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RandomGraph
  • See Also
    • BernoulliGraphDistribution
    • UniformGraphDistribution
    • BarabasiAlbertGraphDistribution
    • PriceGraphDistribution
    • WattsStrogatzGraphDistribution
    • DegreeGraphDistribution
    • SeedRandom

    • Entity Types
    • Graph

    • Interpreter Types
    • Graph
  • Related Guides
    • Random Graphs
    • Social Network Analysis
    • Graph Construction & Representation
    • Graphs & Networks
    • Scientific Models
    • Random Number Generation
    • See Also
      • BernoulliGraphDistribution
      • UniformGraphDistribution
      • BarabasiAlbertGraphDistribution
      • PriceGraphDistribution
      • WattsStrogatzGraphDistribution
      • DegreeGraphDistribution
      • SeedRandom

      • Entity Types
      • Graph

      • Interpreter Types
      • Graph
    • Related Guides
      • Random Graphs
      • Social Network Analysis
      • Graph Construction & Representation
      • Graphs & Networks
      • Scientific Models
      • Random Number Generation

RandomGraph[{n,m}]

gives a pseudorandom graph with n vertices and m edges.

RandomGraph[{n,m},k]

gives a list of k pseudorandom graphs.

RandomGraph[gdist,…]

samples from the random graph distribution gdist.

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Options  
DirectedEdges  
EdgeLabels  
EdgeShapeFunction  
Show More Show More
EdgeStyle  
GraphHighlight  
GraphHighlightStyle  
GraphLayout  
PlotTheme  
Base Themes  
Feature Themes  
VertexCoordinates  
VertexLabels  
VertexShape  
VertexShapeFunction  
VertexSize  
VertexStyle  
Applications  
Properties & Relations  
Possible Issues  
Neat Examples  
See Also
Related Guides
Related Links
History
Cite this Page
BUILT-IN SYMBOL
  • See Also
    • BernoulliGraphDistribution
    • UniformGraphDistribution
    • BarabasiAlbertGraphDistribution
    • PriceGraphDistribution
    • WattsStrogatzGraphDistribution
    • DegreeGraphDistribution
    • SeedRandom

    • Entity Types
    • Graph

    • Interpreter Types
    • Graph
  • Related Guides
    • Random Graphs
    • Social Network Analysis
    • Graph Construction & Representation
    • Graphs & Networks
    • Scientific Models
    • Random Number Generation
    • See Also
      • BernoulliGraphDistribution
      • UniformGraphDistribution
      • BarabasiAlbertGraphDistribution
      • PriceGraphDistribution
      • WattsStrogatzGraphDistribution
      • DegreeGraphDistribution
      • SeedRandom

      • Entity Types
      • Graph

      • Interpreter Types
      • Graph
    • Related Guides
      • Random Graphs
      • Social Network Analysis
      • Graph Construction & Representation
      • Graphs & Networks
      • Scientific Models
      • Random Number Generation

RandomGraph

RandomGraph[{n,m}]

gives a pseudorandom graph with n vertices and m edges.

RandomGraph[{n,m},k]

gives a list of k pseudorandom graphs.

RandomGraph[gdist,…]

samples from the random graph distribution gdist.

Details and Options

  • RandomGraph[{n,m}] is equivalent to RandomGraph[UniformGraphDistribution[n,m]].
  • RandomGraph gives a different sequence of pseudorandom graphs whenever you run the Wolfram Language. By using SeedRandom, you can get a repeatable sequence.
  • Vertices are taken to be integers 1, …, n.
  • A method option to SeedRandom can be given to specify the pseudorandom generator used.
  • RandomGraph[dist,{n1,n2,…}] gives an n1×n2×… array of graphs.
  • RandomGraph has the same options as Graph.
  • List of all options

    • AlignmentPointCenterthe default point in the graphic to align with
      AnnotationRules{}annotations for graph, edges and vertices
      AspectRatioAutomaticratio of height to width
      AxesFalsewhether to draw axes
      AxesLabelNoneaxes labels
      AxesOriginAutomaticwhere axes should cross
      AxesStyle{}style specifications for the axes
      BackgroundNonebackground color for the plot
      BaselinePositionAutomatichow to align with a surrounding text baseline
      BaseStyle{}base style specifications for the graphic
      ContentSelectableAutomaticwhether to allow contents to be selected
      CoordinatesToolOptionsAutomaticdetailed behavior of the coordinates tool
      DirectedEdges Automaticwhether to interpret Rule as DirectedEdge
      EdgeLabels Nonelabels and label placements for edges
      EdgeLabelStyleAutomaticstyle to use for edge labels
      EdgeShapeFunction Automaticgenerate graphic shapes for edges
      EdgeStyle Automaticstyle used for edges
      EdgeWeightAutomaticweights for edges
      Epilog{}primitives rendered after the main plot
      FormatTypeTraditionalFormthe default format type for text
      FrameFalsewhether to put a frame around the plot
      FrameLabelNoneframe labels
      FrameStyle{}style specifications for the frame
      FrameTicksAutomaticframe ticks
      FrameTicksStyle{}style specifications for frame ticks
      GraphHighlight {}graph elements to highlight
      GraphHighlightStyle Automaticstyle for highlight
      GraphLayout Automatichow to lay out vertices and edges
      GridLinesNonegrid lines to draw
      GridLinesStyle{}style specifications for grid lines
      ImageMargins0.the margins to leave around the graphic
      ImagePaddingAllwhat extra padding to allow for labels etc.
      ImageSizeAutomaticthe absolute size at which to render the graphic
      LabelStyle{}style specifications for labels
      MethodAutomaticdetails of graphics methods to use
      PerformanceGoalAutomaticaspects of performance to try to optimize
      PlotLabelNonean overall label for the plot
      PlotRangeAllrange of values to include
      PlotRangeClippingFalsewhether to clip at the plot range
      PlotRangePaddingAutomatichow much to pad the range of values
      PlotRegionAutomaticthe final display region to be filled
      PlotTheme $PlotThemeoverall theme for the graph
      PreserveImageOptionsAutomaticwhether to preserve image options when displaying new versions of the same graphic
      Prolog{}primitives rendered before the main plot
      RotateLabelTruewhether to rotate y labels on the frame
      TicksAutomaticaxes ticks
      TicksStyle{}style specifications for axes ticks
      VertexCoordinates Automaticcoordinates for vertices
      VertexLabels Nonelabels and placements for vertices
      VertexLabelStyleAutomaticstyle to use for vertex labels
      VertexShape Automaticgraphic shape for vertices
      VertexShapeFunction Automaticgenerate graphic shapes for vertices
      VertexSize Mediumsize of vertices
      VertexStyle Automaticstyles for vertices
      VertexWeightAutomaticweights for vertices

