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DiscreteMath`GraphPlot`

GraphPlotの機能が，新しく加わった組込みの Mathematica カーネル関数GraphPlotおよびLayeredGraphPlotで利用できるようになった．
GraphPlot3Dが新しく加わった組込みの Mathematica カーネル関数GraphPlot3Dで利用できるようになった．
TreePlotが，新しく加わった組込みの Mathematica カーネル関数TreePlotで利用できるようになった．
EdgeStyleFunctionオプションが，新しく加わった組込みの Mathematica カーネルオプションEdgeShapeFunctionとして利用できるようになった．
TreeSizeFunctionオプションが新しく加わった組込みの Mathematica カーネルオプションLayerSizeFunctionとして利用できるようになった．
VertexCoordinatesオプションが新しく加わった組込みの Mathematica カーネルオプションVertexCoordinatesとして利用できるようになった．
VertexStyleFunctionオプションが新しく加わった組込みの Mathematica カーネルオプションVertexShapeFunctionとして利用できるようになった．
RootPositionオプションが組込みの Mathematica カーネル関数TreePlotの第2引数として利用できるようになった．

GraphPlot

規則のリストで指定されたグラフをプロットする：

Version 5.2 << DiscreteMath`GraphPlot`; g = GraphPlot[{2 -> 1, 3 -> 1, 3 -> 2, 4 -> 1, 4 -> 2, 5 -> 1, 5 -> 2}]
Wolfram Language code: g = GraphPlot[{2 -> 1, 3 -> 1, 3 -> 2, 4 -> 1, 4 -> 2, 5 -> 1, 5 -> 2}]

GraphPlot3D

グラフを3Dでレイアウトする：

Version 5.2 << DiscreteMath`GraphPlot`; GraphPlot3D[{2 -> 1, 3 -> 1, 3 -> 2, 4 -> 1, 4 -> 2, 5 -> 1, 5 -> 2}]
Wolfram Language code: GraphPlot3D[{2 -> 1, 3 -> 1, 3 -> 2, 4 -> 1, 4 -> 2, 5 -> 1, 5 -> 2}]

TreePlot

二分木を描画する：

Version 5.2 << DiscreteMath`GraphPlot`; g = Flatten[Table[{i -> 2*i, i -> 2*i + 1}, {i, 2^4 - 1}]] TreePlot[g];
Wolfram Language code: g = Flatten[Table[{i -> 2 * i, i -> 2 * i + 1}, {i, 2 ^ 4 - 1}]] TreePlot[g]

EdgeStyleFunction

EdgeShapeFunctionを使って，辺の描画方法を制御する：

Version 5.2 << DiscreteMath`GraphPlot`; GraphPlot[Table[1, {30}, {30}], EdgeStyleFunction -> ({} &)]
Wolfram Language code: GraphPlot[Table[1, {30}, {30}], EdgeShapeFunction -> None]

辺を矢印として描画する別の方法：

Version 5.2 << DiscreteMath`GraphPlot`; GraphPlot[{1 -> 2, 2 -> 3, 3 -> 4, 4 -> 5, 5 -> 6, 6 -> 7, 7 -> 8, 8 -> 1, 1 -> 9, 2 -> 9, 3 -> 10, 4 -> 10, 6 -> 11, 5 -> 11, 7 -> 12, 8 -> 12}, EdgeStyleFunction -> (Arrow[{#1, #2}] &)];
Wolfram Language code: GraphPlot[{1 -> 2, 2 -> 3, 3 -> 4, 4 -> 5, 5 -> 6, 6 -> 7, 7 -> 8, 8 -> 1, 1 -> 9, 2 -> 9, 3 -> 10, 4 -> 10, 6 -> 11, 5 -> 11, 7 -> 12, 8 -> 12}, EdgeShapeFunction -> (Arrow[#1] &)]
Wolfram Language code: GraphPlot[{1 -> 2, 2 -> 3, 3 -> 4, 4 -> 5, 5 -> 6, 6 -> 7, 7 -> 8, 8 -> 1, 1 -> 9, 2 -> 9, 3 -> 10, 4 -> 10, 6 -> 11, 5 -> 11, 7 -> 12, 8 -> 12}, DirectedEdges -> True]

LayerSizeFunction

二分木を描画する：

Version 5.2 << DiscreteMath`GraphPlot`; g = Flatten[Table[{i -> 2*i, i -> 2*i + 1}, {i, 2^4 - 1}]] TreePlot[g];
Wolfram Language code: g = Flatten[Table[{i -> 2 * i, i -> 2 * i + 1}, {i, 2 ^ 4 - 1}]] TreePlot[g]

