Abstract
We prove that the asymptotic logarithmic density of copies of a graph F in the graphs of a nowhere dense class C is integral and we determine the range of its possible values. This leads to a generalization of the trichotomy theorem of Nesetril and Ossona de Mendez (2011) [8] and to a notion of the degree of freedom of a graph F in a class C.
This provides yet another formulation of the somewhere dense-nowhere dense classification. We obtain a structural result concerning the asymptotic shape of graphs with given degree of freedom.