  The (variational) graph auto-encoder is widely used to learn representations
for graph-structured data. However, the formation of real-world graphs is a
complicated and heterogeneous process influenced by latent factors. Existing
encoders are fundamentally holistic, neglecting the entanglement of latent
factors. This reduces the effectiveness of graph analysis tasks, while also
making it more difficult to explain the learned representations. As a result,
learning disentangled graph representations with the (variational) graph
auto-encoder poses significant challenges and remains largely unexplored in the
current research. In this paper, we introduce the Disentangled Graph
Auto-Encoder (DGA) and the Disentangled Variational Graph Auto-Encoder (DVGA)
to learn disentangled representations. Specifically, we first design a
disentangled graph convolutional network with multi-channel message-passing
layers to serve as the encoder. This allows each channel to aggregate
information about each latent factor. The disentangled variational graph
auto-encoder's expressive capability is then enhanced by applying a
component-wise flow to each channel. In addition, we construct a factor-wise
decoder that takes into account the characteristics of disentangled
representations. We improve the independence of representations by imposing
independence constraints on the mapping channels for distinct latent factors.
Empirical experiments on both synthetic and real-world datasets demonstrate the
superiority of our proposed method compared to several state-of-the-art
baselines.
