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Wolfram Language & System Documentation Center
TreeGraph
  • See Also
    • Graph
    • UndirectedEdge
    • DirectedEdge
    • TreeGraphQ
    • KaryTree
    • CompleteKaryTree
    • StarGraph
    • FindSpanningTree
    • TreePlot
    • PathGraph
    • PlanarGraph
    • TextStructure
    • Groupings
  • Related Guides
    • Graph Construction & Representation
    • Tree Construction & Representation
    • Discrete Mathematics
    • Computation on Trees
    • See Also
      • Graph
      • UndirectedEdge
      • DirectedEdge
      • TreeGraphQ
      • KaryTree
      • CompleteKaryTree
      • StarGraph
      • FindSpanningTree
      • TreePlot
      • PathGraph
      • PlanarGraph
      • TextStructure
      • Groupings
    • Related Guides
      • Graph Construction & Representation
      • Tree Construction & Representation
      • Discrete Mathematics
      • Computation on Trees

TreeGraph[{v1,v2,…},{u1,u2,…}]

yields a tree where ui is the predecessor of vi.

TreeGraph[{e1,e2,…}]

yields a tree with edges ej.

TreeGraph[{v1,v2,…},{e1,e2,…}]

yields a tree with vertices vi and edges ej.

TreeGraph[{…,wi[vi,…],…},{…,wj[ej,…],…}]

yields a tree with vertex and edge properties defined by the symbolic wrappers wk.

TreeGraph[{vivj,…}]

uses rules vivj to specify a tree.

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Connectivity  
Wrappers  
Styling  
Labeling  
Options  
AnnotationRules  
DirectedEdges  
EdgeLabels  
Show More Show More
EdgeShapeFunction  
EdgeStyle  
EdgeWeight  
GraphHighlight  
GraphHighlightStyle  
GraphLayout  
PlotTheme  
Base Themes  
Feature Themes  
VertexCoordinates  
VertexLabels  
VertexShape  
VertexShapeFunction  
VertexSize  
VertexStyle  
VertexWeight  
Applications  
Properties & Relations  
See Also
Related Guides
History
Cite this Page
BUILT-IN SYMBOL
  • See Also
    • Graph
    • UndirectedEdge
    • DirectedEdge
    • TreeGraphQ
    • KaryTree
    • CompleteKaryTree
    • StarGraph
    • FindSpanningTree
    • TreePlot
    • PathGraph
    • PlanarGraph
    • TextStructure
    • Groupings
  • Related Guides
    • Graph Construction & Representation
    • Tree Construction & Representation
    • Discrete Mathematics
    • Computation on Trees
    • See Also
      • Graph
      • UndirectedEdge
      • DirectedEdge
      • TreeGraphQ
      • KaryTree
      • CompleteKaryTree
      • StarGraph
      • FindSpanningTree
      • TreePlot
      • PathGraph
      • PlanarGraph
      • TextStructure
      • Groupings
    • Related Guides
      • Graph Construction & Representation
      • Tree Construction & Representation
      • Discrete Mathematics
      • Computation on Trees

TreeGraph

TreeGraph[{v1,v2,…},{u1,u2,…}]

yields a tree where ui is the predecessor of vi.

TreeGraph[{e1,e2,…}]

yields a tree with edges ej.

TreeGraph[{v1,v2,…},{e1,e2,…}]

yields a tree with vertices vi and edges ej.

TreeGraph[{…,wi[vi,…],…},{…,wj[ej,…],…}]

yields a tree with vertex and edge properties defined by the symbolic wrappers wk.

TreeGraph[{vivj,…}]

uses rules vivj to specify a tree.

Details and Options

  • TreeGraph generates a Graph object.
  • TreeGraph supports the same vertices, edges, wrappers, and options as Graph.
  • A tree is a simple connected graph with no cycles.
  • A tree is a connected graph with no cycles.
  • TreeGraph can only represent trees.
  • List of all options

