Let **N**(**S**) denote the set of neighbors of **S** (excluding **S** itself).

The *Vertex Expansion* of a graph is the minimum of |**N**(**S**)| / |**S**|.

Let *E*(**A**,**B**) denote the number of edges with one extremity in **A** and the other in **B**. Let /**S** denote the complement of **S**.

The *Edge Expansion* of a graph is the minimum *E*(**S**,/**S**) / |**S**|.