The relation between metric spaces of being quasi-isometric is an equivalence relation. Also, if \(S\) and \(T\) are generating sets of a group \((G, \cdot)\), the Cayley graphs of \((G, \cdot, S)\) and \((G, \cdot, T)\) with their word metrics are quasi-isometric spaces. This means that properties of a generated group which are quasi-isometric invariants will be independent of the choice of generating set, and therefore informative about the group itself.