  A rich class of network models associate each node with a low-dimensional
latent coordinate that controls the propensity for connections to form. Models
of this type are well established in the network analysis literature, where it
is typical to assume that the underlying geometry is Euclidean. Recent work has
explored the consequences of this choice and has motivated the study of models
which rely on non-Euclidean latent geometries, with a primary focus on
spherical and hyperbolic geometry. In this paper, we examine to what extent
latent features can be inferred from the observable links in the network,
considering network models which rely on spherical and hyperbolic geometries.
For each geometry, we describe a latent space network model, detail constraints
on the latent coordinates which remove the well-known identifiability issues,
and present Bayesian estimation schemes. Thus, we develop computational
procedures to perform inference for network models in which the properties of
the underlying geometry play a vital role. Finally, we assess the validity of
these models on real data.
