  Graph clustering is a longstanding research topic, and has achieved
remarkable success with the deep learning methods in recent years.
Nevertheless, we observe that several important issues largely remain open. On
the one hand, graph clustering from the geometric perspective is appealing but
has rarely been touched before, as it lacks a promising space for geometric
clustering. On the other hand, contrastive learning boosts the deep graph
clustering but usually struggles in either graph augmentation or hard sample
mining. To bridge this gap, we rethink the problem of graph clustering from
geometric perspective and, to the best of our knowledge, make the first attempt
to introduce a heterogeneous curvature space to graph clustering problem.
Correspondingly, we present a novel end-to-end contrastive graph clustering
model named CONGREGATE, addressing geometric graph clustering with Ricci
curvatures. To support geometric clustering, we construct a theoretically
grounded Heterogeneous Curvature Space where deep representations are generated
via the product of the proposed fully Riemannian graph convolutional nets.
Thereafter, we train the graph clusters by an augmentation-free reweighted
contrastive approach where we pay more attention to both hard negatives and
hard positives in our curvature space. Empirical results on real-world graphs
show that our model outperforms the state-of-the-art competitors.
