How many F's are there in G?
Résumé
We prove that the asymptotic logarithmic density of copies of a graph $F$ in the graphs of a nowhere dense class $\mathcal C$ is integral and we determine the range of its possible values. This leads to a generalization of the Trichotomy theorem \cite{ND_characterization} and to a notion of degree of freedom of a graph $F$ in a class $\mathcal C$. This provides yet another formulation of the somewhere dense -- nowhere dense classification. We obtain a structural result about the asymptotic shape of graphs with given degree of freedom.