template graphs converge to the graphon

Let $\{G_n\}$ be a sequence of template graphs sampled from graphon $W$. Then $G_n\to W$ as $n\to \mathrm{\infty }$.

Trivial

• The definition of template graphs is fully deterministic, so there is no randomness here. Since this is the reverse idea of thinking of graphons as graphs with uncountable number of nodes, it is easy to see that the induced graphons $W_n$ converge to $W$ in an $L_2$ way and convergence in L-p implies convergence in cut norm