  Small subgraphs (graphlets) are important features to describe fundamental
units of a large network. The calculation of the subgraph frequency
distributions has a wide application in multiple domains including biology and
engineering. Unfortunately due to the inherent complexity of this task, most of
the existing methods are computationally intensive and inefficient. In this
work, we propose GNNS, a novel representational learning framework that
utilizes graph neural networks to sample subgraphs efficiently for estimating
their frequency distribution. Our framework includes an inference model and a
generative model that learns hierarchical embeddings of nodes, subgraphs, and
graph types. With the learned model and embeddings, subgraphs are sampled in a
highly scalable and parallel way and the frequency distribution estimation is
then performed based on these sampled subgraphs. Eventually, our methods
achieve comparable accuracy and a significant speedup by three orders of
magnitude compared to existing methods.
