Wolfram
Mathematica
8의 신기능: 그래프 및 네트워크 분석
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응용 분야
독립 에지 집합
최대 독립 변 모음으로 누구와 결혼해야 할지 알아 봅니다.
In[1]:=
X
g = \!\(\* GraphicsBox[ NamespaceBox["NetworkGraphics", DynamicModuleBox[{Typeset`graph = HoldComplete[ Graph[{"Rudy", "Oscar", "Michael", "Larry", "John", "James", "David", "Ben", "Nora", "Nancy", "Linda", "Julia", "Felicia", "Elisabeth", "Dorothy", "Carol", "Arlene", "Anna"}, { Null, {{7, 10}, {4, 11}, {1, 18}, {6, 17}, {4, 14}, {2, 16}, {2, 12}, {4, 18}, {6, 13}, {8, 15}, {5, 15}, {4, 15}, { 3, 18}, {7, 17}, {8, 9}, {7, 11}, {5, 16}, {4, 10}, {6, 10}, {3, 17}}}, {EdgeStyle -> { Thickness[Large]}, ImageSize -> {350, Automatic}, PlotRange -> {{-0.2, 1.3}, {-0.6, 0.6}}, VertexCoordinates -> {{0., -0.4153465511805146}, { 0., -0.29667610798608185`}, {0., -0.17800566479164912`}, { 0., -0.059335221597216374`}, {0., 0.059335221597216374`}, { 0., 0.17800566479164912`}, {0., 0.29667610798608185`}, {0., 0.4153465511805146}, {1., -0.5340169943749473}, { 1., -0.4153465511805146}, {1., -0.29667610798608185`}, { 1., -0.17800566479164912`}, {1., -0.059335221597216374`}, { 1., 0.059335221597216374`}, {1., 0.17800566479164912`}, { 1., 0.29667610798608185`}, {1., 0.4153465511805146}, {1., 0.5340169943749473}}, VertexLabels -> {"Nancy" -> Placed[ Style["Nancy", FontFamily -> "Verdana"], After], "Michael" -> Placed[ Style["Michael", FontFamily -> "Verdana"], Before], "Oscar" -> Placed[ Style["Oscar", FontFamily -> "Verdana"], Before], "David" -> Placed[ Style["David", FontFamily -> "Verdana"], Before], "Rudy" -> Placed[ Style["Rudy", FontFamily -> "Verdana"], Before], "Larry" -> Placed[ Style["Larry", FontFamily -> "Verdana"], Before], "Arlene" -> Placed[ Style["Arlene", FontFamily -> "Verdana"], After], "James" -> Placed[ Style["James", FontFamily -> "Verdana"], Before], "Anna" -> Placed[ Style["Anna", FontFamily -> "Verdana"], After], "John" -> Placed[ Style["John", FontFamily -> "Verdana"], Before], "Felicia" -> Placed[ Style["Felicia", FontFamily -> "Verdana"], After], "Linda" -> Placed[ Style["Linda", FontFamily -> "Verdana"], After], "Nora" -> Placed[ Style["Nora", FontFamily -> "Verdana"], After], "Julia" -> Placed[ Style["Julia", FontFamily -> "Verdana"], After], "Dorothy" -> Placed[ Style["Dorothy", FontFamily -> "Verdana"], After], "Carol" -> Placed[ Style["Carol", FontFamily -> "Verdana"], After], "Ben" -> Placed[ Style["Ben", FontFamily -> "Verdana"], Before], "Elisabeth" -> Placed[ Style["Elisabeth", FontFamily -> "Verdana"], After]}, VertexSize -> {Large}}]], Typeset`boxes = GraphicsGroupBox[{{ Directive[ Hue[0.6, 0.2, 0.8], EdgeForm[ Directive[ GrayLevel[0], Opacity[0.7]]]], TagBox[{ TagBox[ DiskBox[{0., -0.4153465511805146}, 0.02373408863888654], "DynamicName", BoxID -> "VertexID$1"], InsetBox[ FormBox[ StyleBox["\"Rudy\"", FontFamily -> "Verdana", StripOnInput -> False], TraditionalForm], Offset[{-2, 0}, DynamicLocation["VertexID$1", Automatic, Left]], ImageScaled[{1, 0.5}], BaseStyle -> "Graphics"]}, "DynamicName", BoxID -> "VertexLabelID$1"], TagBox[{ TagBox[ DiskBox[{0., -0.29667610798608185`}, 0.02373408863888654], "DynamicName", BoxID -> "VertexID$2"], InsetBox[ FormBox[ StyleBox["\"Oscar\"", FontFamily -> "Verdana", StripOnInput -> False], TraditionalForm], Offset[{-2, 0}, DynamicLocation["VertexID$2", Automatic, Left]], ImageScaled[{1, 0.5}], BaseStyle -> "Graphics"]}, "DynamicName", BoxID -> "VertexLabelID$2"], TagBox[{ TagBox[ DiskBox[{0., -0.17800566479164912`}, 0.02373408863888654], "DynamicName", BoxID -> "VertexID$3"], InsetBox[ FormBox[ StyleBox["\"Michael\"", FontFamily -> "Verdana", StripOnInput -> False], TraditionalForm], Offset[{-2, 0}, DynamicLocation["VertexID$3", Automatic, Left]], ImageScaled[{1, 0.5}], BaseStyle -> "Graphics"]}, "DynamicName", BoxID -> "VertexLabelID$3"], TagBox[{ TagBox[ DiskBox[{0., -0.059335221597216374`}, 0.02373408863888654], "DynamicName", BoxID -> "VertexID$4"], InsetBox[ FormBox[ StyleBox["\"Larry\"", FontFamily -> "Verdana", StripOnInput -> False], TraditionalForm], Offset[{-2, 0}, DynamicLocation["VertexID$4", Automatic, Left]], ImageScaled[{1, 0.5}], BaseStyle -> "Graphics"]}, "DynamicName", BoxID -> "VertexLabelID$4"], TagBox[{ TagBox[ DiskBox[{0., 0.059335221597216374`}, 0.02373408863888654], "DynamicName", BoxID -> "VertexID$5"], InsetBox[ FormBox[ StyleBox["\"John\"", FontFamily -> "Verdana", StripOnInput -> False], TraditionalForm], Offset[{-2, 0}, DynamicLocation["VertexID$5", Automatic, Left]], ImageScaled[{1, 0.5}], BaseStyle -> "Graphics"]}, "DynamicName", BoxID -> "VertexLabelID$5"], TagBox[{ TagBox[ DiskBox[{0., 0.17800566479164912`}, 0.02373408863888654], "DynamicName", BoxID -> "VertexID$6"], InsetBox[ FormBox[ StyleBox["\"James\"", FontFamily -> "Verdana", StripOnInput -> False], TraditionalForm], Offset[{-2, 0}, DynamicLocation["VertexID$6", Automatic, Left]], ImageScaled[{1, 0.5}], BaseStyle -> "Graphics"]}, "DynamicName", BoxID -> "VertexLabelID$6"], TagBox[{ TagBox[ DiskBox[{0., 0.29667610798608185`}, 0.02373408863888654], "DynamicName", BoxID -> "VertexID$7"], InsetBox[ FormBox[ StyleBox["\"David\"", FontFamily -> "Verdana", StripOnInput -> False], TraditionalForm], Offset[{-2, 0}, DynamicLocation["VertexID$7", Automatic, Left]], ImageScaled[{1, 0.5}], BaseStyle -> "Graphics"]}, "DynamicName", BoxID -> "VertexLabelID$7"], TagBox[{ TagBox[ DiskBox[{0., 0.4153465511805146}, 0.02373408863888654], "DynamicName", BoxID -> "VertexID$8"], InsetBox[ FormBox[ StyleBox["\"Ben\"", FontFamily -> "Verdana", StripOnInput -> False], TraditionalForm], Offset[{-2, 0}, DynamicLocation["VertexID$8", Automatic, Left]], ImageScaled[{1, 0.5}], BaseStyle -> "Graphics"]}, "DynamicName", BoxID -> "VertexLabelID$8"], TagBox[{ TagBox[ DiskBox[{1., -0.5340169943749473}, 0.02373408863888654], "DynamicName", BoxID -> "VertexID$9"], InsetBox[ FormBox[ StyleBox["\"Nora\"", FontFamily -> "Verdana", StripOnInput -> False], TraditionalForm], Offset[{2, 0}, DynamicLocation["VertexID$9", Automatic, Right]], ImageScaled[{0, 0.5}], BaseStyle -> "Graphics"]}, "DynamicName", BoxID -> "VertexLabelID$9"], TagBox[{ TagBox[ DiskBox[{1., -0.4153465511805146}, 0.02373408863888654], "DynamicName", BoxID -> "VertexID$10"], InsetBox[ FormBox[ StyleBox["\"Nancy\"", FontFamily -> "Verdana", StripOnInput -> False], TraditionalForm], Offset[{2, 0}, DynamicLocation["VertexID$10", Automatic, Right]], ImageScaled[{0, 0.5}], BaseStyle -> "Graphics"]}, "DynamicName", BoxID -> "VertexLabelID$10"], TagBox[{ TagBox[ DiskBox[{1., -0.29667610798608185`}, 0.02373408863888654], "DynamicName", BoxID -> "VertexID$11"], InsetBox[ FormBox[ StyleBox["\"Linda\"", FontFamily -> "Verdana", StripOnInput -> False], TraditionalForm], Offset[{2, 0}, DynamicLocation["VertexID$11", Automatic, Right]], ImageScaled[{0, 0.5}], BaseStyle -> "Graphics"]}, "DynamicName", BoxID -> "VertexLabelID$11"], TagBox[{ TagBox[ DiskBox[{1., -0.17800566479164912`}, 0.02373408863888654], "DynamicName", BoxID -> "VertexID$12"], InsetBox[ FormBox[ StyleBox["\"Julia\"", FontFamily -> "Verdana", StripOnInput -> False], TraditionalForm], Offset[{2, 0}, DynamicLocation["VertexID$12", Automatic, Right]], ImageScaled[{0, 0.5}], BaseStyle -> "Graphics"]}, "DynamicName", BoxID -> "VertexLabelID$12"], TagBox[{ TagBox[ DiskBox[{1., -0.059335221597216374`}, 0.02373408863888654], "DynamicName", BoxID -> "VertexID$13"], InsetBox[ FormBox[ StyleBox["\"Felicia\"", FontFamily -> "Verdana", StripOnInput -> False], TraditionalForm], Offset[{2, 0}, DynamicLocation["VertexID$13", Automatic, Right]], ImageScaled[{0, 0.5}], BaseStyle -> "Graphics"]}, "DynamicName", BoxID -> "VertexLabelID$13"], TagBox[{ TagBox[ DiskBox[{1., 0.059335221597216374`}, 0.02373408863888654], "DynamicName", BoxID -> "VertexID$14"], InsetBox[ FormBox[ StyleBox["\"Elisabeth\"", FontFamily -> "Verdana", StripOnInput -> False], TraditionalForm], Offset[{2, 0}, DynamicLocation["VertexID$14", Automatic, Right]], ImageScaled[{0, 0.5}], BaseStyle -> "Graphics"]}, "DynamicName", BoxID -> "VertexLabelID$14"], TagBox[{ TagBox[ DiskBox[{1., 0.17800566479164912`}, 0.02373408863888654], "DynamicName", BoxID -> "VertexID$15"], InsetBox[ FormBox[ StyleBox["\"Dorothy\"", FontFamily -> "Verdana", StripOnInput -> False], TraditionalForm], Offset[{2, 0}, DynamicLocation["VertexID$15", Automatic, Right]], ImageScaled[{0, 0.5}], BaseStyle -> "Graphics"]}, "DynamicName", BoxID -> "VertexLabelID$15"], TagBox[{ TagBox[ DiskBox[{1., 0.29667610798608185`}, 0.02373408863888654], "DynamicName", BoxID -> "VertexID$16"], InsetBox[ FormBox[ StyleBox["\"Carol\"", FontFamily -> "Verdana", StripOnInput -> False], TraditionalForm], Offset[{2, 0}, DynamicLocation["VertexID$16", Automatic, Right]], ImageScaled[{0, 0.5}], BaseStyle -> "Graphics"]}, "DynamicName", BoxID -> "VertexLabelID$16"], TagBox[{ TagBox[ DiskBox[{1., 0.4153465511805146}, 0.02373408863888654], "DynamicName", BoxID -> "VertexID$17"], InsetBox[ FormBox[ StyleBox["\"Arlene\"", FontFamily -> "Verdana", StripOnInput -> False], TraditionalForm], Offset[{2, 0}, DynamicLocation["VertexID$17", Automatic, Right]], ImageScaled[{0, 0.5}], BaseStyle -> "Graphics"]}, "DynamicName", BoxID -> "VertexLabelID$17"], TagBox[{ TagBox[ DiskBox[{1., 0.5340169943749473}, 0.02373408863888654], "DynamicName", BoxID -> "VertexID$18"], InsetBox[ FormBox[ StyleBox["\"Anna\"", FontFamily -> "Verdana", StripOnInput -> False], TraditionalForm], Offset[{2, 0}, DynamicLocation["VertexID$18", Automatic, Right]], ImageScaled[{0, 0.5}], BaseStyle -> "Graphics"]}, "DynamicName", BoxID -> "VertexLabelID$18"]}, { Directive[ Opacity[0.7], Hue[0.6, 0.7, 0.5]], Thickness[Large], StyleBox[ LineBox[{ DynamicLocation["VertexID$1", Automatic, Center], DynamicLocation["VertexID$18", Automatic, Center]}], Thickness[Large], StripOnInput -> False], StyleBox[ LineBox[{ DynamicLocation["VertexID$2", Automatic, Center], DynamicLocation["VertexID$16", Automatic, Center]}], Thickness[Large], StripOnInput -> False], StyleBox[ LineBox[{ DynamicLocation["VertexID$2", Automatic, Center], DynamicLocation["VertexID$12", Automatic, Center]}], Thickness[Large], StripOnInput -> False], StyleBox[ LineBox[{ DynamicLocation["VertexID$3", Automatic, Center], DynamicLocation["VertexID$18", Automatic, Center]}], Thickness[Large], StripOnInput -> False], StyleBox[ LineBox[{ DynamicLocation["VertexID$3", Automatic, Center], DynamicLocation["VertexID$17", Automatic, Center]}], Thickness[Large], StripOnInput -> False], StyleBox[ LineBox[{ DynamicLocation["VertexID$4", Automatic, Center], DynamicLocation["VertexID$11", Automatic, Center]}], Thickness[Large], StripOnInput -> False], StyleBox[ LineBox[{ DynamicLocation["VertexID$4", Automatic, Center], DynamicLocation["VertexID$14", Automatic, Center]}], Thickness[Large], StripOnInput -> False], StyleBox[ LineBox[{ DynamicLocation["VertexID$4", Automatic, Center], DynamicLocation["VertexID$18", Automatic, Center]}], Thickness[Large], StripOnInput -> False], StyleBox[ LineBox[{ DynamicLocation["VertexID$4", Automatic, Center], DynamicLocation["VertexID$15", Automatic, Center]}], Thickness[Large], StripOnInput -> False], StyleBox[ LineBox[{ DynamicLocation["VertexID$4", Automatic, Center], DynamicLocation["VertexID$10", Automatic, Center]}], Thickness[Large], StripOnInput -> False], StyleBox[ LineBox[{ DynamicLocation["VertexID$5", Automatic, Center], DynamicLocation["VertexID$15", Automatic, Center]}], Thickness[Large], StripOnInput -> False], StyleBox[ LineBox[{ DynamicLocation["VertexID$5", Automatic, Center], DynamicLocation["VertexID$16", Automatic, Center]}], Thickness[Large], StripOnInput -> False], StyleBox[ LineBox[{ DynamicLocation["VertexID$6", Automatic, Center], DynamicLocation["VertexID$17", Automatic, Center]}], Thickness[Large], StripOnInput -> False], StyleBox[ LineBox[{ DynamicLocation["VertexID$6", Automatic, Center], DynamicLocation["VertexID$13", Automatic, Center]}], Thickness[Large], StripOnInput -> False], StyleBox[ LineBox[{ DynamicLocation["VertexID$6", Automatic, Center], DynamicLocation["VertexID$10", Automatic, Center]}], Thickness[Large], StripOnInput -> False], StyleBox[ LineBox[{ DynamicLocation["VertexID$7", Automatic, Center], DynamicLocation["VertexID$10", Automatic, Center]}], Thickness[Large], StripOnInput -> False], StyleBox[ LineBox[{ DynamicLocation["VertexID$7", Automatic, Center], DynamicLocation["VertexID$17", Automatic, Center]}], Thickness[Large], StripOnInput -> False], StyleBox[ LineBox[{ DynamicLocation["VertexID$7", Automatic, Center], DynamicLocation["VertexID$11", Automatic, Center]}], Thickness[Large], StripOnInput -> False], StyleBox[ LineBox[{ DynamicLocation["VertexID$8", Automatic, Center], DynamicLocation["VertexID$15", Automatic, Center]}], Thickness[Large], StripOnInput -> False], StyleBox[ LineBox[{ DynamicLocation["VertexID$8", Automatic, Center], DynamicLocation["VertexID$9", Automatic, Center]}], Thickness[Large], StripOnInput -> False]}}]}, DynamicBox[GraphComputation`NetworkGraphicsBox[ 1, Typeset`graph, Typeset`boxes], { CachedValue :> Typeset`boxes, SingleEvaluation -> True, SynchronousUpdating -> False, TrackedSymbols :> {}}, ImageSizeCache->{{-3.8712873490735333`, 339.5379540157402}, {-133.60396535415438`, 129.60396535415444`}}]]], DefaultBaseStyle->{ "NetworkGraphics", FrontEnd`GraphicsHighlightColor -> Hue[0.8, 1., 0.6]}, FrameTicks->None, ImageSize->{350, Automatic}, PlotRange->{{-0.2, 1.3}, {-0.6, 0.6}}]\);
In[2]:=
X
colorHighlight[edges_] := HighlightGraph[g, Flatten[{Complement[VertexList[g], Join @@ (List @@@ edges)], Table[edges[[ i]] /. {e : _[a_, b_] :> (Style[#, ColorData["Rainbow"][i/Length[edges]]] & /@ {e, a, b})}, {i, Length[edges]}]}], GraphHighlightStyle -> "DehighlightHide"];
In[3]:=
X
colorHighlight[FindIndependentEdgeSet[g]]
Out[3]=
