---
title: "Random Graphs"
language: "en"
type: "Guide"
summary: "Random graphs following a distribution model the mechanism by which the graph is formed, such as adding links to a web page or citations to a paper. These distributions make it possible to study simulated internets, communication networks, citation graphs, social networks, etc. Building on its strong capabilities for distributions, the Wolfram Language provides cohesive and comprehensive random graph support. Using a symbolic representation of a graph distribution makes it easy to simulate its behavior and compute probabilities of its properties."
sections: 
  - 
    title: "Simulation"
    link: "null"
  - 
    title: "Parametric Graph Distributions"
    link: "null"
  - 
    title: "Property Distribution"
    link: "null"
  - 
    title: "Probability and Statistics"
    link: "paclet:guide/ProbabilityAndStatistics"
keywords: 
- random graph
- Barabasi-Albert random graph
- Barabasi-Albert
- Watts-Strogatz random graph
- Watts-Strogatz
- Erdos random graph
- Erdos model
- Renyi model
- Erdos-Renyi model
- small-world network
- small-world graph
- scale-free network
- scale-free graph
- geometric random graph
- spatial random graph
- Bernoulli random graph
- binomial random graph
- exponential random graph
canonical_url: "https://reference.wolfram.com/language/guide/RandomGraphs.html"
source: "Wolfram Language Documentation"
related_guides: 
  - 
    title: "Graphs & Networks"
    link: "https://reference.wolfram.com/language/guide/GraphsAndNetworks.en.md"
  - 
    title: "Graph Construction & Representation"
    link: "https://reference.wolfram.com/language/guide/GraphConstructionAndRepresentation.en.md"
  - 
    title: "Graph Measures and Metrics"
    link: "https://reference.wolfram.com/language/guide/GraphMeasures.en.md"
  - 
    title: "Random Variables"
    link: "https://reference.wolfram.com/language/guide/RandomVariables.en.md"
  - 
    title: "Random Matrices"
    link: "https://reference.wolfram.com/language/guide/MatrixDistributions.en.md"
related_functions: 
  - 
    title: "BarabasiAlbertGraphDistribution"
    link: "https://reference.wolfram.com/language/ref/BarabasiAlbertGraphDistribution.en.md"
  - 
    title: "BernoulliGraphDistribution"
    link: "https://reference.wolfram.com/language/ref/BernoulliGraphDistribution.en.md"
  - 
    title: "DegreeGraphDistribution"
    link: "https://reference.wolfram.com/language/ref/DegreeGraphDistribution.en.md"
  - 
    title: "Distributed"
    link: "https://reference.wolfram.com/language/ref/Distributed.en.md"
  - 
    title: "Expectation"
    link: "https://reference.wolfram.com/language/ref/Expectation.en.md"
  - 
    title: "GraphPropertyDistribution"
    link: "https://reference.wolfram.com/language/ref/GraphPropertyDistribution.en.md"
  - 
    title: "NExpectation"
    link: "https://reference.wolfram.com/language/ref/NExpectation.en.md"
  - 
    title: "NProbability"
    link: "https://reference.wolfram.com/language/ref/NProbability.en.md"
  - 
    title: "PriceGraphDistribution"
    link: "https://reference.wolfram.com/language/ref/PriceGraphDistribution.en.md"
  - 
    title: "Probability"
    link: "https://reference.wolfram.com/language/ref/Probability.en.md"
  - 
    title: "RandomGraph"
    link: "https://reference.wolfram.com/language/ref/RandomGraph.en.md"
  - 
    title: "RandomVariate"
    link: "https://reference.wolfram.com/language/ref/RandomVariate.en.md"
  - 
    title: "SpatialGraphDistribution"
    link: "https://reference.wolfram.com/language/ref/SpatialGraphDistribution.en.md"
  - 
    title: "UniformGraphDistribution"
    link: "https://reference.wolfram.com/language/ref/UniformGraphDistribution.en.md"
  - 
    title: "WattsStrogatzGraphDistribution"
    link: "https://reference.wolfram.com/language/ref/WattsStrogatzGraphDistribution.en.md"
---
# Random Graphs

Random graphs following a distribution model the mechanism by which the graph is formed, such as adding links to a web page or citations to a paper. These distributions make it possible to study simulated internets, communication networks, citation graphs, social networks, etc. 
Building on its strong capabilities for distributions, the Wolfram Language provides cohesive and comprehensive random graph support. Using a symbolic representation of a graph distribution makes it easy to simulate its behavior and compute probabilities of its properties.

---

### Simulation

[`RandomGraph`](https://reference.wolfram.com/language/ref/RandomGraph.en.md) — simulate a random graph

### Parametric Graph Distributions

[`BernoulliGraphDistribution`](https://reference.wolfram.com/language/ref/BernoulliGraphDistribution.en.md) — Bernoulli graph distribution

[`BarabasiAlbertGraphDistribution`](https://reference.wolfram.com/language/ref/BarabasiAlbertGraphDistribution.en.md) — scale-free graph distribution

* [`DegreeGraphDistribution`](https://reference.wolfram.com/language/ref/DegreeGraphDistribution.en.md)
* [`PriceGraphDistribution`](https://reference.wolfram.com/language/ref/PriceGraphDistribution.en.md)
* [`SpatialGraphDistribution`](https://reference.wolfram.com/language/ref/SpatialGraphDistribution.en.md)
* [`UniformGraphDistribution`](https://reference.wolfram.com/language/ref/UniformGraphDistribution.en.md)
* [`WattsStrogatzGraphDistribution`](https://reference.wolfram.com/language/ref/WattsStrogatzGraphDistribution.en.md)

### Property Distribution

[`GraphPropertyDistribution`](https://reference.wolfram.com/language/ref/GraphPropertyDistribution.en.md) — distribution of a graph property

### [Probability and Statistics](https://reference.wolfram.com/language/guide/ProbabilityAndStatistics.en.md)

[`NProbability`](https://reference.wolfram.com/language/ref/NProbability.en.md) — compute probabilities for graph properties

[`NExpectation`](https://reference.wolfram.com/language/ref/NExpectation.en.md) — compute expectations for graph properties

* [`RandomVariate`](https://reference.wolfram.com/language/ref/RandomVariate.en.md)
* [`Probability`](https://reference.wolfram.com/language/ref/Probability.en.md)
* [`Expectation`](https://reference.wolfram.com/language/ref/Expectation.en.md)
* [`Distributed`](https://reference.wolfram.com/language/ref/Distributed.en.md)
* [`...`](https://reference.wolfram.com/language/guide/ProbabilityAndStatistics.en.md)

## Related Guides

* [Graphs & Networks](https://reference.wolfram.com/language/guide/GraphsAndNetworks.en.md)
* [Graph Construction & Representation](https://reference.wolfram.com/language/guide/GraphConstructionAndRepresentation.en.md)
* [Graph Measures and Metrics](https://reference.wolfram.com/language/guide/GraphMeasures.en.md)
* [Random Variables](https://reference.wolfram.com/language/guide/RandomVariables.en.md)
* [Random Matrices](https://reference.wolfram.com/language/guide/MatrixDistributions.en.md)