  In the present paper we consider a dynamic stochastic network model. The
objective is estimation of the tensor of connection probabilities $\Lambda$
when it is generated by a Dynamic Stochastic Block Model (DSBM) or a dynamic
graphon. In particular, in the context of the DSBM, we derive a penalized least
squares estimator $\widehat{\Lambda}$ of $\Lambda$ and show that
$\widehat{\Lambda}$ satisfies an oracle inequality and also attains minimax
lower bounds for the risk. We extend those results to estimation of $\Lambda$
when it is generated by a dynamic graphon function. The estimators constructed
in the paper are adaptive to the unknown number of blocks in the context of the
DSBM or to the smoothness of the graphon function. The technique relies on the
vectorization of the model and leads to much simpler mathematical arguments
than the ones used previously in the stationary set up. In addition, all
results in the paper are non-asymptotic and allow a variety of extensions.
