  Graph representation learning is a fundamental problem for modeling
relational data and benefits a number of downstream applications. Traditional
Bayesian-based graph models and recent deep learning based GNN either suffer
from impracticability or lack interpretability, thus combined models for
undirected graphs have been proposed to overcome the weaknesses. As a large
portion of real-world graphs are directed graphs (of which undirected graphs
are special cases), in this paper, we propose a Deep Latent Space Model (DLSM)
for directed graphs to incorporate the traditional latent variable based
generative model into deep learning frameworks. Our proposed model consists of
a graph convolutional network (GCN) encoder and a stochastic decoder, which are
layer-wise connected by a hierarchical variational auto-encoder architecture.
By specifically modeling the degree heterogeneity using node random factors,
our model possesses better interpretability in both community structure and
degree heterogeneity. For fast inference, the stochastic gradient variational
Bayes (SGVB) is adopted using a non-iterative recognition model, which is much
more scalable than traditional MCMC-based methods. The experiments on
real-world datasets show that the proposed model achieves the state-of-the-art
performances on both link prediction and community detection tasks while
learning interpretable node embeddings. The source code is available at
https://github.com/upperr/DLSM.
