Amenable graph
= Amenable graph
A bounded-degree infinite <graph> is amenable when there are finite nonempty vertex sets $W_n$ such that $|\partial^+W_n|/|W_n|\to0$, where $\partial^+W_n$ is the set of vertices outside $W_n$ adjacent to it. These are graph <Følner sets>. Amenability makes surface contributions negligible compared with volume. The square lattice and any periodic finite decoration of it are examples.