TreePlot
TreePlot[g]
generates a tree plot of the graph g.
TreePlot[{e1,e2,…}]
generates a tree plot of the graph with edges ej.
TreePlot[{…,w[ei],…}]
plots ei with features defined by the symbolic wrapper w.
TreePlot[{vi 1vj 1,…}]
uses rules vi 1vj 1 to specify the graph g.
TreePlot[m]
generates a tree plot of the graph represented by the adjacency matrix m.
TreePlot[…,vpos]
places the root v in the plot at position pos.
Details and Options
- TreePlot is also known as tree diagram.
- TreePlot attempts to place vertices in a tree of successive layers, or a collection of trees.
- TreePlot supports the same vertices and edges as Graph.
- If the graph g is not a tree, TreePlot lays out its vertices on the basis of a spanning tree of each connected component of the graph.
- TreePlot[g] attempts to choose the root so as to make trees have as few layers as possible.
- TreePlot[g,pos] places the roots at position pos.
- Possible positions pos are: Top, Bottom, Left, Right, Center.
- By default, TreePlot places each tree root at the top.
- The following special wrappers can be used for the edges ei:
-
Annotation[ei,label] provide an annotation Button[ei,action] define an action to execute when the element is clicked EventHandler[ei,…] define a general event handler for the element Hyperlink[ei,uri] make the element act as a hyperlink Labeled[ei,…] display the element with labeling PopupWindow[ei,cont] attach a popup window to the element StatusArea[ei,label] display in the status area when the element is moused over Style[ei,opts] show the element using the specified styles Tooltip[ei,label] attach an arbitrary tooltip to the element - TreePlot has the same options as Graphics, with the following additions and changes: [List of all options]
-
DataRange Automatic the range of vertex coordinates to generate DirectedEdges False whether to interpret Rule as DirectedEdge EdgeLabels None labels and placements for edges EdgeLabelStyle Automatic style to use for edge labels EdgeShapeFunction Automatic generate graphic shapes for edges EdgeStyle Automatic styles for edges GraphHighlight {} vertices and edges to highlight GraphHighlightStyle Automatic style for highlight LayerSizeFunction (1) the height to allow for each layer PerformanceGoal Automatic aspects of performance to try to optimize PlotStyle Automatic graphics directives to determine styles PlotTheme Automatic overall theme for the graph VertexCoordinates Automatic coordinates for vertices VertexLabels None labels and placements for vertices VertexLabelStyle Automatic style to use for vertex labels VertexShape Automatic graphic shape for vertices VertexShapeFunction Automatic generate graphic shapes for vertices VertexSize Automatic size of vertices VertexStyle Automatic styles for vertices - Possible settings for PlotTheme include common base themes:
-
"Business" a bright, modern look appropriate for business presentations or infographics 
"Detailed" identify data by employing labels and tooltips 
