A regular equivalence between two graphs 􀀀; 􀀀0 is a pair of uniformly proper Lipschitz maps V 􀀀 ! V 􀀀0 and V 􀀀0 ! V 􀀀. Using separation profiles we prove that there are 2@0 regular equivalence classes of expander graphs, and of finitely generated groups with a representative which isometrically contains expanders