Given a sequence of random graphs generated by an exponential family distribution, known as exponential random graphs (ERG), we define a realized ERG (RERG) as a single snapshot maximum-likelihood estimate of the ERG parameters. RERG's are noisy observations of the latent state variables driving the evolution of the graph over time. They allow to transform a nonlinear state-space graph model into a linear timeseries model, simplifying considerably the inference of a wide class of dynamic networks. Under the assumption that the random graph sequence is dense and of a mixed-membership stochastic block model structure, we show that the ERG parameters and the latent state variables can be estimated at a super-consistent rate of convergence for large cross-sections. We corroborate our findings by using this novel framework to estimate and forecast the unobserved factors driving the evolution of the Italian electronic market of interbank deposits. Empirical evidences support the conclusion that the short-term lending rate is the main factor shaping the topology of the interbank network.
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