 Amenable graph

A bounded-degree infinite graph is amenable when there are finite nonempty vertex sets $W_n$ such that $|{\partial }^{+}{W}_n|/|W_n|\to 0$, 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.