"Marketing" elegant, eye-catching design suitable for marketing needs 
"Minimal" simple graph 
"Monochrome" single-color design 
"Scientific" candid design useful for analyzing detailed data with labels and tooltips 
"Web" clean, bold design suitable for a consumer website or blog 
"Classic" historical design of graph to remain compatible with existing uses - Graph feature themes affect the plots of vertices and edges. Feature themes include:
-
"LargeGraph" large graph 
"ClassicLabeled" classic graph 
"IndexLabeled" index-labeled graph
List of all options
Examples
open all close allBasic Examples (5)
TreePlot[KaryTree[9, 2]]Plot a graph specified by edge rules:
TreePlot[{1 -> 2, 2 -> 3, 3 -> 4, 4 -> 0, 5 -> 1, 6 -> 2, 7 -> 3, 8 -> 4, 9 -> 0}]Plot a graph specified by its adjacency matrix:
TreePlot[{{0, 1, 1, 1, 0}, {1, 0, 0, 0, 1}, {1, 0, 0, 0, 0}, {1, 0, 0, 0, 0}, {0, 1, 0, 0, 0}}]Drawing a tree with different orientation from the default:
TreePlot[{1 -> 4, 1 -> 6, 1 -> 8, 2 -> 6, {3 -> 8, "3->8"}, 4 -> 5, 7 -> 8}, Left]Table[TreePlot[{1 -> 4, 1 -> 6, 1 -> 8, 2 -> 6, 3 -> 8, 4 -> 5, 7 -> 8}, Automatic, root, VertexLabels -> Automatic], {root, {1, 5}}]Scope (10)
Graph Specification (4)
Specify a graph using a graph:
TreePlot[Graph[{14, 17, 25, 34, 45, 56}]]Specify a graph using a rule list:
TreePlot[{1 -> 4, 1 -> 7, 2 -> 5, 3 -> 4, 4 -> 5, 5 -> 6}]Specify a graph using a dense adjacency matrix:
TreePlot[{{0, 1, 0, 0}, {0, 0, 1, 1}, {0, 0, 0, 0}, {0, 0, 0, 0}}]Specify a graph using a sparse adjacency matrix:
TreePlot[SparseArray[{{1, 2}, {2, 3}, {2, 4}} -> 1, {4, 4}]]Graph Styling (6)
TreePlot[{1 -> 2, 3 -> 1, Labeled[2 -> 4, "2->4"], 2 -> 5}]TreePlot[{1 -> 2, 3 -> 1, 2 -> 4, 2 -> 5, 1 -> 2, 5 -> 5, 3 -> 6}, VertexLabels -> Automatic]TreePlot[{1 -> 3, 1 -> 5, 2 -> 6, 2 -> 7, 2 -> 8, 4 -> 6, 5 -> 6}, DirectedEdges -> True]Plot a disconnected graph using different packing methods:
Table[Framed@TreePlot[Table[i -> Mod[i ^ 2, 31], {i, 0, 31}], GraphLayout -> {"PackingLayout" -> pm}], {pm, {Automatic, "ClosestPacking"}}]For large graphs, it is sometimes better not to draw vertices at all:
TreePlot[Table[i -> Mod[i ^ 2, 351], {i, 351}], VertexShapeFunction -> None]Drawing a tree with different orientations:
Grid[Partition[Table[TreePlot[{1 -> 4, 1 -> 6, 1 -> 8, 2 -> 6, {3 -> 8, "3->8"}, 4 -> 5, 7 -> 8}, pos, BaselinePosition -> Top, PlotLabel -> pos], {pos, {Automatic, Left, Top, Right, Bottom, Center}}], {3}]]Options (35)
AspectRatio (1)
By default, the ratio of the height to width for the plot is determined automatically:
t = Flatten[Table[{i -> 2 i + j - 1}, {j, 2}, {i, 7}]];TreePlot[t]AspectRatio1 will make width equal to height:
TreePlot[t, AspectRatio -> 1]AspectRatioFull adjusts the height and width to tightly fit inside other constructs:
plot = TreePlot[t, AspectRatio -> Full];{Framed[Pane[plot, {50, 100}]], Framed[Pane[plot, {100, 100}]], Framed[Pane[plot, {100, 50}]]}Axes (1)
By default, Axes are not drawn:
t = Flatten[Table[{i -> 2 i + j - 1}, {j, 2}, {i, 7}]];TreePlot[t]Use AxesTrue to turn on axes:
