  Numerical interactions leading to users sharing textual content published by
others are naturally represented by a network where the individuals are
associated with the nodes and the exchanged texts with the edges. To understand
those heterogeneous and complex data structures, clustering nodes into
homogeneous groups as well as rendering a comprehensible visualisation of the
data is mandatory. To address both issues, we introduce Deep-LPTM, a
model-based clustering strategy relying on a variational graph auto-encoder
approach as well as a probabilistic model to characterise the topics of
discussion. Deep-LPTM allows to build a joint representation of the nodes and
of the edges in two embeddings spaces. The parameters are inferred using a
variational inference algorithm. We also introduce IC2L, a model selection
criterion specifically designed to choose models with relevant clustering and
visualisation properties. An extensive benchmark study on synthetic data is
provided. In particular, we find that Deep-LPTM better recovers the partitions
of the nodes than the state-of-the art ETSBM and STBM. Eventually, the emails
of the Enron company are analysed and visualisations of the results are
presented, with meaningful highlights of the graph structure.
