---
tag: PHDNBSKECQ
kind: concept
name: Random regular graph
sources:
  - wikipedia: en:10151936@r1289218115
    locator: Random regular graph
    note: adopted
    mention: wikipedia://en/10151936
    sections: [Summary]
same_as:
  wikidata: Q7291988
  wikipedia: Random regular graph
inventory: [6ETPPSE9WQ]
---

## Summary

A **random *r*-regular graph** is a [[graph|00C0BR7D7H]] selected from $\mathcal{G}_{n,r}$, which denotes the [[probability space|0NFPJVJJHX]] of all [[*r*-regular graphs|0KA4S8R39M]] on $n$ vertices, where $3 \le r < n$ and $nr$ is even. It is therefore a particular kind of random graph, but the regularity restriction significantly alters the properties that will hold, since most graphs are not regular.