Let $G$ be a large (simple, unlabeled) dense graph on $n$ vertices. Suppose that we only know, or can estimate, the empirical distribution of number subgraphs $F$ each vertex in participates in, for some fixed small $F$. How many other graphs would look essentially same to us, i.e., have similar local structure? In this paper, derive upper and lower bounds whose lies close (in Kolmogorov-Smirno...