Sparsity of a cut

Given a graph with nodes $V$ and edges in $E\subset V\times V$. The sparsity of a cut $\varphi (S)$ is given by:

$$\varphi (S)=\frac{E(S,\bar{S})}{\text{min}(|S|,|\bar{S}|)}$$

Where $E(S,\bar{S})$ is the sum of weights of edges crossing the cut. Here $\bar{S}=VS$, so $\min (\cdot )$ is the min. number of elements of both sets.