New in Mathematica 9 › Enhanced Graphs and Networks

New and Enhanced Graph Layouts

Adding to an already rich set of graph layouts, Mathematica 9 brings new capabilities to visualize graphs with structures such as planar graphs, multipartite graphs, and trees.

In[1]:=

graphs = {
   KaryTree[40, 5],
   Graph[{1 \[UndirectedEdge] 4, 1 \[UndirectedEdge] 5, 
     2 \[UndirectedEdge] 4, 2 \[UndirectedEdge] 6, 
     3 \[UndirectedEdge] 4, 3 \[UndirectedEdge] 7, 
     4 \[UndirectedEdge] 8, 5 \[UndirectedEdge] 8, 
     6 \[UndirectedEdge] 8, 7 \[UndirectedEdge] 8}],
   CompleteGraph[{3, 3, 2}],
   PathGraph[Range[25]],
   GridGraph[{5, 5}],
   Graph[{1 \[DirectedEdge] 3, 1 \[DirectedEdge] 6, 
     2 \[DirectedEdge] 6, 3 \[DirectedEdge] 8, 4 \[DirectedEdge] 2, 
     4 \[DirectedEdge] 3, 5 \[DirectedEdge] 1, 5 \[DirectedEdge] 2, 
     5 \[DirectedEdge] 7, 6 \[DirectedEdge] 3, 7 \[DirectedEdge] 6, 
     8 \[DirectedEdge] 5, 8 \[DirectedEdge] 7}],
   KnightTourGraph[10, 10],
   Graph[{1 \[UndirectedEdge] 2, 1 \[UndirectedEdge] 3, 
     1 \[UndirectedEdge] 5, 2 \[UndirectedEdge] 4, 
     2 \[UndirectedEdge] 6, 3 \[UndirectedEdge] 4, 
     3 \[UndirectedEdge] 7, 4 \[UndirectedEdge] 8, 
     5 \[UndirectedEdge] 6, 5 \[UndirectedEdge] 7, 
     6 \[UndirectedEdge] 8, 7 \[UndirectedEdge] 8}],
   Graph[Range[11], {1 \[UndirectedEdge] 5, 1 \[UndirectedEdge] 6, 
     2 \[UndirectedEdge] 5, 2 \[UndirectedEdge] 6, 
     3 \[UndirectedEdge] 7, 4 \[UndirectedEdge] 7, 
     4 \[UndirectedEdge] 6, 5 \[UndirectedEdge] 9, 
     11 \[UndirectedEdge] 7, 6 \[UndirectedEdge] 8, 
     6 \[UndirectedEdge] 10, 7 \[UndirectedEdge] 10, 
     6 \[UndirectedEdge] 11}],
   StarGraph[12],
   CompleteGraph[8],
   Graph[Table[
     j -> FromDigits[Drop[IntegerDigits[j, 2], -1], 2], {j, 1, 200}]]
   };
layouts = {"BalloonEmbedding", 
   "BipartiteEmbedding", {"CircularMultipartiteEmbedding", 
    "VertexPartition" -> {3, 3, 2}}, 
   "DiscreteSpiralEmbedding", {"GridEmbedding", 
    "Dimension" -> {5, 5}}, "LayeredDigraphEmbedding", 
   "SpectralEmbedding", 
   "PlanarEmbedding", {"MultipartiteEmbedding", 
    "VertexPartition" -> {4, 3, 4}}, "StarEmbedding", 
   "LinearEmbedding", "RadialEmbedding"};
background = {Hue[.15, .3, .9], Hue[.7, .1, .7], Hue[.15, .2, .9], 
   Hue[.2, .2, .7], Hue[.15, .2, .9], Hue[.5, .8, .7], 
   Hue[.15, .5, .7], Hue[.5, .3, .7], Hue[.2, .3, .8], 
   Hue[.15, .2, .8], Hue[.13, .2, .95], Hue[.2, .3, .5]};
label[{name_, __}] := 
  Style[name, Directive[11, FontFamily -> "Helvetica"]];
label[name_] := Style[name, Directive[11, FontFamily -> "Helvetica"]];
Grid[Partition[
  Item[Labeled[
      SetProperty[#1, { GraphLayout -> #2, ImagePadding -> 15, 
        ImageSize -> {155, 155}, 
        EdgeStyle -> Directive[Thickness[.01], Brown], 
        VertexStyle -> Lighter[ColorData[44, 8], .5], 
        VertexSize -> .3}], label[#2], Top, 
      FrameMargins -> {{0, 0}, {-10, -18}}], Background -> #3] & @@@ 
   Transpose[{graphs, layouts, background}], 3, 3, 1, {}], 
 Spacings -> {.5, 1}, Frame -> All, 
 FrameStyle -> Directive[GrayLevel[.8]]]

Out[1]=