  Representing graph data in a low-dimensional space for subsequent tasks is
the purpose of attributed graph embedding. Most existing neural network
approaches learn latent representations by minimizing reconstruction errors.
Rare work considers the data distribution and the topological structure of
latent codes simultaneously, which often results in inferior embeddings in
real-world graph data. This paper proposes a novel Deep Manifold (Variational)
Graph Auto-Encoder (DMVGAE/DMGAE) method for attributed graph data to improve
the stability and quality of learned representations to tackle the crowding
problem. The node-to-node geodesic similarity is preserved between the original
and latent space under a pre-defined distribution. The proposed method
surpasses state-of-the-art baseline algorithms by a significant margin on
different downstream tasks across popular datasets, which validates our
solutions. We promise to release the code after acceptance.
