---
tag: 7235FH8REJ
kind: statement
role: proposition
name: Expander mixing lemma
sources:
  - wikipedia: en:6230931@r1354782268
    locator: Expander mixing lemma
    note: adopted
    mention: wikipedia://en/6230931
    sections: [Statement]
same_as:
  wikidata: Q5420759
  wikipedia: Expander mixing lemma
inventory: [G0DVS366JX]
---

## Statement

The **expander mixing lemma** intuitively states that the edges of certain $d$-regular graphs are evenly distributed throughout the graph. In particular, the number of edges between two vertex subsets $S$ and $T$ is always close to the expected number of edges between them in a random $d$-[[regular graph|0KA4S8R39M]], namely $\frac dn|S||T|$.