tips for creating Graph diagrams

问题:

I'd like to programmatically create diagrams like this http://yaroslavvb.com/upload/junction-tree-decomposition.png

I imagine I should use GraphPlot with VertexCoordinateRules, VertexRenderingFunction and EdgeRenderingFunction for the graphs. What should I use for colored beveled backgrounds?

Edit Using mainly Simon's ideas, here's a simplified "less robust" version I ended up using

Needs["GraphUtilities`"];
GraphPlotHighlight[edges_, verts_, color_] := Module[{},
  vpos = Position[VertexList[edges], Alternatives @@ verts];
  coords = Extract[GraphCoordinates[edges], vpos];
  (* add .002 because end-cap disappears when segments are almost colinear *)  
  AppendTo[coords, First[coords] + .002];
  Show[Graphics[{color, CapForm["Round"], JoinForm["Round"], 
     Thickness[.2], Line[coords], Polygon[coords]}],
   GraphPlot[edges], ImageSize -> 150]
  ]

SetOptions[GraphPlot, 
  VertexRenderingFunction -> ({White, EdgeForm[Black], Disk[#, .15], 
      Black, Text[#2, #1]} &), 
  EdgeRenderingFunction -> ({Black, Line[#]} &)];
edges = GraphData[{"Grid", {3, 3}}, "EdgeRules"];
colors = {LightBlue, LightGreen, LightRed, LightMagenta};
vsets = {{8, 5, 2}, {7, 5, 8}, {9, 6, 3}, {8, 1, 2}};
MapThread[GraphPlotHighlight[edges, #1, #2] &, {vsets, colors}]

http://yaroslavvb.com/upload/mathematica-graphs.png

回答1:

Generalising Samsdram's answer a bit, I get

GraphPlotHighlight[edges:{((_->_)|{_->_,_})..},hl:{___}:{},opts:OptionsPattern[]]:=Module[{verts,coords,g,sub},
  verts=Flatten[edges/.Rule->List]//.{a___,b_,c___,b_,d___}:>{a,b,c,d};
  g=GraphPlot[edges,FilterRules[{opts}, Options[GraphPlot]]];
  coords=VertexCoordinateRules/.Cases[g,HoldPattern[VertexCoordinateRules->_],2];
  sub=Flatten[Position[verts,_?(MemberQ[hl,#]&)]];
  coords=coords[[sub]];     
  Show[Graphics[{OptionValue[HighlightColor],CapForm["Round"],JoinForm["Round"],Thickness[OptionValue[HighlightThickness]],Line[AppendTo[coords,First[coords]]],Polygon[coords]}],g]
]
Protect[HighlightColor,HighlightThickness];
Options[GraphPlotHighlight]=Join[Options[GraphPlot],{HighlightColor->LightBlue,HighlightThickness->.15}];

Some of the code above could be made a little more robust, but it works:

GraphPlotHighlight[{b->c,a->b,c->a,e->c},{b,c,e},VertexLabeling->True,HighlightColor->LightRed,HighlightThickness->.1,VertexRenderingFunction -> ({White, EdgeForm[Black], Disk[#, .06], 
Black, Text[#2, #1]} &)]

---

EDIT #1: A cleaned up version of this code can be found at http://gist.github.com/663438

EDIT #2: As discussed in the comments below, the pattern that my edges must match is a list of edge rules with optional labels. This is slightly less general than what is used by the GraphPlot function (and by the version in the above gist) where the edge rules are also allowed to be wrapped in a Tooltip.

To find the exact pattern used by GraphPlot I repeatedly used Unprotect[fn];ClearAttributes[fn,ReadProtected];Information[fn] where fn is the object of interest until I found that it used the following (cleaned up) function:

Network`GraphPlot`RuleListGraphQ[x_] := 
  ListQ[x] && Length[x] > 0 && 
    And@@Map[Head[#1] === Rule 
         || (ListQ[#1] && Length[#1] == 2 && Head[#1[[1]]] === Rule) 
         || (Head[#1] === Tooltip && Length[#1] == 2 && Head[#1[[1]]] === Rule)&, 
      x, {1}]

I think that my edges:{((_ -> _) | (List|Tooltip)[_ -> _, _])..} pattern is equivalent and more concise...

回答2:

For simple examples where you are only connecting two nodes (like your example on the far right), you can draw lines with capped end points like this.

vertices = {a, b};
Coordinates = {{0, 0}, {1, 1}};
GraphPlot[{a -> b}, VertexLabeling -> True, 
 VertexCoordinateRules -> 
  MapThread[#1 -> #2 &, {vertices, Coordinates}], 
 Prolog -> {Blue, CapForm["Round"], Thickness[.1], Line[Coordinates]}]

For more complex examples (like second from the right) I would recommend drawing a polygon using the vertex coordinates and then tracing the edge of the polygon with a capped line. I couldn't find a way to add a beveled edge directly to a polygon. When tracing the perimeter of the polygon you need to add the coordinate of the first vertex to the end of the line segment that the line makes the complete perimeter of the polygon. Also, there are two separate graphics directives for lines CapForm, which dictates whether to bevel the ends of the line, and JoinForm, which dictates whether to bevel the intermediate points of the line.

vertices = {a, b, c};
Coordinates = {{0, 0}, {1, 1}, {1, -1}};
GraphPlot[{a -> b, b -> c, c -> a}, VertexLabeling -> True, 
 VertexCoordinateRules -> 
  MapThread[#1 -> #2 &, {vertices, Coordinates}], 
 Prolog -> {Blue, CapForm["Round"], JoinForm["Round"], Thickness[.15],
    Line[AppendTo[Coordinates, First[Coordinates]]], 
   Polygon[Coordinates]}]

回答3:

JoinForm["Round"] will round the joins of line segments.

You'll want a filled polygon around the centers of the vertices in the colored region, then a JoinForm["Round"], ..., Line[{...}] to get the rounded corners.

Consider

foo = GraphPlot[{a -> b, a -> c, b -> d, b -> e, b -> f, c -> e, e -> f}, 
    VertexRenderingFunction -> 
    ({White, EdgeForm[Black], Disk[#, .1], Black, Text[#2, #1]} &)]
Show[
    Graphics[{
      RGBColor[0.6, 0.8, 1, 1],
      Polygon[foo[[1, 1, 1, 1, 1, {2, 5, 6, 2}]]],
      JoinForm["Round"], Thickness[0.2],
      Line[foo[[1, 1, 1, 1, 1, {2, 5, 6, 2}]]]
    }],
    foo
]

where foo[[1,1,1,1,1]] is the list of vertex centers and {2,5,6} pulls out the {b,e,f} vertices. ({2,5,6,2} closes the line back at its starting point.)

There's plenty of room for prettifying, but I think this covers the ingredient you didn't mention above.