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  "body": "\n## Statement\n\nThe **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 $\\frac dn|S||T|$.\n",
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