How to specify custom graph styles for GraphStyle?

Question

There is a way to specify custom themes for plots (Is it possible to define a new PlotTheme?), but themes do not apply to Graph objects, not even to GraphPlot. Graph options are set by the GraphStyle option with which one can select from a few built-in styles:

GraphElementData["GraphStyle"]

{Automatic, "BackgroundBlack", "BackgroundBlue", ..., "VintageDiagram"}

However, GraphElementData definitions cannot be accessed (the function itself is only tangentially touched in the documentation), so I have no idea how to come up with a theme that works as a built-in one. The obvious solution is to set up default options that are passed on to Graph directly or via SetOptions, but I'd like to have a more integrated method where I can call my graph like this:

Graph[{1 -> 2, 2 -> 3, 3 -> 1}, GraphStyle -> "MyGraphTheme"]

and have a result like this:

Graph[{1 -> 2, 2 -> 3, 3 -> 1}, Background -> [email protected],
 EdgeStyle -> Directive[Green, Thick], VertexLabels -> "Name", 
 VertexLabelStyle -> Directive[Orange, 16], ImagePadding -> 20, ImageSize -> 200]

Answer 1

If you are willing to mess around with the internals of Mathematica, I think the necessary graph style code is at top level. So:

Options[addGraphStyle] = {
    BaseStyle->Automatic,
    DirectedEdges->Automatic,
    EdgeLabels->None,
    EdgeLabelStyle->Automatic,
    EdgeShapeFunction->Automatic,
    EdgeStyle->Automatic,
    GraphHighlightStyle->Automatic,
    Options->{},
    VertexLabels->None,
    VertexLabelStyle->Automatic,
    VertexShape->Automatic,
    VertexShapeFunction->Automatic,
    VertexSize->Automatic,
    VertexStyle->Automatic
};

addGraphStyle[style_String, opts:OptionsPattern[]] := Internal`WithLocalSettings[
    Unprotect[GraphComputation`SetGraphStyle],

    Replace[
        OptionValue[EdgeLabels], 
        v_ :> Set[GraphComputation`SetGraphStyle[style, EdgeLabels], v]
    ];
    Replace[
        OptionValue[VertexLabels], 
        v_ :> Set[GraphComputation`SetGraphStyle[style, VertexLabels], v]
    ];
    Replace[
        OptionValue[Options],
        v_ :> Set[GraphComputation`SetGraphStyle[style, Options], v]
    ];
    Map[
        Replace[
            OptionValue[#],
            {
            Automatic :> Quiet @ Unset[GraphComputation`SetGraphStyle[style, #]],
            v_ :> Set[GraphComputation`SetGraphStyle[style, #], v]
            }
        ]&,
        {
        BaseStyle, DirectedEdges, EdgeLabelStyle, EdgeShapeFunction, EdgeStyle,
        GraphHighlightStyle, VertexLabelStyle, VertexShape, VertexShapeFunction, VertexSize, VertexStyle
        }
    ];
    GraphComputation`SetGraphStyle[style<>"3D", rest__] := GraphComputation`SetGraphStyle[style, rest],

    Protect[GraphComputation`SetGraphStyle]
]

Example:

addGraphStyle[
    "Example",
    {
    VertexLabels->"Name",
    EdgeStyle->Directive[Green, Dashed]
    }
]

Visualization:

Graph[{1->2, 2->2}, GraphStyle->"Example"]
Graph[{1->2, 2->2}, GraphStyle->"Example", EdgeStyle->Thickness[.02]]

For the OP example, we have:

addGraphStyle[
    "Istvan",
    Options->{Background->[email protected], ImagePadding->20, ImageSize->200},
    EdgeStyle->Directive[Green, Thick],
    VertexLabels->"Name",
    VertexLabelStyle->Directive[Orange, 16]
]

Graph[{1->2, 2->3, 3->1}, GraphStyle->"Istvan"]

Answer 2

Update 2016.8.13.

