TorusGraph
TorusGraph[{n1,n2,…,nk}]
gives the k-dimensional torus graph with n1×n2×…×nk vertices.
Details and Options

- TorusGraph is also known as toroidal graph.
- TorusGraph[{n1,n2,…,nk}] gives a graph formed from the graph Cartesian product of the cycle graphs
.
- TorusGraph[{n1,n2,…,nk},DirectedEdges->True] gives a directed torus graph.
- TorusGraph takes the same options as Graph.

Examples
open allclose allBasic Examples (2)
Options (83)
DirectedEdges (1)
By default, an undirected graph is generated:
Use DirectedEdges->True to generate 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:
EdgeWeight (3)
GraphHighlight (3)
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 to 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 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)
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 (11)
Basic Applications (6)
Properties & Relations (6)
TorusGraph[{n1,n2,…}] has self-loops if one of is 1:
TorusGraph[{n1,n2,…}] has parallel edges if one of is 2:
TorusGraph[{n}] is a cycle graph:
TorusGraph[{m,n}] is the graph formed from the Cartesian product of the cycle graphs and
:
TorusGraph has the same number of vertices as GridGraph:
The difference between the number of edges of TorusGraph[f] and GridGraph[f]:
Possible Issues (1)
Large torus graphs do not automatically display as a plot of graph:
Use GraphPlot to plot the graph:
Neat Examples (1)
Text
Wolfram Research (2022), TorusGraph, Wolfram Language function, https://reference.wolfram.com/language/ref/TorusGraph.html.
CMS
Wolfram Language. 2022. "TorusGraph." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/TorusGraph.html.
APA
Wolfram Language. (2022). TorusGraph. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/TorusGraph.html