TreePlot[t, Axes -> True]Turn each axis on individually:
{TreePlot[t, Axes -> {True, False}], TreePlot[t, Axes -> {False, True}]}AxesLabel (3)
No axes labels are drawn by default:
TreePlot[Flatten[Table[{i -> 2 i + j - 1}, {j, 2}, {i, 7}]], Axes -> True]
TreePlot[Flatten[Table[{i -> 2 i + j - 1}, {j, 2}, {i, 7}]], Axes -> True, AxesLabel -> y]TreePlot[Flatten[Table[{i -> 2 i + j - 1}, {j, 2}, {i, 7}]], Axes -> True, AxesLabel -> {x, y}]AxesOrigin (2)
The position of the axes is determined automatically:
TreePlot[Flatten[Table[{i -> 2 i + j - 1}, {j, 2}, {i, 7}]], Axes -> True]Specify an explicit origin for the axes:
TreePlot[Flatten[Table[{i -> 2 i + j - 1}, {j, 2}, {i, 7}]], Axes -> True, AxesOrigin -> {2.5, 3}]AxesStyle (4)
Change the style for the axes:
TreePlot[Flatten[Table[{i -> 2 i + j - 1}, {j, 2}, {i, 7}]], Axes -> True, AxesStyle -> Red]Specify the style of each axis:
TreePlot[Flatten[Table[{i -> 2 i + j - 1}, {j, 2}, {i, 7}]], Axes -> True, AxesStyle -> {{Thick, Red}, {Thick, Blue}}]Use different styles for the ticks and the axes:
TreePlot[Flatten[Table[{i -> 2 i + j - 1}, {j, 2}, {i, 7}]], Axes -> True, AxesStyle -> Green, TicksStyle -> Red]Use different styles for the labels and the axes:
TreePlot[Flatten[Table[{i -> 2 i + j - 1}, {j, 2}, {i, 7}]], Axes -> True, AxesStyle -> Green, LabelStyle -> Red]DataRange (1)
DirectedEdges (1)
Frame (4)
TreePlot does not use a frame by default:
TreePlot[{1 -> 4, 1 -> 7, 2 -> 5, 3 -> 4, 4 -> 5, 5 -> 6}]Use FrameTrue to draw a frame around the plot:
TreePlot[{1 -> 4, 1 -> 7, 2 -> 5, 3 -> 4, 4 -> 5, 5 -> 6}, Frame -> True]Draw a frame on the left and right edges:
TreePlot[{1 -> 4, 1 -> 7, 2 -> 5, 3 -> 4, 4 -> 5, 5 -> 6}, Frame -> {{True, True}, {False, False}}]Draw a frame on the left and bottom edges:
TreePlot[{1 -> 4, 1 -> 7, 2 -> 5, 3 -> 4, 4 -> 5, 5 -> 6}, Frame -> {{True, False}, {True, False}}]FrameLabel (4)
Place a label along the bottom frame of the chart:
TreePlot[{1 -> 4, 1 -> 7, 2 -> 5, 3 -> 4, 4 -> 5, 5 -> 6}, Frame -> True, FrameLabel -> {"label"}]Frame labels are placed on the bottom and left frame edges by default:
TreePlot[{1 -> 4, 1 -> 7, 2 -> 5, 3 -> 4, 4 -> 5, 5 -> 6}, Frame -> True, FrameLabel -> {"bottom", "left"}]Place labels on each of the edges in the frame:
TreePlot[{1 -> 4, 1 -> 7, 2 -> 5, 3 -> 4, 4 -> 5, 5 -> 6}, Frame -> True, FrameLabel -> {{"left", "right"}, {"bottom", "top"}}]Use a customized style for both labels and frame tick labels:
TreePlot[{1 -> 4, 1 -> 7, 2 -> 5, 3 -> 4, 4 -> 5, 5 -> 6}, Frame -> True, FrameLabel -> {{"left", "right"}, {"bottom", "top"}}, LabelStyle -> Directive[Bold, Orange]]FrameStyle (2)
Specify the style of the frame:
TreePlot[{1 -> 4, 1 -> 7, 2 -> 5, 3 -> 4, 4 -> 5, 5 -> 6}, Frame -> True, FrameStyle -> Directive[StandardGray, Thick]]Specify the style for each frame edge:
TreePlot[{1 -> 4, 1 -> 7, 2 -> 5, 3 -> 4, 4 -> 5, 5 -> 6}, Frame -> True, FrameStyle -> {{Directive[Green, Thick], Red}, {Directive[Gray, Thick], Blue}}]ImageSize (7)