以下でも同じグラフを描画するが．各レベルの高さ i が1/i2に比例するようにする：

Version 5.2 << DiscreteMath`GraphPlot`; g = Flatten[Table[{i -> 2*i, i -> 2*i + 1}, {i, 2^4 - 1}]] TreePlot[g, TreeSizeFunction -> (1/#^2 &)];
Wolfram Language code: TreePlot[g, LayerSizeFunction -> (1 / # ^ 2 &)]

VertexCoordinates

VertexCoordinatesを使うと，頂点の座標を明示的に指定することができる：

Version 5.2 << DiscreteMath`GraphPlot`; GraphPlot[{1 -> 3, 1 -> 4, 2 -> 4, 2 -> 5, 3 -> 5, 6 -> 7, 7 -> 8, 8 -> 9, 9 -> 10, 6 -> 10, 1 -> 6, 2 -> 7, 3 -> 8, 4 -> 9, 5 -> 10}, VertexCoordinates -> {{0.309017, 0.951057}, {-0.809017, -0.587785}, {0.309017, -0.951057}, \ {-0.809017, 0.587785}, {1., 0}, {0.618034, 1.90211}, {-1.61803, 1.17557}, {-1.61803, -1.17557}, {0.618034, -1.90211}, {2., 0}}
Wolfram Language code: GraphPlot[{1 -> 3, 1 -> 4, 2 -> 4, 2 -> 5, 3 -> 5, 6 -> 7, 7 -> 8, 8 -> 9, 9 -> 10, 6 -> 10, 1 -> 6, 2 -> 7, 3 -> 8, 4 -> 9, 5 -> 10}, VertexCoordinates -> {{0.309017, 0.951057}, {-0.809017, -0.587785}, {0.309017, -0.951057}, {-0.809017, 0.587785}, {1., 0}, {0.618034, 1.90211}, {-1.61803, 1.17557}, {-1.61803, -1.17557}, {0.618034, -1.90211}, {2., 0}}]

VertexStyleFunction

VertexShapeFunctionを使うと頂点の描画方法が制御できる．以下では頂点を描画しない：

Version 5.2 << DiscreteMath`GraphPlot`; GraphPlot[{1 -> 2, 2 -> 3, 3 -> 4, 4 -> 5, 5 -> 6, 6 -> 1}, VertexStyleFunction -> ({} &)]
Wolfram Language code: GraphPlot[{1 -> 2, 2 -> 3, 3 -> 4, 4 -> 5, 5 -> 6, 6 -> 1}, VertexShapeFunction -> None]

ここでは青い大きい頂点を描画する：

Version 5.2 << DiscreteMath`GraphPlot`; GraphPlot[{1 -> 2, 1 -> 3, 1 -> 4, 2 -> 3, 2 -> 4, 3 -> 5, 4 -> 6, 5 -> 7, 5 -> 8, 6 -> 7, 6 -> 8, 7 -> 8}, VertexStyleFunction -> ({Hue[0], Disk[#, 0.03]} &)];
Wolfram Language code: GraphPlot[{1 -> 2, 1 -> 3, 1 -> 4, 2 -> 3, 2 -> 4, 3 -> 5, 4 -> 6, 5 -> 7, 5 -> 8, 6 -> 7, 6 -> 8, 7 -> 8}, VertexShapeFunction -> ({Hue[.7], Disk[#, 0.05]} &)]

RootPosition （TreePlotの引数）

根を左側に置いて木をプロットする：

Version 5.2 << DiscreteMath`GraphPlot`; TreePlot[{1 -> 2, 2 -> 4, 3 -> 6, 4 -> 8, 5 -> 10, 6 -> 12, 1 -> 3, 2 -> 5, 3 -> 7, 4 -> 9, 5 -> 11, 6 -> 13}, RootPosition -> Left]
Wolfram Language code: TreePlot[{1 -> 2, 2 -> 4, 3 -> 6, 4 -> 8, 5 -> 10, 6 -> 12, 1 -> 3, 2 -> 5, 3 -> 7, 4 -> 9, 5 -> 11, 6 -> 13}, Left]
GraphPlot

