binomial random graph

随机图

Combinatorics · Undergraduate · Mathematics Resources editorial compilation (AI-assisted)

Other names / variants: G(n,p) · Erdős–Rényi G(n,p) model

Translation evidence: Literature usage

Meaning in context

For n ≥ 0 and 0 ≤ p ≤ 1, G(n,p) is the random simple graph on a fixed labeled n-vertex set in which each possible edge is included independently with probability p.

本记录限定 G(n,p) 模型：在固定的 n 个有标号顶点上，每条可能的边独立地以概率 p 出现，其中 n≥0、0≤p≤1。

Example

For G(4,1/2)G(4,1/2), the expected number of edges is 6/2=36/2=3.

Usage and distinctions

The Chinese name 随机图 is broader than this model. G(n,m) fixes the number of edges and generally does not have independent edge indicators.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Keller and Trotter — Applied Combinatorics (2016)Section 11.6, proof of Theorem 11.7, random graph with independent edge probability p · Checked 2026-10-14

Translation sources

  1. Reinhard Diestel — 图论，第五版，官方中文目录目录，第十一章「随机图」、§11.1「随机图的概念」（名称证据；本记录限定G(n,p)） · Checked 2026-10-14
Edit source / propose a PRReport a correction

Original encyclopedia and terminology content: CC BY-SA 4.0. Contribute or report a correction.

Open the reading guide for this concept