Use named sizes such as Tiny, Small, Medium and Large:
{TreePlot[Flatten[Table[{i -> 2 i + j - 1}, {j, 2}, {i, 7}]], ImageSize -> Tiny], TreePlot[Flatten[Table[{i -> 2 i + j - 1}, {j, 2}, {i, 7}]], ImageSize -> Small]}Specify the width of the plot:
{TreePlot[Flatten[Table[{i -> 2 i + j - 1}, {j, 2}, {i, 7}]], ImageSize -> 150], TreePlot[Flatten[Table[{i -> 2 i + j - 1}, {j, 2}, {i, 7}]], AspectRatio -> 1, ImageSize -> 150]}Specify the height of the plot:
{TreePlot[Flatten[Table[{i -> 2 i + j - 1}, {j, 2}, {i, 7}]], ImageSize -> {Automatic, 150}], TreePlot[Flatten[Table[{i -> 2 i + j - 1}, {j, 2}, {i, 7}]], AspectRatio -> 2, ImageSize -> {Automatic, 150}]}Allow the width and height to be up to a certain size:
{TreePlot[Flatten[Table[{i -> 2 i + j - 1}, {j, 2}, {i, 7}]], ImageSize -> UpTo[200]], TreePlot[Flatten[Table[{i -> 2 i + j - 1}, {j, 2}, {i, 7}]], AspectRatio -> 2, ImageSize -> UpTo[200]]}Specify the width and height for a graphic, padding with space if necessary:
TreePlot[Flatten[Table[{i -> 2 i + j - 1}, {j, 2}, {i, 7}]], ImageSize -> {200, 200}, Background -> LightBlue]Setting AspectRatioFull will fill the available space:
TreePlot[Flatten[Table[{i -> 2 i + j - 1}, {j, 2}, {i, 7}]], AspectRatio -> Full, ImageSize -> {200, 200}, Background -> LightBlue]Use maximum sizes for the width and height:
{TreePlot[Flatten[Table[{i -> 2 i + j - 1}, {j, 2}, {i, 7}]], ImageSize -> {UpTo[150], UpTo[100]}], TreePlot[Flatten[Table[{i -> 2 i + j - 1}, {j, 2}, {i, 7}]], AspectRatio -> 2, ImageSize -> {UpTo[150], UpTo[100]}]}Use ImageSizeFull to fill the available space in an object:
Framed[Pane[TreePlot[Flatten[Table[{i -> 2 i + j - 1}, {j, 2}, {i, 7}]], ImageSize -> Full, Background -> LightBlue], {200, 100}]]Specify the image size as a fraction of the available space:
Framed[Pane[TreePlot[Flatten[Table[{i -> 2 i + j - 1}, {j, 2}, {i, 7}]], AspectRatio -> Full, ImageSize -> {Scaled[0.5], Scaled[0.5]}, Background -> LightBlue], {200, 100}]]LayerSizeFunction (2)
Draw a tree with the first level of height 1, the second level 2, etc.:
TreePlot[{1 -> 2, 1 -> 3, 2 -> 4, 2 -> 5, 3 -> 6, 3 -> 7}, LayerSizeFunction -> (#&)]Plot a binary tree with random layer size:
TreePlot[Flatten[Table[{i -> 2i + j - 1}, {j, 2}, {i, 2 ^ 7 - 1}]], Center, LayerSizeFunction -> (RandomReal[{-4, 4}]&)]PlotStyle (3)
Specify an overall style for the graph:
Table[TreePlot[{1 -> 3, 1 -> 5, 1 -> 6, 1 -> 7, 2 -> 3, 4 -> 5, 5 -> 8}, PlotStyle -> ps], {ps, {Red, Dashed, Directive[Red, Dashed]}}]PlotStyle can be combined with VertexShapeFunction, which has higher priority:
TreePlot[{1 -> 3, 1 -> 5, 1 -> 6, 1 -> 7, 2 -> 3, 4 -> 5, 5 -> 8}, PlotStyle -> Directive[PointSize[Large], Red], VertexShapeFunction -> Function[{p, l}, {Green, Point[p]}]]PlotStyle can be combined with EdgeShapeFunction, which has higher priority:
TreePlot[{1 -> 3, 1 -> 5, 1 -> 6, 1 -> 7, 2 -> 3, 4 -> 5, 5 -> 8}, PlotStyle -> Directive[Dashed, Red], EdgeShapeFunction -> Function[{p, vl}, {Green, Line[p]}]]Applications (8)
