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Legacy Documentation

Mathematica 8 (2010)

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

View current documentation (Version 14.3)

Mathematica > Mathematics and Algorithms > Graphs & Networks > Constructing Graphs > CompleteGraph >

Mathematica > Visualization and Graphics > Graphs & Networks > Constructing Graphs > CompleteGraph >

BUILT-IN MATHEMATICA SYMBOL

Graph GraphData GraphComplement

CompleteGraph

CompleteGraph [n]
gives the complete graph with n vertices .

CompleteGraph
gives the complete k-partite graph with vertices .

CompleteGraph generates a Graph object.

CompleteGraph [n] gives a graph with n vertices and an edge between every pair of vertices.

CompleteGraph gives a graph with vertices partitioned into disjoint sets with vertices each and edges between all vertices in different sets and , but no edges between vertices in the same set .

CompleteGraph [..., DirectedEdges->True] gives a directed complete graph.

CompleteGraph takes the same options as Graph .

(5)

The first few complete graphs :

Bipartite graphs :

Use a list of length to generate a -partite graph:

Directed complete graphs use two directional edges for each undirected edge:

Directed complete -partite graphs use directed edges from one group to another:

The first few complete graphs :

Out[1]=

Bipartite graphs :

Out[1]=

Use a list of length to generate a -partite graph:

Out[1]=

Directed complete graphs use two directional edges for each undirected edge:

Out[1]=

Directed complete -partite graphs use directed edges from one group to another:

Out[1]=

(1)

Evaluate for a large argument:

(77)

By default an undirected graph is generated:

Use DirectedEdges ->True to generate a directed graph:

Generate directed -partite graphs:

Label the edge :

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 :

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 all edges:

Style individual edges:

Specify a 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 :

Or StatusArea :

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:

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 :

(7)

The GraphCenter of a complete graph includes all its vertices:

The GraphPeriphery includes all vertices:

The VertexEccentricity for all vertices is 1:

Highlight the vertex eccentricity path:

The GraphRadius is 1:

Highlight the radius path:

The GraphDiameter is 1:

Highlight the diameter path:

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

There are 3 vertex-independent paths between any pair of vertices:

The vertex connectivity for CompleteGraph [n] is :

Highlight the vertex degree for CompleteGraph :

Highlight the closeness centrality:

Highlight the eigenvector centrality:

(12)

Number of vertices of CompleteGraph [n]:

Number of edges of CompleteGraph [n]:

A complete graph is an -regular graph:

The subgraph of a complete graph is a complete graph:

The neighborhood of a vertex in a complete graph is the graph itself:

Complete graphs are their own cliques:

The GraphComplement of a complete graph with no edges:

For a complete graph, all entries outside the diagonal are 1s in the AdjacencyMatrix :

For a complete -partite graph, all entries outside the block diagonal are 1s:

The complete graph is the cycle graph :

The complete graph is the wheel graph :

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

(2)

Random collage of complete graphs:

Coloring cycle decompositions in complete graphs on a prime number of vertices:

Graph bullet GraphData bullet GraphComplement

Constructing Graphs

Graphs & Networks

Summary of New Features in Mathematica 8

New in 8.0: Alphabetical Listing

New in 8.0: Mathematics & Algorithms

New in 8