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VertexShapeFunction—Wolfram Documentation

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VertexShapeFunction

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

Details
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
VertexShapeFunction Specification  
VertexShapeFunction Gallery  
Possible Issues  
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VertexShapeFunction

VertexShapeFunction

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

Details

  • VertexShapeFunction is also known as node shape and shape function.
  • VertexShapeFunction is typically used to control the visual appearance of vertices and to display additional information.
  • The following option settings can be used:
  • Automaticthe default vertex function
    Nonedo not render vertices
    "Name"use the vertex name
    "nfunc"a named vertex function
    funca general vertex function
    {vivfi,…}use vertex function vfi for vertex vi
    {pattivfi,…}use vfi for vertices matching the pattern patti
  • VertexShapeFunction->func specifies that each vertex should be rendered with the primitives provided by func[{x,y},v,{w,h}], where {x,y} is the center, v the vertex name, and {w,h} the width and the height.
  • In 3D, VertexShapeFunction->func specifies that each vertex should be rendered with the primitives provided by func[{x,y,z},v,{w,h,d}], where {x,y,z} is the center, v the vertex name and {w,h,d} the width and the height.
  • The vertex function func should render the vertex primitives in the bounding box {{x-w,x+w},{y-h,y+h}} in 2D and {{x-w,x+w},{y-h,y+h},{z-d,z+d}} in 3D automatically computed by layout algorithms.
  • The following named arguments can be used in the vertex function func:
  • #Coordinatescenter {x,y} or {x,y,z}
    #Vertexvertex name v
    #Sizewidth and height {w,h}
  • Use ResourceData["VertexShapeFunction"] to get a list of all named vertex functions "nfunc".
  • Possible vertex shapes "nfunc" include:
  • The wrapper Annotation[v,VertexShapeFunction->f] can be used when creating graphs in functions such as Graph etc.

Examples

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Basic Examples  (4)

Draw vertices using a predefined vertex function:

Wolfram Language code: Graph[{12, 23, 31}, VertexShapeFunction -> "Square", VertexSize -> 0.2]

Specify a vertex function for an individual vertex:

Wolfram Language code: Graph[{12, 23, 31}, VertexShapeFunction -> { 1 -> "Square"}, VertexSize -> 0.2]

Use an Annotation wrapper to specify individual vertex functions:

Wolfram Language code: Graph[{Annotation[1, VertexShapeFunction -> "Square"], 2, 3}, {12, 23, 31}, VertexSize -> 0.2]

Draw vertices by running a program:

Wolfram Language code: vf[{xc_, yc_}, name_, {w_, h_}] := Block[{xmin = xc - w, xmax = xc + w, ymin = yc - h, ymax = yc + h}, Polygon[{{xmin, ymin}, {xmax, ymax}, {xmin, ymax}, {xmax, ymin}}] ];
Wolfram Language code: CompleteGraph[4, VertexShapeFunction -> vf, VertexSize -> 0.2]

Scope  (13)

VertexShapeFunction Specification  (9)

VertexShapeFunction can be used for general graphs:

Wolfram Language code: {Graph[{12, 23, 31}, VertexShapeFunction -> "Square", VertexSize -> 0.2], PathGraph[Range[25], VertexShapeFunction -> "Square", VertexSize -> 0.2]}

Matrix graphs:

Wolfram Language code: AdjacencyGraph[{{0, 1, 1}, {1, 0, 1}, {1, 1, 0}}, VertexShapeFunction -> "Square", VertexSize -> 0.2]

Special graphs:

Wolfram Language code: {PetersenGraph[5, 2, VertexShapeFunction -> "Square", VertexSize -> 0.2], GridGraph[{4, 4}, VertexShapeFunction -> "Square", VertexSize -> 0.2]}

Random graphs:

Wolfram Language code: RandomGraph[UniformGraphDistribution[10, 20], VertexShapeFunction -> "Square", VertexSize -> 0.2]

Use VertexShapeFunction in an Annotation wrapper:

Wolfram Language code: Graph[{Annotation[1, VertexShapeFunction -> "Square"], 2, 3}, {12, 23, 31}, VertexSize -> 0.2]
Wolfram Language code: HighlightGraph[GridGraph[{3, 3}, VertexSize -> 0.2], Annotation[5, VertexShapeFunction -> "Square"]]

VertexShapeFunction works with patterns:

Wolfram Language code: CompleteGraph[5, VertexShapeFunction -> {_ ? EvenQ -> "Star"}, VertexSize -> 0.2]

