Conditions are presented for local identifiability of discrete undirected
graphical models with a binary hidden node. These models can be obtained by
extending the latent class model to allow for conditional associations between
the observed variables. We establish a necessary and sufficient condition for
the model to be locally identified almost everywhere in the parameter space and
we provide expressions of the subspace where identifiability breaks down. The
condition is based on the topology of the undirected graph and relies on the
faithfulness assumption.