  Graph embedding aims to transfer a graph into vectors to facilitate
subsequent graph analytics tasks like link prediction and graph clustering.
Most approaches on graph embedding focus on preserving the graph structure or
minimizing the reconstruction errors for graph data. They have mostly
overlooked the embedding distribution of the latent codes, which unfortunately
may lead to inferior representation in many cases. In this paper, we present a
novel adversarially regularized framework for graph embedding. By employing the
graph convolutional network as an encoder, our framework embeds the topological
information and node content into a vector representation, from which a graph
decoder is further built to reconstruct the input graph. The adversarial
training principle is applied to enforce our latent codes to match a prior
Gaussian or Uniform distribution. Based on this framework, we derive two
variants of adversarial models, the adversarially regularized graph autoencoder
(ARGA) and its variational version, adversarially regularized variational graph
autoencoder (ARVGA), to learn the graph embedding effectively. We also exploit
other potential variations of ARGA and ARVGA to get a deeper understanding on
our designs. Experimental results compared among twelve algorithms for link
prediction and twenty algorithms for graph clustering validate our solutions.