VertexShapeFunction can be combined with VertexStyle:

Wolfram Language code: vf1[{xc_, yc_}, name_, {w_, h_}] := Rectangle[{xc - w, yc - h}, {xc + w, yc + h}]
Wolfram Language code: Graph[{12, 23, 31}, VertexSize -> 0.2, VertexStyle -> Blue, VertexShapeFunction -> vf1]

VertexShapeFunction has higher priority than VertexStyle:

Wolfram Language code: vf2[{xc_, yc_}, name_, {w_, h_}] := {Red, Rectangle[{xc - w, yc - h}, {xc + w, yc + h}]}
Wolfram Language code: Graph[{12, 23, 31}, VertexSize -> 0.2, VertexStyle -> Blue, VertexShapeFunction -> vf2]

VertexShapeFunction can be combined with VertexSize:

Wolfram Language code: Graph[{12, 23, 31}, VertexShapeFunction -> "Star", VertexSize -> {1 -> Small, Medium}]

VertexShapeFunction has higher priority than VertexShape:

Wolfram Language code: Graph[{12, 23, 31}, VertexSize -> 0.2, VertexShapeFunction -> "Star", VertexShape -> [image]]

VertexShapeFunction Gallery  (4)

Get a list of built-in collections for VertexShapeFunction:

Wolfram Language code: ResourceData["VertexShapeFunction"]

Use built-in settings for VertexShapeFunction in the "Basic" collection:

Wolfram Language code: ResourceData["VertexShapeFunction", "Basic"]

Simple basic shapes:

Wolfram Language code: Table[Graph[{12, 23, 31}, VertexShapeFunction -> vf, VertexSize -> 0.2, PlotLabel -> vf], {vf, {"Triangle", "Square", "Rectangle", "Pentagon", "Hexagon", "Octagon"}}]

Common basic shapes:

Wolfram Language code: Table[Graph[{12, 23, 31}, VertexShapeFunction -> vf, VertexSize -> 0.2, PlotLabel -> vf], {vf, {"DownTrapezoid", "UpTrapezoid", "Parallelogram", "FiveDown", "Circle", "Diamond", "Star", "Capsule"}}]

Use built-in settings for VertexShapeFunction in the "Rounded" collection:

Wolfram Language code: ResourceData["VertexShapeFunction", "Rounded"]
Wolfram Language code: Table[Graph[{12, 23, 31}, VertexShapeFunction -> vf, VertexSize -> 0.2, PlotLabel -> Style[vf, 9]], {vf, ResourceData["VertexShapeFunction", "Rounded"]}]

Use built-in settings for VertexShapeFunction in the "Concave" collection:

Wolfram Language code: ResourceData["VertexShapeFunction", "Concave"]
Wolfram Language code: Table[Graph[{12, 23, 31}, VertexShapeFunction -> vf, VertexSize -> 0.2, PlotLabel -> Style[vf, 9]], {vf, ResourceData["VertexShapeFunction", "Concave"]}]

Possible Issues  (2)

Use Inset to render graphics or an image:

Wolfram Language code: Graph[{12, 23, 31}, VertexShapeFunction -> (Inset[[image], #1, Center, 2 * #3]&), VertexSize -> .2]

VertexShape takes graphics or images used for vertices:

Wolfram Language code: Graph[{12, 23, 31}, VertexShape -> [image], VertexSize -> .2]

With the setting VertexShapeFunctionNone, vertices are not displayed:

Wolfram Language code: PetersenGraph[5, 4, VertexShapeFunction -> None]

Use VertexSize0 to get connected lines:

Wolfram Language code: PetersenGraph[5, 4, VertexShapeFunction -> None, VertexSize -> 0]
Wolfram Research (2010), VertexShapeFunction, Wolfram Language function, https://reference.wolfram.com/language/ref/VertexShapeFunction.html (updated 2026).

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2026_vertexshapefunction, author="Wolfram Research", title="{VertexShapeFunction}", year="2026", howpublished="\url{https://reference.wolfram.com/language/ref/VertexShapeFunction.html}", note=[Accessed: 14-November-2026]}

BibLaTeX

@online{reference.wolfram_2026_vertexshapefunction, organization={Wolfram Research}, title={VertexShapeFunction}, year={2026}, url={https://reference.wolfram.com/language/ref/VertexShapeFunction.html}, note=[Accessed: 14-November-2026]}