VertexCoordinate Rules and VertexList from GraphPlot Graphic

Question

Is there any way of abstracting the vertex order that GraphPlot applies to VertexCoordinate Rules from the (FullForm or InputForm) of the graphic produced by GraphPlot? I d

Answer 1

With vertex labeling, one way is to get coordinates of the labels. Notice that output of GraphPlot is in GraphicsComplex where coordinates of coordinate aliases are as first label, you can get it as

points = Cases[gp1, GraphicsComplex[points_, __] :> points, Infinity] // First

Looking at FullForm you'll see that labels are in text objects, extract them as

labels = Cases[gp1, Text[___], Infinity]

The actual label seems to be two levels deep so you get

actualLabels = labels[[All, 1, 1]];

Coordinate alias is the second parameter so you get them as

 coordAliases = labels[[All, 2]]

Actual coordinates were specified in GraphicsComplex, so we get them as

 actualCoords = points[[coordAliases]]

There a 1-1 correspondence between list of coordinates and list of labels, so you can use Thread to return them as list of "label"->coordinate pairs.

here's a function that this all together

getLabelCoordinateMap[gp1_] := 
 Module[{points, labels, actualLabels, coordAliases, actualCoords},
  points = 
   Cases[gp1, GraphicsComplex[points_, __] :> points, Infinity] // 
    First;
  labels = Cases[gp1, Text[___], Infinity];
  actualLabels = labels[[All, 1, 1]];
  coordAliases = labels[[All, 2]];
  actualCoords = points[[coordAliases]];
  Thread[actualLabels -> actualCoords]
  ];
getLabelCoordinateMap[gp1]

Not that this only works on labelled GraphPlot. For ones without labels you could try to extract from other graphics objects, but you may get different results depending on what objects you extract the mapping from because there seems to be a bug which sometimes assigns line endpoints and vertex labels to different vertices. I've reported it. The way to work around the bug is to either always use explicit vertex->coordinate specification for VertexCoordinateList, or always use "adjacency matrix" representation. Here's an example of discrepancy

graphName = {"Grid", {3, 3}};
gp1 = GraphPlot[Rule @@@ GraphData[graphName, "EdgeIndices"], 
  VertexCoordinateRules -> GraphData[graphName, "VertexCoordinates"], 
  VertexLabeling -> True]
gp2 = GraphPlot[GraphData[graphName, "AdjacencyMatrix"], 
  VertexCoordinateRules -> GraphData[graphName, "VertexCoordinates"], 
  VertexLabeling -> True]

BTW, as an aside, here are the utility functions I use for converting between adjacency matrix and edge rule representation

edges2mat[edges_] := Module[{a, nodes, mat, n},
   (* custom flatten to allow edges be lists *)

   nodes = Sequence @@@ edges // Union // Sort;
   nodeMap = (# -> (Position[nodes, #] // Flatten // First)) & /@ 
     nodes;
   n = Length[nodes];
   mat = (({#1, #2} -> 1) & @@@ (edges /. nodeMap)) // 
     SparseArray[#, {n, n}] &
   ];
mat2edges[mat_List] := Rule @@@ Position[mat, 1];
mat2edges[mat_SparseArray] := 
 Rule @@@ (ArrayRules[mat][[All, 1]] // Most)