DiscreteMath`GraphPlot`の関数の多くが組込みの Mathematica カーネル関数として利用できるようになった．

以下では37個の頂点を持つグラフをプロットする：

Version 5.2 << DiscreteMath`GraphPlot`; GraphPlot[\!\(\* TagBox[ RowBox[{"g", "=", RowBox[{"{", RowBox[{ RowBox[{"1", "->", "2"}], ",", RowBox[{"1", "->", "6"}], ",", RowBox[{"1", "->", "7"}], ",", RowBox[{"2", "->", "3"}], ",", RowBox[{"2", "->", "7"}], ",", RowBox[{"3", "->", "30"}], ",", RowBox[{"3", "->", "26"}], ",", RowBox[{"3", "->", "4"}], ",", RowBox[{"3", "->", "32"}], ",", RowBox[{"4", "->", "5"}], ",", RowBox[{"4", "->", "9"}], ",", RowBox[{"5", "->", "9"}], ",", RowBox[{"5", "->", "10"}], ",", RowBox[{"6", "->", "7"}], ",", RowBox[{"6", "->", "11"}], ",", RowBox[{"7", "->", "8"}], ",", RowBox[{"7", "->", "30"}], ",", RowBox[{"7", "->", "12"}], ",", RowBox[{"8", "->", "9"}], ",", RowBox[{"8", "->", "26"}], ",", RowBox[{"8", "->", "13"}], ",", RowBox[{"9", "->", "10"}], ",", RowBox[{"9", "->", "32"}], ",", RowBox[{"9", "->", "14"}], ",", RowBox[{"10", "->", "15"}], ",", RowBox[{"11", "->", "16"}], ",", RowBox[{"11", "->", "27"}], ",", RowBox[{"11", "->", "30"}], ",", RowBox[{"11", "->", "35"}], ",", RowBox[{"12", "->", "13"}], ",", RowBox[{"12", "->", "17"}], ",", RowBox[{"12", "->", "27"}], ",", RowBox[{"13", "->", "31"}], ",", RowBox[{"13", "->", "33"}], ",", RowBox[{"13", "->", "14"}], ",", RowBox[{"13", "->", "36"}], ",", RowBox[{"13", "->", "18"}], ",", RowBox[{"13", "->", "34"}], ",", RowBox[{"14", "->", "28"}], ",", RowBox[{"14", "->", "19"}], ",", RowBox[{"15", "->", "32"}], ",", RowBox[{"15", "->", "28"}], ",", RowBox[{"15", "->", "37"}], ",", RowBox[{"15", "->", "20"}], ",", RowBox[{"16", "->", "17"}], ",", RowBox[{"16", "->", "21"}], ",", RowBox[{"17", "->", "21"}], ",", RowBox[{"17", "->", "22"}], ",", RowBox[{"17", "->", "35"}], ",", RowBox[{"17", "->", "18"}], ",", RowBox[{"18", "->", "19"}], ",", RowBox[{"18", "->", "29"}], ",", RowBox[{"19", "->", "37"}], ",", RowBox[{"19", "->", "20"}], ",", RowBox[{"19", "->", "24"}], ",", RowBox[{"19", "->", "25"}], ",", RowBox[{"20", "->", "25"}], ",", RowBox[{"21", "->", "22"}], ",", RowBox[{"22", "->", "23"}], ",", RowBox[{"23", "->", "24"}], ",", RowBox[{"23", "->", "29"}], ",", RowBox[{"23", "->", "35"}], ",", RowBox[{"23", "->", "37"}], ",", RowBox[{"24", "->", "25"}], ",", RowBox[{"30", "->", "31"}], ",", RowBox[{"32", "->", "33"}], ",", RowBox[{"34", "->", "35"}], ",", RowBox[{"36", "->", "37"}]}], "}"}]}], Short[#, 1000]& ]\), VertexStyleFunction -> Automatic];
Wolfram Language code: GraphPlot[g = {1 -> 2, 1 -> 6, 1 -> 7, 2 -> 3, 2 -> 7, 3 -> 30, 3 -> 26, 3 -> 4, 3 -> 32, 4 -> 5, 4 -> 9, 5 -> 9, 5 -> 10, 6 -> 7, 6 -> 11, 7 -> 8, 7 -> 30, 7 -> 12, 8 -> 9, 8 -> 26, 8 -> 13, 9 -> 10, 9 -> 32, 9 -> 14, 10 -> 15, 11 -> 16, 11 -> 27, 11 -> 30, 11 -> 35, 12 -> 13, 12 -> 17, 12 -> 27, 13 -> 31, 13 -> 33, 13 -> 14, 13 -> 36, 13 -> 18, 13 -> 34, 14 -> 28, 14 -> 19, 15 -> 32, 15 -> 28, 15 -> 37, 15 -> 20, 16 -> 17, 16 -> 21, 17 -> 21, 17 -> 22, 17 -> 35, 17 -> 18, 18 -> 19, 18 -> 29, 19 -> 37, 19 -> 20, 19 -> 24, 19 -> 25, 20 -> 25, 21 -> 22, 22 -> 23, 23 -> 24, 23 -> 29, 23 -> 35, 23 -> 37, 24 -> 25, 30 -> 31, 32 -> 33, 34 -> 35, 36 -> 37}]

グラフの直径を計算する：

Version 5.2 << DiscreteMath`GraphPlot`; ug = Join[g, Reverse /@ g]; PseudoDiameter[ug]
Wolfram Language code: ug = Join[g, Reverse /@ g]; GraphDiameter[ug]

頂点1と頂点25の間の距離を計算する：

Version 5.2 << DiscreteMath`GraphPlot`; GraphDistance[ug, 1, 25]
Wolfram Language code: GraphDistance[ug, 1, 25]