2,3,5},{1,4,6},{1,4,7},{2,3,8},{1,6,7},{2,5,8},{3,5,8},{4,6,7}},{{1,2,3}},3,"StatesList"]
In[]:=
Out[]=
​
GraphData["TetrahedralGraph"]
In[]:=
Out[]=
EdgeList[%]
In[]:=
{12,13,14,23,24,34}
Out[]=
List@@@%
In[]:=
{{1,2},{1,3},{1,4},{2,3},{2,4},{3,4}}
Out[]=
Rest/@TableVertexOutComponent
,i,1,{i,4}
In[]:=
{{2,3,4},{1,3,4},{1,2,4},{1,2,3}}
Out[]=
GraphPlot[SimpleGraph[HypergraphToGraph[#]]]&/@WolframModel[{{1,2,3}}{{1,4,6},{2,5,4},{3,6,5}},{{2,3,4},{1,3,4},{1,2,4},{1,2,3}},4,"StatesList"]
In[]:=
Out[]=
VertexReplace
{1->{2,3,4},2->{1,3,4},3->{1,2,4},4->{1,2,3}}
In[]:=
{1{2,3,4},2{1,3,4},3{1,2,4},4{1,2,3}}/.RuleTwoWayRule
In[]:=
{1{2,3,4},2{1,3,4},3{1,2,4},4{1,2,3}}
Out[]=
SimpleGraph[Flatten[Thread/@#]]&/@NestList[Flatten[#/.(x_<->{a_,b_,c_}):>Module[{ap,bp,cp},{ap{a,bp,cp},bp{ap,b,cp},cp{ap,bp,c}}]]&,{1{2,3,4},2{1,3,4},3{1,2,4},4{1,2,3}},3]
In[]:=
Out[]=
Thread/@{1{2,3,4},2{1,3,4},3{1,2,4},4{1,2,3}}
In[]:=
{{12,13,14},{21,23,24},{31,32,34},{41,42,43}}
Out[]=
Graph
,GraphLayout#&/@{"BipartiteEmbedding","CircularEmbedding","CircularMultipartiteEmbedding","DiscreteSpiralEmbedding","GridEmbedding","LinearEmbedding","MultipartiteEmbedding","SpiralEmbedding","StarEmbedding","BalloonEmbedding","RadialEmbedding","LayeredDigraphEmbedding","LayeredEmbedding","GravityEmbedding","HighDimensionalEmbedding","PlanarEmbedding","SpectralEmbedding","SpringElectricalEmbedding","SpringEmbedding","TutteEmbedding"}
In[]:=
Out[]=
{{6,1,4},{2,4,5},{6,3,5}}
Graph[Rule@@@{{6,4},{5,4},{6,5}}]
In[]:=
Out[]=
4+{{2,3,4},{1,3,4},{1,2,4},{1,2,3}}
In[]:=
{{6,7,8},{5,7,8},{5,6,8},{5,6,7}}
Out[]=
HypergraphPlot/@WolframModel[{{1,2,3,4}}{{1,6,7,8},{2,5,7,8},{3,5,6,8},{4,5,6,7}},{{1,2,3,4}},3,"StatesList"]
In[]:=
Out[]=
GraphPlot3D[SimpleGraph[HypergraphToGraph[#],GraphLayout->"SpringElectricalEmbedding"]]&/@WolframModel[{{1,2,3,4}}{{1,6,7,8},{2,5,7,8},{3,5,6,8},{4,5,6,7}},{{1,2,3,4}},3,"StatesList"]
In[]:=
Out[]=
{5,6,7,8}

4-ary edges

HypergraphPlot/@WolframModel[{{1,2,3,4}}{{2,5,6,7},{3,6,7,8},{4,7,8,5},{1,8,5,6}},{{1,2,3,4}},3,"StatesList"]
In[]:=
Out[]=
{{1,2,3,4}}{{2,5,6,7},{3,6,7,8},{4,7,8,5},{1,8,5,6}}
RulePlot[WolframModel[{{1,2},{2,3},{3,4},{4,1}}{{1,5},{5,2},{2,6},{6,3},{3,7},{7,4},{4,8},{8,1},{8,9},{5,9},{6,9},{7,9},{9,7},{9,8},{9,5},{9,6}}],VertexLabelsAutomatic]
In[]:=
Out[]=
Out[]=
RulePlot[WolframModel[{{1,2},{2,3},{3,1}}{{1,2},{2,3},{3,1},{1,5},{2,5},{3,5}}],VertexLabelsAutomatic]
In[]:=
Out[]=
Graph[Rule@@@#]&/@WolframModel[{{1,2},{2,3},{3,1}}{{1,2},{2,3},{3,1},{1,5},{2,5},{3,5}},{{1,2},{2,3},{3,1}},6,"StatesList"]
In[]:=
Out[]=
Graph[Rule@@@#]&/@WolframModel[{{1,2},{2,3},{3,1}}{{1,2},{2,3},{3,1},{1,5},{5,1},{2,5},{5,2},{3,5},{5,3}},{{1,2},{2,3},{3,1}},6,"StatesList"]
In[]:=
Out[]=