WOLFRAM NOTEBOOK

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Graph[WolframModel[{{x,y},{z,y}}{{x,z},{y,z},{w,z}},{{0,0},{0,0}},10,"LayeredCausalGraph"],VertexLabelsAutomatic,PerformanceGoal"Quality"]
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Graph[WolframModel[{{x,y},{z,y}}{{x,z},{y,z},{w,z}},{{0,0},{0,0}},12,"CausalGraph"],VertexLabelsAutomatic]//LayeredGraphPlot
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NeighborhoodGraph[Graph[WolframModel[{{x,y},{z,y}}{{x,z},{y,z},{w,z}},{{0,0},{0,0}},16,"CausalGraph","EventOrderingFunction""Random"],VertexLabelsAutomatic],{1},2]//LayeredGraphPlot
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Table[NeighborhoodGraph[Graph[WolframModel[{{x,y},{z,y}}{{x,z},{y,z},{w,z}},{{0,0},{0,0}},20,"CausalGraph","EventOrderingFunction""Random"],VertexLabelsAutomatic],{1},2]//LayeredGraphPlot,5]
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Table[NeighborhoodGraph[Graph[WolframModel[{{x,y},{z,y}}{{x,z},{y,z},{w,z}},{{0,0},{0,0}},5,"CausalGraph","EventOrderingFunction""Random"],VertexLabelsAutomatic],{1},2]//LayeredGraphPlot,5]
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Graph[WolframModel[{{x,y},{z,y}}{{x,z},{y,z},{w,z}},{{0,0},{0,0}},12,"CausalGraph","EventOrderingFunction""Random"],VertexLabelsAutomatic]//LayeredGraphPlot
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A Different Rule

DrawFoliations

For generations, one must use the longest distance from the root

Shortest path foliation [ it is not a foliation ]

find other foliations

Note: this rendering “sorts in time”, because all arrows are pointing down.
In a valid causal foliation, the leaves cannot cross.....

Sequence of leaves in a causal foliation corresponds to a path in the multiway system (?)

In other words, every evolution history defines a set of spacelike hypersurfaces (?)

What is a valid foliation sequence?

We could look at “valid updating orders” which have the property that they respect the partial ordering....

What happens in a trivial “diamond” graph

The partial order criterion is .....

Total orders

Comparability graphs (?)

Join spacelike separated nodes

Multiway Graph

Any particular causal graph contains some subset of these events
Any particular path defines a single sequence of events

Can a causal graph have closed timeline curves?

(Maybe due to accidental isomorphism?)

Non-overlapping multiway graph

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