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Graph autoencoders (GAE) and variational graph autoencoders (VGAE) emerged aspowerful methods for link prediction. Their performances are less impressive oncommunity detection problems where, according to recent and concurringexperimental evaluations, they are often outperformed by simpler alternativessuch as the Louvain method. It is currently still unclear to which extent onecan improve community detection with GAE and VGAE, especially in the absence ofnode features. It is moreover uncertain whether one could do so whilesimultaneously 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-preservingmessage passing scheme, doping our GAE and VGAE encoders by considering boththe initial graph structure and modularity-based prior communities whencomputing embedding spaces. We also propose novel training and optimizationstrategies, including the introduction of a modularity-inspired regularizercomplementing the existing reconstruction losses for joint link prediction andcommunity detection. We demonstrate the empirical effectiveness of ourapproach, referred to as Modularity-Aware GAE and VGAE, through in-depthexperimental validation on various real-world graphs.

Modularity-Aware Graph Autoencoders for Joint Community Detection and Link Prediction