Definitions
Definitions
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Vols[graph_,start_:All,max_:Automatic]:=MeanAround/@Transpose[Values[ResourceFunction["GraphNeighborhoodVolumes"][graph,start,max]]]
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RandVols[graph_,n_Integer,max_:Automatic]:=Vols[graph,"Random"n,max]
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Dims[vols_]:=ListLinePlotTable[(Log[vols[[r+1]]]-Log[vols[[r]]])/(Log[r+1]-Log[r]),{r,Length[vols]-1}],
Trivial Structures
Trivial Structures
Square (Torus) Grid
Square (Torus) Grid
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Dims[RandVols[TorusGraph[{40,40}],1000]]
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Vols[TorusGraph[{10,10}]]
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{1,5,13,25,41,59,75,87,95,99,100}
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Dims[RandVols[TorusGraph[{200,200}],1000]]
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Dims[RandVols[TorusGraph[{50,50}],1000]]
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Hexagonal Grid & Other Lattices
Hexagonal Grid & Other Lattices
In[]:=
<<IGraphM`;HypergraphPlot[Catenate[Partition[#,3,2,-1]&/@MeshCells[IGLatticeMesh["Hexagonal",Polygon@CirclePoints[3,6],MeshCellLabel{2"Index"}],2][[All,1]]]]
IGraph/M 0.3.112 (May 7, 2019)
Evaluate to get started.
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?IGLatticeMesh
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IGLatticeMesh[]
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{Square,Hexagonal,Triangular,Trihexagonal,SmallRhombitrihexagonal,TruncatedSquare,SnubSquare,TruncatedHexagonal,ElongatedTriangular,GreatRhombitrihexagonal,SnubHexagonal,Rhombille,DeltoidalTrihexagonal,TetrakisSquare,CairoPentagonal,TriakisTriangular,PrismaticPentagonal,BisectedHexagonal,FloretPentagonal,DellaRobbiaWeave,Portugal,StackBond,Herringbone,Basketweave,PersianHexagonalWeave,Hopscotch,StretcherBond,Pinwheel,BrickworkSquare,Chickenwire,Corridor,CorridorHorizontal,Brickweave,Trellis,HeeschIsohedral,PPentomino,Chevron,Shingle,Zigzag,Kite,FalseCubic,TrihexAndHex,GlideReflection,PentagonType1,PentagonType2,PentagonType3,PentagonType4,PentagonType5,PentagonType6,PentagonType7,PentagonType8,PentagonType9,PentagonType10,PentagonType11,PentagonType12,PentagonType13,PentagonType14,PentagonType15}
In[]:=
GraphData["Fullerene"]
(( lots of Fullerenes ... ))
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GraphData[{"Fullerene",{50,244}}]
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GraphData[{"Fullerene",{70,4085}}]
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Known Figures
Known Figures
Pseudosphere
Pseudosphere
Real-Life Graphs
Real-Life Graphs
From First Section
From First Section
[[[[ Max says the volumes grow exponentially Nov 24 10:55 pm ]]]]