This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

CompleteKaryTree

 CompleteKaryTree[n] gives the complete binary tree with n levels. CompleteKaryTreegives the complete k-ary tree with n levels.
• The complete k-ary tree with n levels is a rooted tree with k branches at each node and n levels deep.
• The complete k-ary tree with n levels has vertices.
A complete binary tree with 5 levels:
A complete ternary tree with 3 levels:
Use directed edges:
A complete binary tree with 5 levels:
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A complete ternary tree with 3 levels:
 Out[1]=

Use directed edges:
 Out[1]=
 Options   (75)
By default an undirected graph is generated:
Use DirectedEdges->True to generate a directed graph:
Label the edge :
Label all edges individually:
Use any expression as a label:
Use explicit coordinates to place labels:
Vary positions within the label:
Place multiple labels:
Use automatic labeling by values through Tooltip and StatusArea:
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:
Style edges:
Style individual edges:
Specify the weight for all edges:
Use any numeric expression as a weight:
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:
Highlight the vertex :
Highlight the edge :
Highlight the vertices and edges:
Get a list of built-in settings for GraphHighlightStyle:
Use built-in settings for GraphHighlightStyle:
Get a list of built-in settings for GraphStyle:
Use built-in settings for GraphStyle:
Specify a property for vertices:
Edges:
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:
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:
Use more elaborate formatting functions:
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:
Get a list of built-in collections for VertexShapeFunction:
Use built-in settings for VertexShapeFunction in the collection:
Simple basic shapes:
Common basic shapes:
Use built-in settings for VertexShapeFunction in the collection:
Use built-in settings for VertexShapeFunction in the 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:
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:
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:
 Applications   (7)
The GraphCenter of a complete k-ary tree:
Highlight the vertex eccentricity path:
Highlight the diameter path:
Highlight the vertex degree for CompleteKaryTree:
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 tree is 1 for all vertex pairs:
CompleteKaryTree has vertices:
CompleteKaryTree has edges:
A complete k-ary tree with vertices has edges:
A complete k-ary tree is a tree graph:
A complete k-ary tree is a bipartite graph:
A complete k-ary tree is acyclic:
A complete k-ary tree is loop free:
A complete k-ary tree is a special case of a k-ary tree:
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