    • AlignmentPointCenterthe default point in the graphic to align with
      AnnotationRules {}annotations for graph, edges and vertices
      AspectRatioAutomaticratio of height to width
      AxesFalsewhether to draw axes
      AxesLabelNoneaxes labels
      AxesOriginAutomaticwhere axes should cross
      AxesStyle{}style specifications for the axes
      BackgroundNonebackground color for the plot
      BaselinePositionAutomatichow to align with a surrounding text baseline
      BaseStyle{}base style specifications for the graphic
      ContentSelectableAutomaticwhether to allow contents to be selected
      CoordinatesToolOptionsAutomaticdetailed behavior of the coordinates tool
      DirectedEdges Automaticwhether to interpret Rule as DirectedEdge
      EdgeLabels Nonelabels and label placements for edges
      EdgeLabelStyleAutomaticstyle to use for edge labels
      EdgeShapeFunction Automaticgenerate graphic shapes for edges
      EdgeStyle Automaticstyle used for edges
      EdgeWeight Automaticweights for edges
      Epilog{}primitives rendered after the main plot
      FormatTypeTraditionalFormthe default format type for text
      FrameFalsewhether to put a frame around the plot
      FrameLabelNoneframe labels
      FrameStyle{}style specifications for the frame
      FrameTicksAutomaticframe ticks
      FrameTicksStyle{}style specifications for frame ticks
      GraphHighlight {}graph elements to highlight
      GraphHighlightStyle Automaticstyle for highlight
      GraphLayout Automatichow to lay out vertices and edges
      GridLinesNonegrid lines to draw
      GridLinesStyle{}style specifications for grid lines
      ImageMargins0.the margins to leave around the graphic
      ImagePaddingAllwhat extra padding to allow for labels etc.
      ImageSizeAutomaticthe absolute size at which to render the graphic
      LabelStyle{}style specifications for labels
      MethodAutomaticdetails of graphics methods to use
      PerformanceGoalAutomaticaspects of performance to try to optimize
      PlotLabelNonean overall label for the plot
      PlotRangeAllrange of values to include
      PlotRangeClippingFalsewhether to clip at the plot range
      PlotRangePaddingAutomatichow much to pad the range of values
      PlotRegionAutomaticthe final display region to be filled
      PlotTheme $PlotThemeoverall theme for the graph
      PreserveImageOptionsAutomaticwhether to preserve image options when displaying new versions of the same graphic
      Prolog{}primitives rendered before the main plot
      RotateLabelTruewhether to rotate y labels on the frame
      TicksAutomaticaxes ticks
      TicksStyle{}style specifications for axes ticks
      VertexCoordinates Automaticcoordinates for vertices
      VertexLabels Nonelabels and placements for vertices
      VertexLabelStyleAutomaticstyle to use for vertex labels
      VertexShape Automaticgraphic shape for vertices
      VertexShapeFunction Automaticgenerate graphic shapes for vertices
      VertexSize Mediumsize of vertices
      VertexStyle Automaticstyles for vertices
      VertexWeight Automaticweights for vertices

Examples

open all close all

Basic Examples  (1)

A tree from pairs of children and parents:

A tree from a list of vertices and edges:

Scope  (25)

Connectivity  (6)

Create an undirected graph using  characters; enter the character as ue:

Create a directed graph using  characters; enter the character as de:

Create a directed graph from a list of rules:

Create an undirected graph from a list of rules:

Use VertexList and EdgeList to get vertices and edges:

The ordering for edges is the order in which they were entered:

The ordering for vertices is the order in which they were entered in the edges:

Use an explicit vertex list to control the ordering used by VertexList:

The input vertex list controls the resulting vertex order:

Any expression can be used as vertices:

Wrappers  (5)

Use wrappers on vertices or edges:

Wrappers can be nested:

Add interactive behavior by wrappers such as Tooltip:

Any object can be used in the tooltip:

Use Button to trigger actions when clicking an edge or vertex:

Use PopupWindow to provide information drilldown:

Styling  (8)

Set the style for all vertices or edges:

Style individual vertices or edges using options:

Use wrappers for individual styling:

Adjust the size of vertices using symbolic sizes:

Or use sizes in terms of the smallest distance between vertex centers:

Use built-in collections for VertexShapeFunction:

Rounded shapes:

Concave shapes:

Draw individual vertices:

Combine with a default vertex function:

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

Use built-in collections for EdgeShapeFunction:

Directed edges including solid arrows:

Line arrows:

Open arrows:

Specify an edge function for an individual edge:

Combine with a different default edge function:

Labeling  (6)

Label any edge or vertex:

Use any expression as a label:

Control the placement of vertex labels using Placed, including symbolic inside positions:

Symbolic outside positions:

Coordinate-based positions:

Place multiple labels using Placed in a wrapper:

Any number of labels can be used:

Place multiple labels using VertexLabels:

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

Use explicit coordinates to place labels:

Place multiple labels using Placed in a wrapper:

Any number of labels can be used:

Place multiple labels using EdgeLabels:

Options  (82)

AnnotationRules  (3)

Specify an annotation for vertices:

Edges:

Graph itself:

DirectedEdges  (2)

By default, a directed tree is generated when giving a list of rules:

Use DirectedEdges->False to interpret rules as undirected edges:

Use DirectedEdge or UndirectedEdge to directly specify whether a graph is directed or not:

EdgeLabels  (7)

Label the edge 12:

Label all edges:

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 using Placed in a wrapper:

Any number of labels can be used:

Place multiple labels using EdgeLabels:

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 the 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)

Get a list of built-in settings for GraphHighlightStyle:

Use built-in settings for GraphHighlightStyle:

GraphLayout  (5)

By default, the layout is chosen automatically:

Specify layouts on special curves:

Specify layouts that satisfy optimality criteria:

VertexCoordinates overrides GraphLayout coordinates:

Use AbsoluteOptions to extract VertexCoordinates computed using a layout algorithm:

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 using Placed in a wrapper:

Any number of labels can be used:

Place multiple labels using VertexLabels:

Use the argument to Placed to control formatting including Tooltip:

Or StatusArea:

Use more elaborate formatting functions:

VertexShape  (5)

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

Specify vertex shapes for individual vertices:

VertexShape can be combined with VertexSize:

VertexShape is not affected by VertexStyle:

VertexShapeFunction has higher priority than VertexShape:

VertexShapeFunction  (10)

Get a list of built-in collections for VertexShapeFunction:

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

Simple basic shapes:

Common basic shapes:

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

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

Draw individual vertices:

Combine with a default vertex function:

Draw vertices using a predefined graphic:

Draw vertices by running a program:

VertexShapeFunction can be combined with VertexStyle:

VertexShapeFunction has higher priority than VertexStyle:

VertexShapeFunction can be combined with VertexSize:

VertexShapeFunction has higher priority than VertexShape:

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 sizes for individual vertices:

VertexSize can be combined with VertexShapeFunction:

VertexSize can be combined with VertexShape:

VertexStyle  (5)

Style all vertices:

Style individual vertices:

VertexShapeFunction can be combined with VertexStyle:

VertexShapeFunction has higher priority than VertexStyle:

VertexStyle can be combined with BaseStyle:

VertexStyle has higher priority than BaseStyle:

VertexShape is not affected by VertexStyle:

VertexWeight  (2)

Set the weight for all vertices:

Use any numeric expression as a weight:

Applications  (4)

Generate a random tree:

Highlight the GraphCenter and GraphPeriphery:

The VertexEccentricity:

Highlight the vertex eccentricity path:

The GraphRadius:

Highlight the radius path:

The GraphDiameter:

Highlight the diameter path:

Properties & Relations  (9)

Use VertexCount and EdgeCount to count vertices and edges:

Use VertexList and EdgeList to enumerate vertices and edges in standard order:

Edges and vertices are given in the order they are input:

Compute the AdjacencyMatrix from a graph:

A tree graph is connected:

A tree graph does not have any loops or cycles:

A tree graph with vertices has edges:

A tree graph is a bipartite graph:

A tree graph with vertices with has at least two and at most vertices of degree 1:

A star graph is a tree graph:

See Also

Graph  UndirectedEdge  DirectedEdge  TreeGraphQ  KaryTree  CompleteKaryTree  StarGraph  FindSpanningTree  TreePlot  PathGraph  PlanarGraph  TextStructure  Groupings

Function Repository: PruferCodeToLabeledTree

Related Guides

    ▪
  • Graph Construction & Representation
  • ▪
  • Tree Construction & Representation
  • ▪
  • Discrete Mathematics
  • ▪
  • Computation on Trees

History

Introduced in 2010 (8.0) | Updated in 2015 (10.3)

Wolfram Research (2010), TreeGraph, Wolfram Language function, https://reference.wolfram.com/language/ref/TreeGraph.html (updated 2015).

Text

Wolfram Research (2010), TreeGraph, Wolfram Language function, https://reference.wolfram.com/language/ref/TreeGraph.html (updated 2015).

CMS

Wolfram Language. 2010. "TreeGraph." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2015. https://reference.wolfram.com/language/ref/TreeGraph.html.

APA

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

BibTeX

@misc{reference.wolfram_2025_treegraph, author="Wolfram Research", title="{TreeGraph}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/TreeGraph.html}", note=[Accessed: 01-December-2025]}

BibLaTeX

@online{reference.wolfram_2025_treegraph, organization={Wolfram Research}, title={TreeGraph}, year={2015}, url={https://reference.wolfram.com/language/ref/TreeGraph.html}, note=[Accessed: 01-December-2025]}

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