Define a complete binary tree of depth 3:
t = Flatten[Table[{i -> 2i + j - 1}, {j, 2}, {i, 7}]]Table[TreePlot[t, p], {p, {Top, Left, Bottom, Right, Center}}]
TreePlot[KaryTree[40, 3], Center]Generate and plot a random tree:
TreePlot[RandomInteger[#] -> # + 1 & /@ Range[0, 30]]Delete random connections in a binary tree:
TreePlot[Delete[Flatten[Table[{i -> 2i + j - 1}, {j, 2}, {i, 100}]], List /@ RandomInteger[{1, 100}, {40}]]]Link a number with one that is rotated one bit right:
TreePlot[Table[j -> FromDigits[RotateRight[IntegerDigits[j, 2]], 2], {j, 0, 2 ^ 8 - 1}], Center]Link a number with one that is rotated one bit left:
TreePlot[Table[j -> FromDigits[RotateLeft[IntegerDigits[j, 2]], 2], {j, 0, 2 ^ 6 - 1}]]Link a number with itself but with the last bit dropped:
TreePlot[Table[j -> FromDigits[Drop[IntegerDigits[j, 2], -1], 2], {j, 0, 2 ^ 8 - 1}], Center]Link a number with itself but with the first bit dropped:
TreePlot[Table[j -> FromDigits[Drop[IntegerDigits[j, 2], 1], 2], {j, 0, 2 ^ 6 - 1}]]Properties & Relations (4)
If the graph is not a tree, it is laid out based on a spanning tree of this graph:
TreePlot[{1 -> 2, 2 -> 3, 3 -> 4, 4 -> 1, 3 -> 5, 1 -> 2, 5 -> 5}]Use LayeredGraphPlot for hierarchical-style drawing of a directed graph:
Table[pt[{1 -> 4, 1 -> 6, 1 -> 8, 2 -> 6, 3 -> 8, 4 -> 5, 7 -> 8}, PlotLabel -> pt, DirectedEdges -> True, PlotTheme -> "DiagramBlue"], {pt, {TreePlot, LayeredGraphPlot}}]Use GraphPlot or GraphPlot3D for general undirected graph drawing:
g = {1 -> 2, 1 -> 6, 1 -> 20, 2 -> 3, 2 -> 17, 3 -> 4, 3 -> 12, 4 -> 5, 4 -> 15, 5 -> 6, 5 -> 10, 6 -> 7, 7 -> 8, 7 -> 16, 8 -> 9, 8 -> 19, 9 -> 10, 9 -> 14, 10 -> 11, 11 -> 12, 11 -> 20, 12 -> 13, 13 -> 14, 13 -> 18, 14 -> 15, 15 -> 16, 16 -> 17, 17 -> 18, 18 -> 19, 19 -> 20};{GraphPlot[g], GraphPlot3D[g]}Use ArrayPlot or MatrixPlot to display sparse matrices:
g = ExampleData[{"Matrix", "Bai/bfwa62"}, "Matrix"]{ArrayPlot[g], MatrixPlot[g]}Possible Issues (2)
For nontree graphs, edges may overlap:
TreePlot[{1 -> 2, 1 -> 3, 1 -> 4, 2 -> 3, 2 -> 4, 3 -> 4}, VertexLabels -> Automatic]Use LayeredGraphPlot or GraphPlot to avoid overlapping edges:
LayeredGraphPlot[{1 -> 2, 1 -> 3, 1 -> 4, 2 -> 3, 2 -> 4, 3 -> 4}, VertexLabels -> Automatic]GraphPlot[{1 -> 2, 1 -> 3, 1 -> 4, 2 -> 3, 2 -> 4, 3 -> 4}, VertexLabels -> Automatic]TreePlot automatically chooses the base node to minimize tree height:
TreePlot[{1 -> 2, 2 -> 3}, PlotTheme -> "DiagramGreen"]Explicitly specify a top node, which in this case is also the root node:
TreePlot[{1 -> 2, 2 -> 3}, Top, 1, PlotTheme -> "DiagramGreen"]Text
Wolfram Research (2007), TreePlot, Wolfram Language function, https://reference.wolfram.com/language/ref/TreePlot.html (updated 2020).
CMS
Wolfram Language. 2007. "TreePlot." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2020. https://reference.wolfram.com/language/ref/TreePlot.html.
APA
Wolfram Language. (2007). TreePlot. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/TreePlot.html