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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.

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

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

BUILT-IN MATHEMATICA SYMBOL

Graph GraphData CirculantGraph

CycleGraph

CycleGraph [n]
gives the cycle graph with n vertices .

CycleGraph [n] gives a graph with vertices , with edges between i and i+1 as well as between n and .

CycleGraph [..., DirectedEdges->True] gives a directed cycle graph.

CycleGraph takes the same options as Graph .

(2)

The first few cycle graphs :

Directed cycle graphs:

The first few cycle graphs :

Out[1]=

Directed cycle graphs:

Out[1]=

(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 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 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 properties 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:

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 direction:

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 cycle 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 CycleGraph :

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 cycle is 2 for all vertex pairs:

(10)

CycleGraph [n] has n vertices:

CycleGraph [n] has n edges:

is the triangle graph:

is the square graph:

The line graph of a cycle graph is isomorphic to itself:

Cycle graph is a path:

Cycle graph is not acyclic:

Cycle graph is -regular:

The adjacency matrix is banded:

The incidence matrix is banded:

Graph bullet GraphData bullet CirculantGraph

Constructing Graphs

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