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  "body": "\n## Statement\n\nThe **counting lemmas** this article discusses are statements in [[combinatorics|0JKW7W7XFR]] and graph theory. The first one extracts information from $\\epsilon$-regular pairs of subsets of vertices in a graph $G$, in order to guarantee patterns in the entire graph; more explicitly, these patterns correspond to the count of copies of a certain graph $H$ in $G$. The second counting lemma provides a similar yet more general notion on the space of graphons, in which a scalar of the cut distance between two graphs is correlated to the homomorphism density between them and $H$.\n",
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