# Causal Diagrams using Wolfram?

How can one use Wolfram to make diagrams like

with the arrows labeled as well (to label "mediating factors" between the causal elements)?

vertices = {"rush hour", "bad weather", "accident", "traffic jam", "sirens"};

edges = DirectedEdge @@@ {"rush hour" -> "traffic jam", "bad weather" -> "accident",
"accident" -> "traffic jam", "bad weather" -> "traffic jam",
"accident" -> "sirens"};

edgelabels = RandomWord["Noun", Length @ edges];

Graph[edges,
PlotTheme -> "IndexLabeled",
VertexSize -> Large,
EdgeLabels -> Thread[edges -> edgelabels]]


Use additional options to embellish the picture:

elabeling = AssociationThread[edges, edgelabels];

eSF = {Arrowheads[{{.04, .75},
{.05, .45, Graphics @ Text[Framed[Style[elabeling @ #2, 14],
FrameStyle -> None,  Background -> White]]}}],
Last @ GraphElementData["Arrow"][##]} &;

coords = Drop[Join @@ Array[{ #2, (3 - #)}&, {2, 3}], {4}]

Graph[vertices, edges,
VertexLabelStyle -> 14,
ImageSize -> Large,
GraphStyle -> "IndexLabeled",
VertexSize -> .4,
EdgeShapeFunction -> eSF,
VertexCoordinates -> coords]


We can also construct the graphics primitives from scratch:

radius = Offset @  Max[(1.2/2)
Rasterize[Style[#, 14, "Graphics"], "RasterSize"][[1]] & /@ vertices];

Graphics[{{Arrowheads[{{.02, .75}, {.05, .45,
Graphics @Text[Framed[Style[elabeling @ #, 14], FrameStyle -> None,
Background -> White], {0, 0}, {0, .25}]}}],
Arrow[List @@ # /. Thread[vertices -> coords]]} & /@ edges,
FaceForm[White], EdgeForm[Gray], Disk[#, radius] & /@ coords,
MapThread[Text, {Style[#, 16] & /@ vertices, coords}]},
ImageSize -> 800, PlotRangePadding -> Scaled[.2]]


Update: From comments: "Ideally a user just supplies a list of relationships (with possible labels)..."

elist = {{"rush hour" -> "traffic jam",  "empty"},
{"bad weather" -> "accident", "canyon"},
{"accident" -> "traffic jam", "sweatshirt"},
{"bad weather" -> "traffic jam", "pump"},
{"accident" -> "sirens", "nominative"}};


You can use GraphComputationLayeredGraphPlotLegacy or GraphComputationGraphPlotLegacy (if you have access to versions before v12 you can use LayeredGraphPlot and GraphPlot, respectively):

GraphComputationLayeredGraphPlotLegacy[elist,
DirectedEdges -> True, EdgeLabeling -> True, VertexLabeling -> True,
ImageSize -> 500, BaseStyle -> 15, PlotStyle -> Black]


GraphComputationGraphPlotLegacy[elist,
DirectedEdges -> True, EdgeLabeling -> True, VertexLabeling -> True,
ImageSize -> 500, BaseStyle -> 15, PlotStyle -> Black,
Method -> "LayeredDigraphDrawing"]


same picture

To render vertices as disks add the option

VertexRenderingFunction -> ({White, EdgeForm[Black], Disk[#, .3], Black, Text[#2, #1]} &)


to get

• kglr: Can you explain more the syntax behind eSF with ArrowHeads? – George Aug 15 at 17:56
• I'm trying to make this generalizable to arbitrary vertices/edges (including undirected edges). Ideally a user just supplies a list of relationships (with possible labels) into a function and everything is automatically drawn. I've removed the coords field since that lets Wolfram draw the layout. – George Aug 15 at 18:02
• @George, thank you for the accept. The function eSF takes the built-in edge shape function GraphElementData["Arrow"] and injects the edge label into the Arrowheads directive so that the label has the same orientation as the arrow. See Arrowheads >> Scope >> Custom Arrowheads for more examples of how custom arrowheads work. I use coords to match the picture. In general, it is more convenient to use the built-in vertex layouts. – kglr Aug 15 at 18:36
• If you have access to versions before v12 you might consider GraphPlot. (Unfortunately, v12 updates to GraphPlot eliminated all the convenient features of GraphPlot and turned it into a redundant / bugs-and-all clone of Graph :() – kglr Aug 15 at 18:50
• kglr: I love how the eSF creates space in the edges so that the text is always legible (i.e., the edge and the edge label never overlap). The problem with the eSF is that sometimes labels can be upside down if the nodes are configured in the right way. Is there a way to adjust the eSF so that the labels are always rightside up (like the first graph in your answer), but the spacing in between the edges and the text is preserved so that the labels are always legible? – George Sep 13 at 19:08

r = 1; (*radius of each disk*)

(*center of each disk. Numbers left to right, top to bottom*)
c1 = {0, 0}; c2 = {r + 2, 0}; c3 = {r + 5, 0}; c4 = {r + 2, -(r + 2)};
c5 = {r + 5, -(r + 2)};

makeDisk[r_, c_] := {EdgeForm[Black],LightYellow, Disk[c, r]}(*change as needed*)

makeArrow[from_, to_, dir_] := Module[{z = Cos[Pi/4]},
Which[
dir == "right",
Arrow[{{from[[1]] + r, from[[2]]}, {to[[1]] - r, to[[2]]}}],

dir == "down",
Arrow[{{from[[1]], from[[2]] - r}, {to[[1]], to[[2]] + r}}],

dir == "right-down",
Arrow[{{from[[1]] + z, from[[2]] - z}, {to[[1]] - z, to[[2]] + z}}],

dir == "left-down",
Arrow[{{from[[1]] - z, from[[2]] - z}, {to[[1]] + z, to[[2]] + z}}]

]
];
putLabel[txt_, at_] := Style[Text[txt, at], Bold, 12]
Graphics[{
makeDisk[1, c1],
makeDisk[1, c2],
makeDisk[1, c3],
makeDisk[1, c4],
makeDisk[1, c5],
makeArrow[c2, c3, "right"],
makeArrow[c2, c4, "down"],
makeArrow[c3, c5, "down"],
makeArrow[c1, c4, "right-down"],
makeArrow[c3, c4, "left-down"],
putLabel["rush hour", c1],