  Communication networks such as emails or social networks are now ubiquitous
and their analysis has become a strategic field. In many applications, the goal
is to automatically extract relevant information by looking at the nodes and
their connections. Unfortunately, most of the existing methods focus on
analysing the presence or absence of edges and textual data is often discarded.
However, all communication networks actually come with textual data on the
edges. In order to take into account this specificity, we consider in this
paper networks for which two nodes are linked if and only if they share textual
data. We introduce a deep latent variable model allowing embedded topics to be
handled called ETSBM to simultaneously perform clustering on the nodes while
modelling the topics used between the different clusters. ETSBM extends both
the stochastic block model (SBM) and the embedded topic model (ETM) which are
core models for studying networks and corpora, respectively. The inference is
done using a variational-Bayes expectation-maximisation algorithm combined with
a stochastic gradient descent. The methodology is evaluated on synthetic data
and on a real world dataset.
