  Learning representations for graphs plays a critical role in a wide spectrum
of downstream applications. In this paper, we summarize the limitations of the
prior works in three folds: representation space, modeling dynamics and
modeling uncertainty. To bridge this gap, we propose to learn dynamic graph
representation in hyperbolic space, for the first time, which aims to infer
stochastic node representations. Working with hyperbolic space, we present a
novel Hyperbolic Variational Graph Neural Network, referred to as HVGNN. In
particular, to model the dynamics, we introduce a Temporal GNN (TGNN) based on
a theoretically grounded time encoding approach. To model the uncertainty, we
devise a hyperbolic graph variational autoencoder built upon the proposed TGNN
to generate stochastic node representations of hyperbolic normal distributions.
Furthermore, we introduce a reparameterisable sampling algorithm for the
hyperbolic normal distribution to enable the gradient-based learning of HVGNN.
Extensive experiments show that HVGNN outperforms state-of-the-art baselines on
real-world datasets.
