WOLFRAM NOTEBOOK

Graph Layout Requirements for SetReplace

Quit
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<<SetReplace`
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$SetReplaceGitSHA
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058a7e03c07eaed2b3b2cb82ed4d14617f970b01

RulePlot

RulePlot works by plotting one of the sides first, and then using the constraints for that side to layout the other side.
The problem: this produces suboptimal results in some cases:
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RulePlot[WolframModel[{{1,2},{1,3},{1,4}}{{2,2},{2,2},{2,5},{3,2}}]]
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This is due to the fact that the scale of the spring (i.e., the distance two vertices are from one another in a single-edge two vertex graph) is not fixed with respect to coordinates.
I.e., the following does not push the middle vertex out of the way as one would expect:
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Graph[{12,23},VertexCoordinates{1{0,0},3{#,0}}]&/@{1/1000000,1,1000000}
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“HyperedgeRendering” “Branes”

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Quit
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<<SetReplace`
Using 664b855b41f081b89b518ec306b7bbffe1dd1d70.
Similar issue happens with branes. Single graphs work fine (because one giant graph containing everything is made and constraints are never used).
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HypergraphPlot[{{1,1,1},{1,2,3},{3,3,3}},"HyperedgeRendering""Branes"]
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But RulePlot does not work:
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RulePlot[WolframModel[{{1,2,2},{2,3,4}}{{1,1,4},{5,4,4},{4,3,5}}],FrameFalse,"HyperedgeRendering""Branes"]
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Notice that all of the vertices on the right-hand side are bunched up together. This is unavoidable, as no matter the distance between them, they will always be bunched up. The only way around that is to be able to specify the string scale.
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HypergraphPlot[{{1,1,4},{5,4,4},{4,3,5}},"HyperedgeRendering""Branes"]
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Joint Embedding [consistent plots of subsequent steps]

Joint embedding is the embedding of multiple graphs such that the shared vertices take the same positions.
This is both useful for RulePlot, and for displaying subsequent steps of the evolution.
One possibility is to have a version of “SpringElectricalEmbedding” where the spring force is still enabled for all edges, but the electrical force is only enabled between the vertices that appear in the same hypergraph.
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