Graph Neural Networks (GNNs) have achieved state-of-the-art results on many
graph analysis tasks such as node classification and link prediction. However,
important unsupervised problems on graphs, such as graph clustering, have
proved more resistant to advances in GNNs. In this paper, we study unsupervised
training of GNN pooling in terms of their clustering capabilities.
We start by drawing a connection between graph clustering and graph pooling:
intuitively, a good graph clustering is what one would expect from a GNN
pooling layer. Counterintuitively, we show that this is not true for
state-of-the-art pooling methods, such as MinCut pooling. To address these
deficiencies, we introduce Deep Modularity Networks (DMoN), an unsupervised
pooling method inspired by the modularity measure of clustering quality, and
show how it tackles recovery of the challenging clustering structure of
real-world graphs. In order to clarify the regimes where existing methods fail,
we carefully design a set of experiments on synthetic data which show that DMoN
is able to jointly leverage the signal from the graph structure and node
attributes. Similarly, on real-world data, we show that DMoN produces high
quality clusters which correlate strongly with ground truth labels, achieving
state-of-the-art results