  Modeling generative process of growing graphs has wide applications in social
networks and recommendation systems, where cold start problem leads to new
nodes isolated from existing graph. Despite the emerging literature in learning
graph representation and graph generation, most of them can not handle isolated
new nodes without nontrivial modifications. The challenge arises due to the
fact that learning to generate representations for nodes in observed graph
relies heavily on topological features, whereas for new nodes only node
attributes are available. Here we propose a unified generative graph
convolutional network that learns node representations for all nodes adaptively
in a generative model framework, by sampling graph generation sequences
constructed from observed graph data. We optimize over a variational lower
bound that consists of a graph reconstruction term and an adaptive
Kullback-Leibler divergence regularization term. We demonstrate the superior
performance of our approach on several benchmark citation network datasets.
