 For example, 
Sidorenko's conjecture is a major open problem in extremal graph theory, which asserts that for any graph formula_59 on formula_26 vertices with average degree formula_202 (for some formula_203) and bipartite graph formula_127 on formula_205 vertices and formula_206 edges, the number of homomorphisms from formula_127 to formula_59 is at least formula_209.Since this is quantity is the expected number of labeled subgraphs of formula_127 in a random graph formula_14,
the conjecture can be interpreted as the claim 
that for any bipartite graph formula_127, the random graph achieves (in expectation) the minimum number of copies of formula_127 over all graphs with some fixed edge density.Many approaches to Sidorenko's conjecture formulate the problem as an integral inequality on graphons, which then allows the problem to be attacked using other analytical approaches.