Examples

open all close all

Basic Examples  (2)

Generate a random graph on 5 vertices and 6 edges:

Simulate a graph property distribution:

Scope  (12)

Generate a pseudorandom graph with a given number of vertices and edges:

A directed pseudorandom graph:

Generate arrays of different sizes and dimensions:

An array of graphs:

Generate random graphs distributed according to the Barabasi–Albert model:

Generate random graphs that are Bernoulli distributed:

Generate random graphs that are uniformly distributed:

Generate random graphs with given degree sequence:

Generate random spatial graphs:

Generate random graphs distributed according to the Price model:

Generate random graphs distributed according to the Watts–Strogatz model:

Generate random graphs of large size:

Options  (70)

DirectedEdges  (1)

By default, an undirected graph is generated:

Use DirectedEdges->True to generate a directed graph:

EdgeLabels  (6)

Label the edge 12:

Label all edges:

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:

GraphHighlight  (3)

Highlight the vertex 1:

Highlight the edge 23:

Highlight vertices and edges:

GraphHighlightStyle  (2)

Get a list of built-in settings for GraphHighlightStyle:

Use built-in settings for GraphHighlightStyle:

GraphLayout  (4)

By default, the layout is chosen automatically:

Specify layouts on special curves:

Specify layouts that satisfy optimality criteria:

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  (9)

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 by running a program:

VertexShapeFunction can be combined with VertexStyle:

VertexShapeFunction has higher priority than VertexStyle:

VertexShapeFunction can be combined with VertexShape:

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  (4)

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:

Applications  (3)

Generate random data for a property of a graph distribution and compare its histogram to the PDF:

Verify that the degree for a vertex in a Bernoulli graph follows a binomial distribution:

Simulate interaction networks, knowing the number of interactions of each node within the group:

Properties & Relations  (10)

RandomGraph uses integer vertices:

Use VertexReplace to replace vertices in the graph:

Use SeedRandom to get repeatable random graphs:

Use BlockRandom to block one use of RandomGraph from affecting others:

RandomVariate generates variates from probability distributions:

RandomInteger generates uniform discrete random variates:

RandomReal generates uniform continuous variates:

RandomChoice generates random choices with replacement from a list:

RandomSample generates random choice without replacement from a list:

RandomPrime generates a random prime number:

RandomImage generates a random image:

Possible Issues  (1)

The number of edges of a simple graph on n vertices is less than or equal to TemplateBox[{n, 2}, Binomial]:

RandomGraph[{n,Binomial[n,2]}] always gives the complete graph with n vertices:

Neat Examples  (1)

Generate random star constellations:

See Also

BernoulliGraphDistribution  UniformGraphDistribution  BarabasiAlbertGraphDistribution  PriceGraphDistribution  WattsStrogatzGraphDistribution  DegreeGraphDistribution  SeedRandom

Entity Types: Graph

Interpreter Types: Graph

Function Repository: RandomHypergraph

Related Guides

    ▪
  • Random Graphs
  • ▪
  • Social Network Analysis
  • ▪
  • Graph Construction & Representation
  • ▪
  • Graphs & Networks
  • ▪
  • Scientific Models
  • ▪
  • Random Number Generation

Related Links

  • An Elementary Introduction to the Wolfram Language : Graphs and Networks

History

Introduced in 2010 (8.0)

Wolfram Research (2010), RandomGraph, Wolfram Language function, https://reference.wolfram.com/language/ref/RandomGraph.html.

Text

Wolfram Research (2010), RandomGraph, Wolfram Language function, https://reference.wolfram.com/language/ref/RandomGraph.html.

CMS

Wolfram Language. 2010. "RandomGraph." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/RandomGraph.html.

APA

Wolfram Language. (2010). RandomGraph. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/RandomGraph.html

BibTeX

@misc{reference.wolfram_2025_randomgraph, author="Wolfram Research", title="{RandomGraph}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/RandomGraph.html}", note=[Accessed: 01-May-2026]}

BibLaTeX

@online{reference.wolfram_2025_randomgraph, organization={Wolfram Research}, title={RandomGraph}, year={2010}, url={https://reference.wolfram.com/language/ref/RandomGraph.html}, note=[Accessed: 01-May-2026]}

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