  Graph autoencoders (GAE) and variational graph autoencoders (VGAE) emerged as
powerful methods for link prediction. Their performances are less impressive on
community detection problems where, according to recent and concurring
experimental evaluations, they are often outperformed by simpler alternatives
such as the Louvain method. It is currently still unclear to which extent one
can improve community detection with GAE and VGAE, especially in the absence of
node features. It is moreover uncertain whether one could do so while
simultaneously preserving good performances on link prediction. In this paper,
we show that jointly addressing these two tasks with high accuracy is possible.
For this purpose, we introduce and theoretically study a community-preserving
message passing scheme, doping our GAE and VGAE encoders by considering both
the initial graph structure and modularity-based prior communities when
computing embedding spaces. We also propose novel training and optimization
strategies, including the introduction of a modularity-inspired regularizer
complementing the existing reconstruction losses for joint link prediction and
community detection. We demonstrate the empirical effectiveness of our
approach, referred to as Modularity-Aware GAE and VGAE, through in-depth
experimental validation on various real-world graphs.
