  Graph Neural Networks (GNNs) and Variational Autoencoders (VAEs) have been
widely used in modeling and generating graphs with latent factors. However,
there is no clear explanation of what these latent factors are and why they
perform well. In this work, we present Dirichlet Graph Variational Autoencoder
(DGVAE) with graph cluster memberships as latent factors. Our study connects
VAEs based graph generation and balanced graph cut, and provides a new way to
understand and improve the internal mechanism of VAEs based graph generation.
Specifically, we first interpret the reconstruction term of DGVAE as balanced
graph cut in a principled way. Furthermore, motivated by the low pass
characteristics in balanced graph cut, we propose a new variant of GNN named
Heatts to encode the input graph into cluster memberships. Heatts utilizes the
Taylor series for fast computation of heat kernels and has better low pass
characteristics than Graph Convolutional Networks (GCN). Through experiments on
graph generation and graph clustering, we demonstrate the effectiveness of our
proposed framework.
