---
tag: 4S189K88T3
kind: concept
name: Universal graph
sources:
  - wikipedia: en:1452141@r1368641504
    locator: Universal graph
    note: adopted
    mention: wikipedia://en/1452141
    sections: [Summary]
same_as:
  wikidata: Q7894131
  wikipedia: Universal graph
inventory: [MKPFQFTWB3]
---

## Summary

In mathematics, a **universal graph** is an infinite [[graph|00C0BR7D7H]] that contains *every* finite (or at-most-countable) graph as an induced subgraph. A universal graph of this type was first constructed by Richard Rado and is now called the Rado graph or random graph. More recent work  has focused on universal graphs for a graph family $F$: that is, an infinite graph belonging to $F$ that contains all finite graphs in $F$. For instance, the Henson graphs are universal in this sense for the $i$-clique-free graphs.