Questions on discrete mathematics generally: "the study of mathematical structures that are fundamentally discrete rather than continuous"

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Expansion vs Sparsest cut

let $G=(V,E)$ and $S\subsetneq V$ then expansion of set $S$ is $$\alpha(S)=\frac{|E(S,\overline{S})|}{\min\{|S|,|\overline{S}|)\}}$$ where $\bar{S}=V\setminus{S}$ and $E(S,\bar{S})$ are edges ...