# RelationGraph

RelationGraph[f,{v1,v2,}]

gives the graph with vertices vi and edges from vi to vj whenever f[vi,vj] is True.

RelationGraph[f,{v1,v2,},{w1,w2,}]

gives the graph with vertices vi,wj and edges from vi to wj whenever f[vi,wj] is True.

# Details and Options

• RelationalGraph takes the same options as Graph.
• The option DirectedEdges can be used to control whether an undirected or directed graph is constructed.
• The following settings for DirectedEdges can be used in RelationalGraph:
•  Automatic undirected graph if crit[vi,vj]==crit[vj,vi] True construct a directed graph False construct an undirected graph

# Examples

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## Basic Examples(2)

Construct a bipartite graph:

A coprime graph:

## Scope(4)

RelationGraph works with any binary Boolean function:

Boolean expressions:

RelationGraph works with any expression including integers:

Strings:

Define a binary relation between two sets:

By default, a symmetric relation generates an undirected graph:

A nonsymmetric relation generates a directed graph:

## Options(83)

### AnnotationRules(3)

Specify an annotation for vertices:

Edges:

Graph itself:

### DirectedEdges(3)

By default, a symmetric relation generates an undirected graph:

Use to generate a directed graph:

By default, a nonsymmetric matrix generates a directed graph:

### 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 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 has higher priority than 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(12)

Construct a suffix graph:

Construct a prefix graph:

Construct a substring graph:

Generate a network of "nearby" words in a dictionary:

Construct a divisibility graph:

Construct a coprime graph:

Connect a number to another that is one bit reversed:

Connect a number to another that is one bit rotated right:

Connect a number to itself but with the first bit dropped:

Visualize self-loops in a reflexive relation:

Visualize a transitive relation:

Find the adjacent countries in South America:

## Properties & Relations(4)

Use VertexCount and EdgeCount to count vertices and edges:

Use VertexList and EdgeList to enumerate vertices and edges in standard order:

Compute the AdjacencyMatrix from a graph:

Use RelationGraph to construct a graph from its adjacency matrix: