  We investigate correspondences between extreme amenability and amenability of
automorphism groups of Fra\"iss\'e-Hrushovski generic structures that are
obtained from smooth classes, and their Ramsey type properties of their smooth
classes, similar to Kechris, Pestov and Todorcevic, and Tatch Moore. In
particular, we focus on some Fra\"iss\'e-Hrushovski generic structures that are
obtained from pre-dimension functions. Using these correspondences, we prove
that automorphism groups of ordered Hrushovski generic graphs are not extremely
amenable in both cases of collapsed and uncollapsed. Moreover, we prove that
automorphism groups of Fra\"iss\'e-Hrushovski generic structures that are
obtained from pre-dimension functions with rational coefficients are not
amenable.
