Title: Consistent structure estimation of exponential-family random graph models with block structure,
Abstract: We consider the challenging problem of statistical inference for
exponential-family random graph models based on a single observation of a
random graph with complex dependence. To facilitate statistical inference, we
consider random graphs with additional structure in the form of block
structure. We have shown elsewhere that when the block structure is known, it
facilitates consistency results for $M$-estimators of canonical and curved
exponential-family random graph models with complex dependence, such as
transitivity. In practice, the block structure is known in some applications
(e.g., multilevel networks), but is unknown in others. When the block structure
is unknown, the first and foremost question is whether it can be recovered with
high probability based on a single observation of a random graph with complex
dependence. The main consistency results of the paper show that it is possible
to do so provided the number of blocks grows as fast as in high-dimensional
stochastic block models. These results confirm that exponential-family random
graph models with block structure constitute a promising direction of
statistical network analysis.