StarGraph—Wolfram Documentation (original) (raw)

StarGraph[n]

gives the star graph with n vertices .

Details and Options

Examples

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Basic Examples (2)

The first few star graphs :

Directed star graphs:

Options (81)

AnnotationRules (3)

Specify an annotation for vertices:

Edges:

Graph itself:

DirectedEdges (1)

By default, an undirected graph is generated:

Use DirectedEdges->True to generate a directed graph:

EdgeLabels (7)

Label the edge 12:

Label all edges individually:

Use any expression as a label:

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

Use explicit coordinates to place labels:

Vary positions within the label:

Place multiple labels:

Use automatic labeling by values through Tooltip and StatusArea:

EdgeShapeFunction (6)

Get a list of built-in settings for EdgeShapeFunction:

Undirected edges including the basic line:

Lines with different glyphs on the edges:

Directed edges including solid arrows:

Line arrows:

Open arrows:

Specify an edge function for an individual edge:

Combine with a different default edge function:

Draw edges by running a program:

EdgeShapeFunction can be combined with EdgeStyle:

EdgeShapeFunction has higher priority than EdgeStyle:

EdgeStyle (2)

Style all edges:

Style individual edges:

EdgeWeight (2)

Specify a weight for all edges:

Use any numeric expression as a weight:

GraphHighlight (3)

Highlight the vertex 1:

Highlight the edge 13:

Highlight vertices and edges:

GraphHighlightStyle (2)

GraphLayout (5)

PlotTheme (4)

Base Themes (2)

Use a common base theme:

Use a monochrome theme:

Feature Themes (2)

Use a large graph theme:

Use a classic diagram theme:

VertexCoordinates (3)

By default, any vertex coordinates are computed automatically:

Extract the resulting vertex coordinates using AbsoluteOptions:

Specify a layout function along an ellipse:

Use it to generate vertex coordinates for a graph:

VertexCoordinates has higher priority than GraphLayout:

VertexLabels (13)

Use vertex names as labels:

Label individual vertices:

Label all vertices:

Use any expression as a label:

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

Symbolic outside corner positions:

Symbolic inside positions:

Symbolic inside corner positions:

Use explicit coordinates to place the center of labels:

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

Place multiple labels:

Any number of labels can be used:

Use the argument to Placed to control formatting including Tooltip:

Or StatusArea:

Use more elaborate formatting functions:

VertexShape (5)

VertexShapeFunction (10)

VertexSize (8)

By default, the size of vertices is computed automatically:

Specify the size of all vertices using symbolic vertex size:

Use a fraction of the minimum distance between vertex coordinates:

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

Specify size in both the and directions:

Specify the size for individual vertices:

VertexSize can be combined with VertexShapeFunction:

VertexSize can be combined with VertexShape:

VertexStyle (5)

VertexWeight (2)

Set the weight for all vertices:

Use any numeric expression as a weight:

Applications (7)

The GraphCenter of star graphs:

The GraphPeriphery:

The VertexEccentricity:

Highlight the vertex eccentricity path:

The GraphRadius:

Highlight the radius path:

The GraphDiameter:

Highlight the diameter path:

Highlight the vertex degree for StarGraph:

Highlight the closeness centrality:

Highlight the eigenvector centrality:

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

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

Properties & Relations (6)

StarGraph[n] has vertices:

StarGraph[n] has edges:

The complete bipartite graph is a star graph with vertices:

A star graph is a tree:

A star graph is bipartite:

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

Neat Examples (1)

Random collage of star graphs:

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.

CMS

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

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: 17-May-2026]}

BibLaTeX

@online{reference.wolfram_2025_stargraph, organization={Wolfram Research}, title={StarGraph}, year={2010}, url={https://reference.wolfram.com/language/ref/StarGraph.html}, note=[Accessed: 17-May-2026]}