DeBruijnGraph

DeBruijnGraph[m,n]

gives the n-dimensional De Bruijn graph with m symbols.

DeBruijnGraph[m,n,type]

gives the De Bruijn graph with connectivity given by type.

Details and Options

  • DeBruijnGraph[m,n] has mn vertices, consisting of all length-n sequences of m symbols. Given two vertices v={s1,,sn} and ={t1,,tn}, there is an edge from v to , provided s2==t1, s3==t2, , sn==tn-1.
  • DeBruijnGraph[m,n,type] specifies different connectivity types. The following types can be given:
  • "Noncyclic"s_(2)⩵t_(1), , s_(n)⩵t_(n-1)
    "LeftShift"s_(1)⩵t_(n), s2t1, , sn t_(n-1)
    "RightShift"s_1⩵t_(2), , s_(n-1)⩵t_(n), s_(n)⩵t_(1)
  • DeBruijnGraph[] is a directed graph.
  • DeBruijnGraph takes the same options as Graph.

Examples

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Basic Examples  (3)

The first few De Bruijn graphs with two symbols and different dimensions:

De Bruijn graphs with different numbers of symbols in dimension two:

De Bruijn graphs with different connectivity types:

Options  (79)

AnnotationRules  (2)

Specify an annotation for vertices:

Edges:

EdgeLabels  (7)

Label the edge 12:

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:

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 a weight for all edges:

Use any numeric expression as a weight:

GraphHighlight  (3)

Highlight the vertex 1:

Highlight the edge 23:

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:

Any number of labels can be used:

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 size 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  (6)

The GraphCenter of De Bruijn 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 DeBruijnGraph:

Highlight the closeness centrality:

Highlight the eigenvector centrality:

Properties & Relations  (4)

DeBruijnGraph[m,n] has vertices:

DeBruijnGraph[m,n] has edges:

Each vertex has exactly incoming and outgoing edges:

The number of outgoing edges of each vertex:

The number of incoming edges of each vertex:

DeBruijnGraph[m,n] is the line graph of the DeBruijnGraph[m,n-1] with the same symbols:

Possible Issues  (1)

The setting DirectedEdges->False does not apply to DeBruijnGraph:

Introduced in 2010
 (8.0)