# The Erdős-Rényi Random Graph

DevFeed: [The Erdős-Rényi Random Graph](<https://devfeed.tech/articles/the-erdos-renyi-random-graph-40329.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2013/08/22/the-erdos-renyi-random-graph/>)

Published: 2013-08-22T16:11:18Z

Content type: tutorial

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [Graphs](<https://devfeed.tech/topics/graphs.md>), [graph theory](<https://devfeed.tech/topics/graph-theory.md>), [math](<https://devfeed.tech/topics/math.md>), [Networks](<https://devfeed.tech/topics/networks.md>)

Tags: [color](<https://devfeed.tech/tags/color.md>), [combinatorics](<https://devfeed.tech/tags/combinatorics.md>), [erdos](<https://devfeed.tech/tags/erdos.md>), [giant-component](<https://devfeed.tech/tags/giant-component.md>), [graph](<https://devfeed.tech/tags/graph.md>), [graph-coloring](<https://devfeed.tech/tags/graph-coloring.md>), [graph-theory](<https://devfeed.tech/tags/graph-theory.md>), [properties](<https://devfeed.tech/tags/properties.md>), [random-graph](<https://devfeed.tech/tags/random-graph.md>), [random-graphs](<https://devfeed.tech/tags/random-graphs.md>), [renyi](<https://devfeed.tech/tags/renyi.md>), [social-networks](<https://devfeed.tech/tags/social-networks.md>), [structure](<https://devfeed.tech/tags/structure.md>)

## AI overview

This tutorial introduces the Erdős-Rényi random graph model G(n,p), in which each possible edge between n vertices is included independently with probability p. It discusses the model's role in combinatorics and network analysis, along with basic properties, applications, and computational exploration.

## Source excerpt

During the 1950's the famous mathematician Paul Erdős and Alfred Rényi put forth the concept of a random graph and in the subsequent years of study transformed the world of combinatorics. The random graph is the perfect example of a good mathematical definition: it's simple, has surprisingly intricate structure, and yields many applications. In this post we'll explore basic facts about random graphs, slowly detail a proof on their applications to graph theory, and explore their more interesting properties computationally (a prelude to proofs about their structure).