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
open allclose allScope (4)
RelationGraph works with any binary Boolean function:
RelationGraph works with any expression including integers:
Define a binary relation between two sets:
By default, a symmetric relation generates an undirected graph:
Options (83)
DirectedEdges (3)
By default, a symmetric relation generates an undirected graph:
Use DirectedEdges->True to generate a directed graph:
By default, a nonsymmetric matrix generates a directed graph:
EdgeLabels (7)
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:
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:
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:
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)
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 any expression as a label:
Use Placed with symbolic locations to control label placement, including outside positions:
Symbolic outside corner 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:
Any number of labels can be used:
Use the argument Placed to control formatting including Tooltip:
Or StatusArea:
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:
Use built-in settings for VertexShapeFunction in the "Rounded" collection:
Use built-in settings for VertexShapeFunction in the "Concave" collection:
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)
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 (12)
Generate a network of "nearby" words in a dictionary:
Construct a divisibility 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:
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:
Use AdjacencyGraph:
Text
Wolfram Research (2015), RelationGraph, Wolfram Language function, https://reference.wolfram.com/language/ref/RelationGraph.html.
CMS
Wolfram Language. 2015. "RelationGraph." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/RelationGraph.html.
APA
Wolfram Language. (2015). RelationGraph. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/RelationGraph.html