Isoperimetric number of a graph ($i(G)={\min }_{0<|A|\le |V(G)|/2}|{\partial }_{e}A|/|A|$)

For a finite graph with at least two vertices, the displayed minimum measures the fewest outgoing edges per vertex in a nonempty set occupying at most half the graph. It uses the edge boundary, rather than the external vertex boundary. For the hypercube graph $Q_n$, $n\ge 1$, it equals one: edge-isoperimetry gives the lower bound and a coordinate half-cube attains it.