WOLFRAM

gives the star graph with n vertices .

Details and Options

Examples

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Basic Examples  (2)Summary of the most common use cases

The first few star graphs :

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Directed star graphs:

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Options  (81)Common values & functionality for each option

AnnotationRules  (3)

Specify an annotation for vertices:

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Edges:

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Graph itself:

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DirectedEdges  (1)

By default, an undirected graph is generated:

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Use DirectedEdges->True to generate a directed graph:

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EdgeLabels  (7)

Label the edge 12:

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Label all edges individually:

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Use any expression as a label:

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Use Placed with symbolic locations to control label placement along an edge:

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Use explicit coordinates to place labels:

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Vary positions within the label:

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Place multiple labels:

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Use automatic labeling by values through Tooltip and StatusArea:

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EdgeShapeFunction  (6)

Get a list of built-in settings for EdgeShapeFunction:

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Undirected edges including the basic line:

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Lines with different glyphs on the edges:

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Directed edges including solid arrows:

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Line arrows:

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Open arrows:

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Specify an edge function for an individual edge:

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Combine with a different default edge function:

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Draw edges by running a program:

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EdgeShapeFunction can be combined with EdgeStyle:

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EdgeShapeFunction has higher priority than EdgeStyle:

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EdgeStyle  (2)

Style all edges:

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Style individual edges:

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EdgeWeight  (2)

Specify a weight for all edges:

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Use any numeric expression as a weight:

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GraphHighlight  (3)

Highlight the vertex 1:

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Highlight the edge 13:

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Highlight vertices and edges:

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GraphHighlightStyle  (2)

Get a list of built-in settings for GraphHighlightStyle:

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Use built-in settings for GraphHighlightStyle:

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GraphLayout  (5)

By default, the layout is chosen automatically:

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Specify layouts on special curves:

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Specify layouts that satisfy optimality criteria:

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VertexCoordinates overrides GraphLayout coordinates:

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Use AbsoluteOptions to extract VertexCoordinates computed using a layout algorithm:

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PlotTheme  (4)

Base Themes  (2)

Use a common base theme:

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Use a monochrome theme:

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Feature Themes  (2)

Use a large graph theme:

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Use a classic diagram theme:

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VertexCoordinates  (3)

By default, any vertex coordinates are computed automatically:

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Extract the resulting vertex coordinates using AbsoluteOptions:

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Specify a layout function along an ellipse:

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Use it to generate vertex coordinates for a graph:

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VertexCoordinates has higher priority than GraphLayout:

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VertexLabels  (13)

Use vertex names as labels:

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Label individual vertices:

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Label all vertices:

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Use any expression as a label:

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Use Placed with symbolic locations to control label placement, including outside positions:

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Symbolic outside corner positions:

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Symbolic inside positions:

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Symbolic inside corner positions:

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Use explicit coordinates to place the center of labels:

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Place all labels at the upper-right corner of the vertex and vary the coordinates within the label:

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Place multiple labels:

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Any number of labels can be used:

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Use the argument to Placed to control formatting including Tooltip:

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Or StatusArea:

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Use more elaborate formatting functions:

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VertexShape  (5)

Use any Graphics, Image, or Graphics3D as a vertex shape:

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Specify vertex shapes for individual vertices:

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VertexShape can be combined with VertexSize:

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VertexShape is not affected by VertexStyle:

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VertexShapeFunction has higher priority than VertexShape:

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VertexShapeFunction  (10)

Get a list of built-in collections for VertexShapeFunction:

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

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Simple basic shapes:

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Common basic shapes:

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

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

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Draw individual vertices:

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Combine with a default vertex function:

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Draw vertices using a predefined graphic:

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Draw vertices by running a program:

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VertexShapeFunction can be combined with VertexStyle:

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VertexShapeFunction has higher priority than VertexStyle:

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VertexShapeFunction can be combined with VertexSize:

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VertexShapeFunction has higher priority than VertexShape:

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VertexSize  (8)

By default, the size of vertices is computed automatically:

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Specify the size of all vertices using symbolic vertex size:

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Use a fraction of the minimum distance between vertex coordinates:

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Use a fraction of the overall diagonal for all vertex coordinates:

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Specify size in both the and directions:

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Specify the size for individual vertices:

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VertexSize can be combined with VertexShapeFunction:

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VertexSize can be combined with VertexShape:

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VertexStyle  (5)

Style all vertices:

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Style individual vertices:

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VertexShapeFunction can be combined with VertexStyle:

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VertexShapeFunction has higher priority than VertexStyle:

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VertexStyle can be combined with BaseStyle:

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VertexStyle has higher priority than BaseStyle:

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VertexShape is not affected by VertexStyle:

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VertexWeight  (2)

Set the weight for all vertices:

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Use any numeric expression as a weight:

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Applications  (7)Sample problems that can be solved with this function

The GraphCenter of star graphs:

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The GraphPeriphery:

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The VertexEccentricity:

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Highlight the vertex eccentricity path:

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The GraphRadius:

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Highlight the radius path:

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The GraphDiameter:

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Highlight the diameter path:

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Highlight the vertex degree for StarGraph:

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Highlight the closeness centrality:

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Highlight the eigenvector centrality:

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Vertex connectivity from to is the number of vertex-independent paths from to :

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The vertex connectivity for a star is 1 for all vertex pairs:

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Properties & Relations  (6)Properties of the function, and connections to other functions

StarGraph[n] has vertices:

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StarGraph[n] has edges:

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The complete bipartite graph is a star graph with vertices:

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A star graph is a tree:

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A star graph is bipartite:

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The line graph of the star graph is a complete graph :

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Neat Examples  (1)Surprising or curious use cases

Random collage of star graphs:

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

Text

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

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

CMS

Wolfram Language. 2010. "StarGraph." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/StarGraph.html.

Wolfram Language. 2010. "StarGraph." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/StarGraph.html.

APA

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

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

BibTeX

@misc{reference.wolfram_2025_stargraph, author="Wolfram Research", title="{StarGraph}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/StarGraph.html}", note=[Accessed: 23-April-2025 ]}

@misc{reference.wolfram_2025_stargraph, author="Wolfram Research", title="{StarGraph}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/StarGraph.html}", note=[Accessed: 23-April-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_stargraph, organization={Wolfram Research}, title={StarGraph}, year={2010}, url={https://reference.wolfram.com/language/ref/StarGraph.html}, note=[Accessed: 23-April-2025 ]}

@online{reference.wolfram_2025_stargraph, organization={Wolfram Research}, title={StarGraph}, year={2010}, url={https://reference.wolfram.com/language/ref/StarGraph.html}, note=[Accessed: 23-April-2025 ]}