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EdgeShapeFunction—Wolfram Documentation

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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  
See Also
Related Guides
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: 14-November-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: 14-November-2026]}