Use uma abordagem multiparadigma para programação de grafos

Use uma abordagem multiparadigma para a programação de grafos com matrizes, otimização e estruturas booleanas.

In[1]:=

g = \!\(\*
GraphicsBox[
NamespaceBox["NetworkGraphics",
DynamicModuleBox[{Typeset`graph = HoldComplete[
Graph[{2, 3, 1, 4, 5, 7, 8, 6, 9, 
         10}, {{{1, 2}, {2, 3}, {2, 4}, {4, 3}, {4, 5}, {4, 6}, {4, 
          7}, {8, 3}, {8, 9}, {7, 3}, {7, 10}, {9, 3}, {9, 1}, {9, 
          10}, {10, 9}}, Null}, {EdgeStyle -> {
Arrowheads[0.06]}, ImageSize -> 120, PerformanceGoal -> "Quality"}]], 
       Typeset`boxes, Typeset`boxes$s2d = GraphicsGroupBox[{{
Arrowheads[0.027557679514756052`], 
Directive[
Opacity[0.7], 
Hue[0.6, 0.7, 0.5]], 
Arrowheads[0.06], 
ArrowBox[{
DynamicLocation["VertexID$1", Automatic, Center], 
DynamicLocation["VertexID$2", Automatic, Center]}], 
ArrowBox[{
DynamicLocation["VertexID$2", Automatic, Center], 
DynamicLocation["VertexID$3", Automatic, Center]}], 
ArrowBox[{
DynamicLocation["VertexID$2", Automatic, Center], 
DynamicLocation["VertexID$4", Automatic, Center]}], 
ArrowBox[{
DynamicLocation["VertexID$4", Automatic, Center], 
DynamicLocation["VertexID$3", Automatic, Center]}], 
ArrowBox[{
DynamicLocation["VertexID$4", Automatic, Center], 
DynamicLocation["VertexID$5", Automatic, Center]}], 
ArrowBox[{
DynamicLocation["VertexID$4", Automatic, Center], 
DynamicLocation["VertexID$6", Automatic, Center]}], 
ArrowBox[{
DynamicLocation["VertexID$4", Automatic, Center], 
DynamicLocation["VertexID$7", Automatic, Center]}], 
ArrowBox[{
DynamicLocation["VertexID$7", Automatic, Center], 
DynamicLocation["VertexID$3", Automatic, Center]}], 
ArrowBox[{
DynamicLocation["VertexID$7", Automatic, Center], 
DynamicLocation["VertexID$10", Automatic, Center]}], 
ArrowBox[{
DynamicLocation["VertexID$8", Automatic, Center], 
DynamicLocation["VertexID$3", Automatic, Center]}], 
ArrowBox[{
DynamicLocation["VertexID$8", Automatic, Center], 
DynamicLocation["VertexID$9", Automatic, Center]}], 
ArrowBox[{
DynamicLocation["VertexID$9", Automatic, Center], 
DynamicLocation["VertexID$1", Automatic, Center]}], 
ArrowBox[{
DynamicLocation["VertexID$9", Automatic, Center], 
DynamicLocation["VertexID$3", Automatic, Center]}], 
ArrowBox[
BezierCurveBox[{
DynamicLocation["VertexID$9", Automatic, Center], {0.7308395626536534,
              0.5282228657692112}, 
DynamicLocation["VertexID$10", Automatic, Center]}]], 
ArrowBox[
BezierCurveBox[{
DynamicLocation["VertexID$10", Automatic, Center], {
             0.41059435103558733`, 0.44551757601287606`}, 
DynamicLocation["VertexID$9", Automatic, Center]}]]}, {
Directive[
Hue[0.6, 0.2, 0.8], 
EdgeForm[
Directive[
GrayLevel[0], 
Opacity[0.7]]]], 
TagBox[
DiskBox[{0.6826993823276208, 2.023780937065023}, 0.03281640017374192],
            "DynamicName", BoxID -> "VertexID$1"], 
TagBox[
DiskBox[{1.619658067166264, 1.8235816784316954`}, 
            0.03281640017374192], "DynamicName", 
           BoxID -> "VertexID$2"], 
TagBox[
DiskBox[{1.2059053823417645`, 1.1212523575685285`}, 
            0.03281640017374192], "DynamicName", 
           BoxID -> "VertexID$3"], 
TagBox[
DiskBox[{2.380054579532232, 1.101041702945713}, 0.03281640017374192], 
           "DynamicName", BoxID -> "VertexID$4"], 
TagBox[
DiskBox[{3.3672346895409793`, 0.5672588034601881}, 
            0.03281640017374192], "DynamicName", 
           BoxID -> "VertexID$5"], 
TagBox[
DiskBox[{3.3598596261921987`, 1.6495568300534234`}, 
            0.03281640017374192], "DynamicName", 
           BoxID -> "VertexID$6"], 
TagBox[
DiskBox[{1.6076061591533763`, 0.35906995124773267`}, 
            0.03281640017374192], "DynamicName", 
           BoxID -> "VertexID$7"], 
TagBox[
DiskBox[{0., 1.2960348999753026`}, 0.03281640017374192], 
           "DynamicName", BoxID -> "VertexID$8"], 
TagBox[
DiskBox[{0.4449797366404249, 0.9737404417818881}, 
            0.03281640017374192], "DynamicName", 
           BoxID -> "VertexID$9"], 
TagBox[
DiskBox[{0.6964541770488158, 0.}, 0.03281640017374192], "DynamicName",
            BoxID -> "VertexID$10"]}}], $CellContext`flag}, 
TagBox[
DynamicBox[GraphComputation`NetworkGraphicsBox[
         3, Typeset`graph, Typeset`boxes, $CellContext`flag], {
         CachedValue :> Typeset`boxes, SingleEvaluation -> True, 
          SynchronousUpdating -> False, 
          TrackedSymbols :> {$CellContext`flag}},
ImageSizeCache->{{1.38, 117.61999999999998`}, {-38.715199999999975`, 
          32.816940714746956`}}],
MouseAppearanceTag["NetworkGraphics"]],
AllowKernelInitialization->False,
UnsavedVariables:>{$CellContext`flag}]],
DefaultBaseStyle->{
      "NetworkGraphics", 
       FrontEnd`GraphicsHighlightColor -> Hue[0.8, 1., 0.6]},
FrameTicks->None,
GridLinesStyle->Directive[
GrayLevel[0.5, 0.4]],
ImageSize->120]\);

Redução transitiva usando estruturas booleanas.

In[2]:=