Figuring out how AbsoluteOptions works with Graphs

I am puzzled by how AbsoluteOptions works with Graph objects. I would have expected that one could use it to obtain all the options used to draw a graph. There are several ways in which it behaves contrary to my expectations.

First, let' s make a simple graph, g, and set some custom options:

g = RandomGraph[{6, 11}, VertexStyle -> {1 -> Red, 2 -> Green},
VertexSize -> {1 -> Large, 2 -> Large}, VertexLabels -> "Name",
ImagePadding -> 15, EdgeLabels -> "Name", Axes -> True]


1 - Why won' t all the options work again?

One expects that the options used for g could be obtained through AbsoluteOptions[g] and redeployed. However, this does not work. Either the code below locks up completely or the Out cell has a tooltip: "$Failed is not a Graphics primitive or directive". allOptions = AbsoluteOptions[g]; g2 = Graph[EdgeList[g], allOptions]  2 - Some options work as expected, others do not. Why? Let's take a subset of the options of g; namely, {VertexCoordinates, EdgeLabels, Axes, VertexLabels, VertexSize, AlignmentPoint, ImagePadding}. Now let's compare g and the partial replication, g3, side by side: someOptions = Sort@AbsoluteOptions[ g, {VertexCoordinates, EdgeLabels, Axes, VertexLabels, VertexSize, AlignmentPoint, ImagePadding}] g; g3 = Graph[EdgeList[g], someOptions] someOptions3 = Sort@AbsoluteOptions[ g3, {VertexCoordinates, EdgeLabels, Axes, VertexLabels, VertexSize, AlignmentPoint, ImagePadding}] (* Out someOptions3*) {AlignmentPoint -> Center, Axes -> {True, True}, EdgeLabels -> {"Name"}, ImagePadding -> 15., VertexCoordinates -> {{0.518253, 0.817802}, {1.61587, 0.866512}, {2.05896, 0.336143}, {1.03973, 1.21024}, {1.04431, 0.}, {0., 0.377097}}, VertexLabels -> {"Name"}, VertexSize -> {1 -> Large, 2 -> Large}}  The vertex sizes are the same in each case, as expected. Also, the VertexStyle is different. That's fine: g3 has the default vertex style. But why are the vertices in different locations? After all, we passed the VertexCoordinates option to g3. And the vertex coordinates returned by AbsoluteOptions[g3... do not correspond to the coordinates used for the vertices. 3 - What are failed options? If we inspect the options used by g, we will notice that two of them failed, even though g was drawn with no apparent issues. AbsoluteOptions[g, {VertexShapeFunction, EdgeShapeFunction}] (* Out *) {VertexShapeFunction ->$Failed, EdgeShapeFunction -> $Failed}  If you look at the graph, g, you see that the default vertex shapes and edge shapes were correctly rendered? So, whence the fail? 4 - Why is it insufficient to remove failed options? If we remove the failed options and try to implement all the other options, MMA does one of two things: (1) It returns the unparsed Graph command or (2) it produces only a small portion of the graph, g. Any help would be appreciated. I'm not trying to correct a particular program but rather understand the strengths and limitations of AbsoluteOptions. • AbsoluteOptions is hit and miss for many functions. You'll find options not recognized, options that are recognized but do not return the correct values, options that are recognized but only return correct values sometimes, i.e. conflicts between the option you want and other option values cause it to fail, ...and so on. Wolfram tech support have acknowledged that it is a flawed function. Commented Apr 21, 2012 at 22:56 • @MikeHoneychurch That verdict certainly matches my experience. Commented Apr 21, 2012 at 23:24 1 Answer The difference in layout between g and g3 can be explained from the fact that their VertexLists are different: g = RandomGraph[{6, 11}, VertexStyle -> {1 -> Red, 2 -> Green}, VertexSize -> {1 -> Large, 2 -> Large}, VertexLabels -> "Name", ImagePadding -> 15, EdgeLabels -> "Name"]; VertexList[g] (* ==> {1, 2, 3, 4, 5, 6} *) g3 = Graph[EdgeList[g], someOptions]; VertexList[g3] VertexList[g3] (* ==> {1, 6, 3, 5, 2, 4} *)  Try for example {g, Graph[VertexList[g], EdgeList[g], someOptions]}  • Nice. That explains one big part of the mystery. Commented Apr 21, 2012 at 17:57 • Namely, question 2. However mostOptions = DeleteCases[allOptions, x_ /; MemberQ[{VertexShapeFunction ->$Failed , EdgeShapeFunction -> \$Failed}, x]]; Graph[VertexList[g], EdgeList[g], mostOptions] still does not work. Commented Apr 21, 2012 at 18:04
• Try removing the options PlotRange and AspectRatio from someOptions. It seems that AbsoluteOptions doesn't return the right plot range when PlotRange is set to All. Commented Apr 21, 2012 at 18:38
• You're right. Also, Ticks gives incorrect values so it can not be relied on. Commented Apr 21, 2012 at 19:37