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Graph generation poses a significant challenge as it involves predicting acomplete graph with multiple nodes and edges based on simply a given label.This task also carries fundamental importance to numerous real-worldapplications, including de-novo drug and molecular design. In recent years,several successful methods have emerged in the field of graph generation.However, these approaches suffer from two significant shortcomings: (1) theunderlying Graph Neural Network (GNN) architectures used in these methods areoften underexplored; and (2) these methods are often evaluated on only alimited number of metrics. To fill this gap, we investigate the expressivenessof GNNs under the context of the molecular graph generation task, by replacingthe underlying GNNs of graph generative models with more expressive GNNs.Specifically, we analyse the performance of six GNNs on six different moleculargenerative objectives on the ZINC-250k dataset in two different generativeframeworks: autoregressive generation models, such as GCPN and GraphAF, andone-shot generation models, such as GraphEBM. Through our extensiveexperiments, we demonstrate that advanced GNNs can indeed improve theperformance of GCPN, GraphAF, and GraphEBM on molecular generation tasks, butGNN expressiveness is not a necessary condition for a good GNN-based generativemodel. Moreover, we show that GCPN and GraphAF with advanced GNNs can achievestate-of-the-art results across 17 other non-GNN-based graph generativeapproaches, such as variational autoencoders and Bayesian optimisation models,on the proposed molecular generative objectives (DRD2, Median1, Median2), whichare important metrics for de-novo molecular design.

Will More Expressive Graph Neural Networks do Better on Generative Tasks?