  We analyze the information-theoretic limits for the recovery of node labels
in several network models. This includes the Stochastic Block Model, the
Exponential Random Graph Model, the Latent Space Model, the Directed
Preferential Attachment Model, and the Directed Small-world Model. For the
Stochastic Block Model, the non-recoverability condition depends on the
probabilities of having edges inside a community, and between different
communities. For the Latent Space Model, the non-recoverability condition
depends on the dimension of the latent space, and how far and spread are the
communities in the latent space. For the Directed Preferential Attachment Model
and the Directed Small-world Model, the non-recoverability condition depends on
the ratio between homophily and neighborhood size. We also consider dynamic
versions of the Stochastic Block Model and the Latent Space Model.
