Szemerédi’s regularity lemma

Szemerédi’s regularity lemma states that any large, complex network (or graph) can be broken down into a limited number of smaller parts where most connections between these parts are random and evenly distributed. In essence, it allows mathematicians to analyze complicated structures by approximating them with a simpler, "regular" pattern, making their properties easier to study. The key idea is that, regardless of the complexity of the network, a large enough graph can be approximated by a collection of nearly uniform, predictable interactions between its parts.