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8: Graph & Network Analysis
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Showing the edge cover reveals that each course will be taught by one professor, and that Larry has been assigned to teach two courses.
In[1]:=
X
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Thickness[Large], StripOnInput -> False], StyleBox[ LineBox[{ DynamicLocation["VertexID$13", Automatic, Center], DynamicLocation["VertexID$32", Automatic, Center]}], Thickness[Large], StripOnInput -> False], StyleBox[ LineBox[{ DynamicLocation["VertexID$13", Automatic, Center], DynamicLocation["VertexID$26", Automatic, Center]}], Thickness[Large], StripOnInput -> False], StyleBox[ LineBox[{ DynamicLocation["VertexID$14", Automatic, Center], DynamicLocation["VertexID$21", Automatic, Center]}], Thickness[Large], StripOnInput -> False], StyleBox[ LineBox[{ DynamicLocation["VertexID$15", Automatic, Center], DynamicLocation["VertexID$25", Automatic, Center]}], Thickness[Large], StripOnInput -> False], StyleBox[ LineBox[{ DynamicLocation["VertexID$16", Automatic, Center], DynamicLocation["VertexID$28", Automatic, Center]}], Thickness[Large], StripOnInput -> False], StyleBox[ LineBox[{ DynamicLocation["VertexID$16", Automatic, Center], DynamicLocation["VertexID$24", Automatic, Center]}], Thickness[Large], StripOnInput -> False], StyleBox[ LineBox[{ DynamicLocation["VertexID$16", Automatic, Center], DynamicLocation["VertexID$36", Automatic, Center]}], Thickness[Large], StripOnInput -> False], StyleBox[ LineBox[{ DynamicLocation["VertexID$16", Automatic, Center], DynamicLocation["VertexID$32", Automatic, Center]}], Thickness[Large], StripOnInput -> False], StyleBox[ LineBox[{ DynamicLocation["VertexID$17", Automatic, Center], DynamicLocation["VertexID$32", Automatic, Center]}], Thickness[Large], StripOnInput -> False], StyleBox[ LineBox[{ DynamicLocation["VertexID$17", Automatic, Center], DynamicLocation["VertexID$31", Automatic, Center]}], Thickness[Large], StripOnInput -> False], StyleBox[ LineBox[{ DynamicLocation["VertexID$17", Automatic, Center], DynamicLocation["VertexID$34", Automatic, Center]}], Thickness[Large], StripOnInput -> False], StyleBox[ LineBox[{ DynamicLocation["VertexID$18", Automatic, Center], DynamicLocation["VertexID$37", Automatic, Center]}], Thickness[Large], StripOnInput -> False], StyleBox[ LineBox[{ DynamicLocation["VertexID$18", Automatic, Center], DynamicLocation["VertexID$31", Automatic, Center]}], Thickness[Large], StripOnInput -> False], StyleBox[ LineBox[{ DynamicLocation["VertexID$18", Automatic, Center], DynamicLocation["VertexID$34", Automatic, Center]}], Thickness[Large], StripOnInput -> False], StyleBox[ LineBox[{ DynamicLocation["VertexID$19", Automatic, Center], DynamicLocation["VertexID$32", Automatic, Center]}], Thickness[Large], StripOnInput -> False], StyleBox[ LineBox[{ DynamicLocation["VertexID$19", Automatic, Center], DynamicLocation["VertexID$35", Automatic, Center]}], Thickness[Large], StripOnInput -> False]}}]}, DynamicBox[GraphComputation`NetworkGraphicsBox[ 1, Typeset`graph, Typeset`boxes], { CachedValue :> Typeset`boxes, SingleEvaluation -> True, SynchronousUpdating -> False, TrackedSymbols :> {}}, ImageSizeCache->{{-12.516689461762894`, 435.9712349163083}, {-160.8406561528305, 155.38611069828494`}}]]], DefaultBaseStyle->{ "NetworkGraphics", FrontEnd`GraphicsHighlightColor -> Hue[0.8, 1., 0.6]}, FrameTicks->None, ImageSize->{438., Automatic}, PlotRange->{{-0.9, 1.3}, {-0.8, 0.8}}]\);
In[2]:=
X
colorHighlight[comp_] := HighlightGraph[g, Join @@ Table[(Style[#, ColorData["Rainbow"][i/Length[comp]]]) & /@ Join[comp[[i]], EdgeList[Subgraph[g, comp[[i]]]]], {i, Length[comp]}], GraphHighlightStyle -> "DehighlightHide"];
In[3]:=
X
colorHighlight[ConnectedComponents[Graph@FindEdgeCover[g]]]
Out[3]=