Graph magnification ratio ($D_k(G)={\min }_{\varnothing \ne Z\subseteq V_0}|{\mathrm{Im}}^{(k)}Z|/|Z|$)

This is the smallest ratio of the size of a $k$-step image to the size of its nonempty starting set in the bottom layer. For a Plünnecke graph, the roots $D_k^{1/k}$ are nonincreasing. The minimum, rather than just the image of the whole layer, is essential.