BUILT-IN MATHEMATICA SYMBOL

BernoulliGraphDistribution

represents a Bernoulli graph distribution for n-vertex graphs with edge probability p.

The Bernoulli graph is constructed starting with the complete graph with n vertices and selecting each edge independently through a Bernoulli trial with probability p.

Generate an undirected random graph with 5 vertices and edge probability 0.6:

Generate a directed random graph with 5 vertices and edge probability 0.6:

Generate several graphs:

Generate an undirected random graph with 5 vertices and edge probability 0.6:

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Generate a directed random graph with 5 vertices and edge probability 0.6:

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Generate several graphs:

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Find the largest component fraction when the mean vertex degree is

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Average the result over 100 runs and plot it for different numbers of vertices:

Using edge probability 1 results in the CompleteGraph:

The Bernoulli graph distribution selects each edge from the complete graph with probability

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Mean and standard deviation:

Compare data and distribution cases:

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Mean and standard deviation:

Compare data and distribution cases:

Show the in- and out-degree histogram for BernoulliGraphDistribution

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The in- and out-degree distribution follows BinomialDistribution

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Show them all together:

Random colored vertices: