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EdgeShapeFunction

is an option and annotation for Graph and related functions that specifies a function to use to generate primitives for rendering each edge.

Details
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
EdgeShapeFunction Specification  
EdgeShapeFunction Gallery  
Possible Issues  
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History
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EdgeShapeFunction

EdgeShapeFunction

is an option and annotation for Graph and related functions that specifies a function to use to generate primitives for rendering each edge.

Details

  • EdgeShapeFunction is also known as edge routing.
  • EdgeShapeFunction is typically used to control the visual appearance of paths connecting vertices.
  • The following option settings can be used:
  • Automaticthe default edge function
    Nonedo not render edges
    "nfunc"a named edge function
    funca general edge function
    {vivj->efij,…}use edge function efij for edge vivj
    {pattiefi,…}use edge function efi for edges matching the pattern patti
  • EdgeShapeFunction->func specifies that each edge should be rendered with the primitives provided by func[{{x1,y1},{x2,y2},…},vw], where {{x1,y1},{x2,y2},…} are line segments and vw is the edge.
  • In 3D, EdgeShapeFunction->func specifies that each vertex should be rendered with the primitives provided by func[{{x1,y1,z1},{x2,y2,z2},…},vw], where {{x1,y1,z1},{x2,y2,z2},…} are line segments and vw is the edge.
  • The following named arguments can be used in the edge function func:
  • #Coordinatesline segments {{x1,y1}, …}
    #Edgeedge vw
  • Use ResourceData["EdgeShapeFunction"] to get a list of all named edge functions "nfunc":
  • The wrapper Annotation[vw,EdgeShapeFunction->f] can be used when creating graphs in functions such as Graph etc.

Examples

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Basic Examples  (4)

Draw edges using a predefined edge function:

Wolfram Language code: Graph[{12, 23, 31}, EdgeShapeFunction -> {{"HalfFilledArrow", "ArrowSize" -> .1}}]

Specify an edge function for an individual edge:

Wolfram Language code: Graph[{12, 23, 31}, EdgeShapeFunction -> {12 -> {"HalfFilledArrow", "ArrowSize" -> .1}}]

Combine with a different default edge function:

Wolfram Language code: Graph[{12, 23, 31}, EdgeShapeFunction -> {12 -> "HalfFilledArrow", "CarvedArrow"}]

Use an Annotation wrapper to specify individual edge functions:

Wolfram Language code: Graph[{Annotation[12, EdgeShapeFunction -> {"CarvedArrow", "ArrowSize" -> .1}], 23, 31}]

Draw edges by running a program:

Wolfram Language code: ef[pts_List, e_] := Block[{s = 0.015, g = [image]}, {Arrowheads[{{s, 0.33, g}, {s, 0.67, g}}], Arrow[pts]}]
Wolfram Language code: Graph[{12, 23, 31}, EdgeShapeFunction -> ef]

Scope  (10)

EdgeShapeFunction Specification  (7)

EdgeShapeFunction can be used for general graphs:

Wolfram Language code: {Graph[{12, 23, 31}, EdgeShapeFunction -> "CarvedArrow"], PathGraph[Range[25], EdgeShapeFunction -> "CarvedArrow"]}

Matrix graphs:

Wolfram Language code: AdjacencyGraph[{{0, 1, 0}, {0, 0, 1}, {1, 0, 0}}, EdgeShapeFunction -> "CarvedArrow"]

Special graphs:

Wolfram Language code: {PetersenGraph[5, 2, EdgeShapeFunction -> "CarvedArrow"], GridGraph[{3, 3}, EdgeShapeFunction -> "CarvedArrow"]}

Random graphs:

Wolfram Language code: RandomGraph[UniformGraphDistribution[10, 20], EdgeShapeFunction -> "CarvedArrow"]

Use EdgeShapeFunction in an Annotation wrapper:

