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ParallelMapMonitored[With[{w=WolframModelTest[#,Automatic]},{HypergraphPlot[w["FinalState"]],w["EvolutionObject"]["CausalGraph"]}]&,{{{x,y},{x,z}}{{y,z},{y,w},{z,w},{w,x}},{{x,y},{y,z}}{{x,y},{y,x},{w,x},{w,z}},{{x,y},{y,z}}{{w,y},{y,z},{z,w},{x,w}}}]
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Length[WolframModelTest[#,Automatic]["Sizes"]]&/@{{{x,y},{x,z}}{{y,z},{y,w},{z,w},{w,x}},{{x,y},{y,z}}{{x,y},{y,x},{w,x},{w,z}},{{x,y},{y,z}}{{w,y},{y,z},{z,w},{x,w}}}
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{10,8,8}
{{{x,y},{x,z}}{{y,z},{y,w},{z,w},{w,x}},{{x,y},{y,z}}{{x,y},{y,x},{w,x},{w,z}},{{x,y},{y,z}}{{w,y},{y,z},{z,w},{x,w}}}
{{{x,y,z},{x,u,v}}{{x,w,u},{v,w,y},{w,y,z}}
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ParallelMapMonitored[With[{w=WolframModel[#,{{0,0},{0,0}},12]},{HypergraphPlot[w["FinalState"]],LayeredGraphPlot[w["CausalGraph"],AspectRatio1/3],w["CausalGraph"]}]&,{{{x,y},{x,z}}{{y,z},{y,w},{z,w},{w,x}},{{x,y},{y,z}}{{x,y},{y,x},{w,x},{w,z}},{{x,y},{y,z}}{{w,y},{y,z},{z,w},{x,w}}}]
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LayeredGraphPlot[#,AspectRatio1/3]&/@(Last/@%124)
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RuleSignatureForm[{{2,2}}{{4,2}}]
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2
2
4
2
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WolframModel[{{x,y,z},{x,u,v}}{{x,w,u},{v,w,y},{w,y,z}},{{0,0,0},{0,0,0}},1000,"CausalGraph"]
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WolframModel[{{x,x,y},{z,u,x}}{{u,u,z},{v,u,v},{v,y,x}},{{0,0,0},{0,0,0}},2000,"CausalGraph"]
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GraphPlot3D[%]
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Head[%135]
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Graph
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ReconstructedSurface[List@@@EdgeList[%135]]
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3-ary examples
3-ary examples