This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# RandomGraph

 RandomGraph gives a pseudorandom graph with n vertices and m edges. RandomGraphgives a list of k pseudorandom graphs. RandomGraphsamples from the random graph distribution gdist.
• RandomGraph gives a different sequence of pseudorandom graphs whenever you run Mathematica. By using SeedRandom you can get a repeatable sequence.
• Vertices are taken to be integers , ..., n.
• A Method option to SeedRandom can be given to specify the pseudorandom generator used.
Generate a random graph on 5 vertices and 6 edges:
Generate random graphs where each edge occurs with probability 0.6:
Generate a random graph on 5 vertices and 6 edges:
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Generate random graphs where each edge occurs with probability 0.6:
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 Scope   (7)
Generate an undirected simple random graph:
Generate three random graphs on 6 vertices and 7 edges:
Generate a directed simple random graph:
Generate random graphs that are Bernoulli distributed:
Generate random graphs that are uniformly distributed:
Generate a random undirected graph with Barabasi-Albert graph distribution:
Generate random graphs of large size:
 Options   (68)
By default a directed graph is generated:
Use DirectedEdges->True to generate a directed graph:
Label the edge :
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:
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:
Style all edges:
Style individual edges:
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:
Highlight the vertex :
Highlight the edge :
Highlight vertices and edges:
Get a list of built-in settings for GraphHighlightStyle:
Use built-in settings for GraphHighlightStyle:
Get a list of built-in settings for GraphStyle:
Use built-in settings for GraphStyle:
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:
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:
Use more elaborate formatting functions:
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:
Get a list of built-in collections for VertexShapeFunction:
Use built-in settings for VertexShapeFunction in the collection:
Simple basic shapes:
Common basic shapes:
Use built-in settings for VertexShapeFunction in the collection:
Use built-in settings for VertexShapeFunction in the 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:
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:
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)
The edge count for BernoulliGraphDistribution follows a BinomialDistribution:
Mean and standard deviation:
Compare data and distribution cases:
The vertex degrees for BernoulliGraphDistribution follow a BinomialDistribution:
Mean and standard deviation:
Compare data and distribution cases:
The expected distance for BernoulliGraphDistribution between two vertices is 2-p:
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:
The row-column ordering is given by VertexList:
Use SeedRandom to get repeatable random graphs:
Use BlockRandom to block one use of RandomGraph from affecting others:
The number of edges of a simple graph on n vertices is less than or equal to :
RandomGraph[{n, Binomial[n, 2]}] always gives the complete graph with n vertices:
Different-density random graphs:
New in 8