Wolfram Language code: Graph[{Annotation[12, EdgeShapeFunction -> "CarvedArrow"], 23, 31}]
Wolfram Language code: HighlightGraph[GridGraph[{2, 3}], Annotation[13, EdgeShapeFunction -> "CarvedArrow"]]

EdgeShapeFunction works with patterns:

Wolfram Language code: CompleteGraph[5, EdgeShapeFunction -> {_2 -> "CarvedArrow"}]

EdgeShapeFunction can be combined with EdgeStyle:

Wolfram Language code: Graph[{12, 23, 31}, EdgeStyle -> Blue, EdgeShapeFunction -> (Line[#1]&)]

EdgeShapeFunction has higher priority than EdgeStyle:

Wolfram Language code: Graph[{12, 23, 31}, EdgeStyle -> Blue, EdgeShapeFunction -> ({Red, Line[#1]}&)]

EdgeShapeFunction Gallery  (3)

Get a list of built-in settings for EdgeShapeFunction:

Wolfram Language code: ResourceData["EdgeShapeFunction"]

Undirected edges including the basic line:

Wolfram Language code: Graph[{12, 23, 31}, EdgeShapeFunction -> "Line"]

Lines with different glyphs on the edges:

Wolfram Language code: Table[Graph[{12, 23, 31}, EdgeShapeFunction -> {{ef, "ArrowSize" -> 0.1}}, PlotLabel -> ef], {ef, {"BoxLine", "DiamondLine", "DotLine"}}]

Directed edges including solid arrows:

Wolfram Language code: Table[Graph[{12, 23, 31}, EdgeShapeFunction -> {{ef, "ArrowSize" -> 0.1}}, PlotLabel -> ef], {ef, ResourceData["EdgeShapeFunction", "FilledArrow"]}]

Line arrows:

Wolfram Language code: Table[Graph[{12, 23, 31}, EdgeShapeFunction -> {{ef, "ArrowSize" -> 0.1}}, PlotLabel -> ef], {ef, ResourceData["EdgeShapeFunction", "UnfilledArrow"]}]

Open arrows:

Wolfram Language code: Table[Graph[{12, 23, 31}, EdgeShapeFunction -> {{ef, "ArrowSize" -> 0.1}}, PlotLabel -> ef], {ef, ResourceData["EdgeShapeFunction", "CarvedArrow"]}]

Possible Issues  (1)

Using Rule to indicate edges does not work:

Wolfram Language code: Graph[{1 -> 2, 2 -> 3, 3 -> 1}, EdgeShapeFunction -> {1 -> 2 -> "CarvedArrow"}]

Use parentheses to get correct parsing:

Wolfram Language code: 1 -> 2 -> "CarvedArrow"//FullForm
Wolfram Language code: (1 -> 2) -> "CarvedArrow"//FullForm
Wolfram Language code: Graph[{1 -> 2, 2 -> 3, 3 -> 1}, EdgeShapeFunction -> {(1 -> 2) -> "CarvedArrow"}]
Wolfram Research (2010), EdgeShapeFunction, Wolfram Language function, https://reference.wolfram.com/language/ref/EdgeShapeFunction.html (updated 2026).

Text

Wolfram Research (2010), EdgeShapeFunction, Wolfram Language function, https://reference.wolfram.com/language/ref/EdgeShapeFunction.html (updated 2026).

CMS

Wolfram Language. 2010. "EdgeShapeFunction." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2026. https://reference.wolfram.com/language/ref/EdgeShapeFunction.html.

APA

Wolfram Language. (2010). EdgeShapeFunction. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/EdgeShapeFunction.html

BibTeX

@misc{reference.wolfram_2026_edgeshapefunction, author="Wolfram Research", title="{EdgeShapeFunction}", year="2026", howpublished="\url{https://reference.wolfram.com/language/ref/EdgeShapeFunction.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_edgeshapefunction, organization={Wolfram Research}, title={EdgeShapeFunction}, year={2026}, url={https://reference.wolfram.com/language/ref/EdgeShapeFunction.html}, note=[Accessed: 13-June-2026]}