  Local dependence random graph models are a class of block models for network
data which allow for dependence among edges under a local dependence assumption
defined around the block structure of the network. Since being introduced by
Schweinberger and Handcock (2015), research in the statistical network analysis
and network science literatures have demonstrated the potential and utility of
this class of models. In this work, we provide the first statistical
disclaimers which provide conditions under which estimation and inference
procedures can be expected to provide accurate and valid inferences. This is
accomplished by deriving convergence rates of inference procedures for local
dependence random graph models based on a single observation of the graph,
allowing both the number of model parameters and the sizes of blocks to tend to
infinity. First, we derive the first non-asymptotic bounds on the
$\ell_2$-error of maximum likelihood estimators, along with convergence rates.
Second, and more importantly, we derive the first non-asymptotic bounds on the
error of the multivariate normal approximation. In so doing, we introduce the
first principled approach to providing statistical disclaimers through
quantifying the uncertainty about statistical conclusions based on data.
