---
tag: VQ0Z1XTSDC
kind: concept
name: Common graph
sources:
  - wikipedia: en:69389162@r1292431244
    locator: Common graph
    note: adopted
    mention: wikipedia://en/69389162
    sections: [Summary]
same_as:
  wikidata: Q112132167
  wikipedia: Common graph
inventory: [CB7RX64R5C]
---

## Summary

In graph theory, an area of mathematics, **common graphs** belong to a branch of extremal graph theory concerning inequalities in homomorphism densities. Roughly speaking, $F$ is a common [[graph|00C0BR7D7H]] if it "commonly" appears as a subgraph, in a sense that the total number of copies of $F$ in any graph $G$ and its [[complement|0MCYJ72VGA]] $\overline{G}$ is a large fraction of all possible copies of $F$ on the same vertices. Intuitively, if $G$ contains few copies of $F$, then its complement $\overline{G}$ must contain lots of copies of $F$ in order to compensate for it.