7
$\begingroup$

I'm graphing a Markov process 

mp = DiscreteMarkovProcess[{1, 0, 0}, ({
     {0.6, 0.1, 0.3},
     {0.2, 0.7, 0.1},
     {0.3, 0.3, 0.4}
    })];

and would like to have arrows whose thicknesses corresponds to the transition probabilities, with arrowheads of a different color in the exact center of each edge. But all my attempts end up a mess. 

g = Graph[mp];
Scan[(PropertyValue[{g, #}, EdgeLabels] = 
     PropertyValue[{g, #}, "Probability"]) &, EdgeList[g]];
Scan[(PropertyValue[{g, #}, EdgeStyle] =
     Directive[Arrowheads[{{.045, .575}}], GrayLevel[.7], 
      Thickness[PropertyValue[{g, #}, "Probability"]/20]]) &, 
  EdgeList[g]];
g

The thick edges leave gaps between their ends and the nodes of the graph, and I can't figure out how to change the color of the arrow heads so that they stand out against the color of the edges.

How can I change the color of the arrowheads in my figure. How can I avoid the gaps that appear between nodes and the ends of the edges?

Improve this question
$\endgroup$
2
  • $\begingroup$ Take a look at EdgeShapeFunction. $\endgroup$ – wxffles May 7 '14 at 22:47
  • $\begingroup$ @wxffles: Looks intriguing; but I'm not sure where to go with it. It seems to amount to "build it from scratch". $\endgroup$ – orome May 7 '14 at 23:21
7
$\begingroup$

Using an EdgeShapeFunction seems to do what you want. Adapting from the examples in the help:

ef[pts_List, e_] :=
 {Arrowheads[{{0.1, 0.5, Graphics@{Red, Arrowheads[0.5], Arrow[{{0, 0}, {0.5, 0}}]}}}], 
  Arrow[pts]}

g = Graph[mp];
Scan[(PropertyValue[{g, #}, EdgeLabels] = 
    PropertyValue[{g, #}, "Probability"]) &, EdgeList[g]];
Scan[(PropertyValue[{g, #}, EdgeStyle] = 
    Directive[GrayLevel[.7], Thickness[PropertyValue[{g, #}, "Probability"]/20]]) &, 
    EdgeList[g]];
Scan[(PropertyValue[{g, #}, EdgeShapeFunction] = ef) &, EdgeList[g]];
g

red arrows

It's a bit ugly, with mysterious red dots within the arrowheads. But this only reflects how little time I've put into it. With some competence and patience I suspect it could do what you want.

Edit: Something nicer:

ef[pts_List, e_] := {Arrowheads[{{0.02, 0.65, 
    Graphics@{Red, EdgeForm[Gray], Polygon[{{-1.5, -1}, {1.5, 0}, {-1.5, 1}}]}
  }}], Arrow[pts]}

red arrows 2

Improve this answer
$\endgroup$
3
  • $\begingroup$ Is there a way to keep the arc shapes of the original? $\endgroup$ – orome May 8 '14 at 0:47
  • $\begingroup$ Not easily as far as I can tell. It's just using the points that it gets passed. I'm not sure what the default EdgeShapeFunctions do to it. $\endgroup$ – wxffles May 8 '14 at 1:05
  • $\begingroup$ @wxffles How to access the built-in set of arrow heads is described here. $\endgroup$ – Alexey Popkov May 8 '14 at 7:09
2
$\begingroup$

If you don't mind having a Graphics object, you can replace the Arrowheads directives with wxffles's Arrowheads specification, and get to keep the arc shapes of the orginial g:

arrowheads = Arrowheads[{{0.02, 0.65, Graphics@{Red, EdgeForm[Gray], 
    Polygon[{{-1.5, -1}, {1.5, 0}, {-1.5, 1}}]}}}];

g2 = Show[g] /. TagBox -> (# &) /. _Arrowheads :> arrowheads

enter image description here

If you have to have a Graph object, you can extract the edge primitives from g2 and use them as EdgeShapeFunction for g:

edgehapefunctions = Function /@ 
   Cases[g2[[1]], {dirs___, _Arrowheads, _ArrowBox}, {0, Infinity}];

SetProperty[g, EdgeShapeFunction -> Thread[EdgeList[g] -> edgehapefunctions]]

enter image description here

Improve this answer
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.