In Mathematica v11.0, Graph were modified to be able to use directly the PlotTheme option. While there are reliable ways to construct new themes (see here and here), unfortunately the theme system is still not fully compatible with graphs. At the moment, you cannot add Graph-specific rules like Themes`AddThemeRules["myGraph", Graph, VertexLabelStyle -> Green] to have any effect when called e.g. Graph[{1->2, 2->3, 3->1}, PlotTheme -> "myGraph"].

---

I've constructed a more-or-less safe way to do this. I aimed for the more general case: to directly use available plotting themes with graphs, at least the relevant options. I even started to wonder why PlotTheme was not designed to cooperate with all graphics object (like Graph, Graphics, GeoGraphics, etc.).

(* Define a new theme *)
Themes`AddThemeRules[
  "Dark", {Background -> [email protected], 
   EdgeStyle -> Directive[Green, Thick], VertexLabels -> "Name", 
   VertexLabelStyle -> Directive[Orange, 16], ImagePadding -> 20, 
   ImageSize -> 200, PlotRange -> All, 
   DefaultPlotStyle -> Directive[Green, Thick], 
   LabelStyle -> Directive[Orange, 12]}];

Unprotect@Graph;
Graph[arg__, pre : OptionsPattern[], PlotTheme -> t_, post___] := 
  If[MemberQ[GraphElementData@"GraphStyle", t],
   Graph[arg, pre, GraphStyle -> t, post],
   Module[{th = Charting`ResolvePlotTheme[t, Graph]},
    (* Exclude functional ticks and method as Graph can't handle these *)
    th = DeleteCases[th, _[FrameTicks | Ticks, _?(MemberQ[Flatten@{#}, _Function] &)] |
    _[Method, _]];
    Graph[arg, FilterRules[
      DeleteDuplicatesBy[Flatten@{pre, theme, post}, First], 
      Options@Graph]]
    ]];

{Plot[Sin[x], {x, 0, 10}, PlotTheme -> "Dark"],
 Graph[{1 <-> 2, 2 <-> 3, 3 <-> 1}, PlotTheme -> "Dark"],
 Graph[{1 <-> 2, 2 <-> 3, 3 <-> 1}, PlotTheme -> "Scientific", 
  ImageSize -> 200],
 Graph[{1 <-> 2, 2 <-> 3, 3 <-> 1}, 
  EdgeStyle -> Directive[Thick, Red], PlotTheme -> "Dark"],
 Graph[{1 <-> 2, 2 <-> 3, 3 <-> 1}, PlotTheme -> "DiagramGold"]}

As you can see, it recognizes built-in GraphStyle-s. User-options take precedence over themes, if supplied before PlotTheme. Trying some of the built-in plot themes:

Multicolumn[
 Graph[{1 <-> 2, 2 <-> 3, 3 <-> 1}, PlotTheme -> #, PlotLabel -> #, 
    ImageSize -> 150] & /@ {"Business", "Detailed", "Marketing", 
   "Minimal", "Monochrome", "Scientific", "Web", "Classic"}, 4, 
 Appearance -> "Horizontal"]

Answer 3

On the first try, I can't find a way to make something like " GraphTheme " work. Perhaps there is a way to do it, but I don't see it.

A quick hack to make this work without using themes is something like:

myGraphOptions = {Background -> [email protected], 
 EdgeStyle -> Directive[Green, Thick], VertexLabels -> "Name", 
 VertexLabelStyle -> Directive[Orange, 16]}
Graph[{1 -> 2, 2 -> 3, 3 -> 1}, myGraphOptions]

This appears to have the desired effect, more or less. (Not sure if you wanted the ImageSize or ImagePadding in the "theme" -- I didn't include it.)

One thing to keep in mind though is if you want to override some of these, you'll want to put those options before the myGraphOptions.

Graph[{1 -> 2, 2 -> 3, 3 -> 1}, EdgeStyle -> Red, myGraphOptions]

Note that in this case, the edges are red, but also not thick.

But I agree a "theme" type of construction for Graph would be better.