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HypergraphPlot[WolframModel[{{1,2,3},{4,2,5}}{{6,3,1},{3,6,4},{1,2,6}},{{0,0,0},{0,0,0}},800,"FinalState"]]
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2^(rLog[r])
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rLog[r]
2
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Plot[{r^2,2^(rLog[r]),r^Sqrt[r],2^r},{r,0,5}]
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AsymptoticLess[r^Sqrt[r],2^(rLog[r]),r->Infinity]
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True
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AsymptoticLess[r,2^(rLog[r]),r->Infinity]
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True
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AsymptoticLess[2^r,2^(rLog[r]),r->Infinity]
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True
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Asymptotic[r^Sqrt[r]/2^(rLog[r]),{r,Infinity,2}]
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-rLog[r]
2
r
r
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Plot[%,{r,0,10}]
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Asymptotic[2^(rLog[r]),{r,Infinity,2}]
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rLog[r]
2
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NeighborhoodGraph[IndexGraph[TorusGraph[{20,20}]],{1},2]
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gr=UndirectedGraph[Rule@@@WolframModel[{{x,y},{x,z}}{{x,z},{x,w},{y,w},{z,w}},{{1,2},{1,3}},10,"FinalState"]]
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With[{gr=UndirectedGraph[Rule@@@WolframModel[{{x,y},{x,z}}{{x,z},{x,w},{y,w},{z,w}},{{1,2},{1,3}},10,"FinalState"]]},ReverseSortBy[(Graph[First[#],GraphLayout"SpringElectricalEmbedding",VertexCoordinatesAutomatic,ImageSize30]->Length[#])&/@Gather[NeighborhoodGraph[gr,#,1]&/@VertexList[gr],IsomorphicGraphQ],Last]]
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With[{gr=UndirectedGraph[Rule@@@WolframModel[{{x,y},{x,z}}{{x,z},{x,w},{y,w},{z,w}},{{1,2},{1,3}},11,"FinalState"]]},ReverseSortBy[(Graph[First[#],GraphLayout"SpringElectricalEmbedding",VertexCoordinatesAutomatic,ImageSize30]->Length[#])&/@Gather[NeighborhoodGraph[gr,#,1]&/@VertexList[gr],IsomorphicGraphQ],Last]]
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With[{gr=UndirectedGraph[Rule@@@WolframModel[{{x,y},{x,z}}{{x,z},{x,w},{y,w},{z,w}},{{1,2},{1,3}},12,"FinalState"]]},ReverseSortBy[(Graph[First[#],GraphLayout"SpringElectricalEmbedding",VertexCoordinatesAutomatic,ImageSize30]->Length[#])&/@Gather[NeighborhoodGraph[gr,#,1]&/@VertexList[gr],IsomorphicGraphQ],Last]]
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With[{gr=UndirectedGraph[Rule@@@WolframModel[{{x,y},{x,z}}{{x,z},{x,w},{y,w},{z,w}},{{1,2},{1,3}},13,"FinalState"]]},ReverseSortBy[(Graph[CanonicalGraph[First[#]],GraphLayout"SpringElectricalEmbedding",VertexCoordinatesAutomatic,ImageSize30]->Length[#])&/@Gather[NeighborhoodGraph[gr,#,1]&/@VertexList[gr],IsomorphicGraphQ],Last]]
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