Originality: The task of the conditional generation of graphs is new, as well as the constraint of permutation invariance, and the flexibility in terms of the generated graph structures (non-fixed set of nodes). The work is a combination of known techniques: a VAE-GAN architecture adapted to graphs, using graph convolutional neural networks and incorporating the permutation invariance constraint. To the best of my knowledge, the literature review is clear and related work adequately cited. Quality: This paper is technically sound and the VAE-GAN-GCN methodology is rigorously described. The authors also provide the code associated with this paper. It is definitely a complete piece of work. Clarity: The paper is clearly written and organized. It provides enough information for even a non-expert reader. Figure 2 is great. I believe that an expert reader can easily reproduce the results. Significance: The contributions are significant for deep generative modeling of graphs.

This is an interesting and well-written paper that aims at unifying graph NNs, VAE and GAN. The node ordering study is important. I have a few questions/comments: a. It is not clear to me how the model can generate output graphs with a number of nodes different from the input graph? b. Spectral embedding requires to solve a linear system, which costs n^3 and thus cannot be scaled to large graphs. How do you scale to large graphs? What is the complexity of the learning system? c. Spectral embedding is an important part of the proposed. It should be presented (what is g(A)?) and also explained why it provides independence wrt node re-ordering. d. An important application of graph generation is for molecule generation, which presents a challenging real-world challenge. It would have been good to evaluate the performance of the proposed system wrt [46] which proposed a competitive GNN+GAN+RL molecule generation model.

Originality: The work studies the problem of generating graphs given semantic conditions and proposes a new algorithm to conquer technical difficulties by combining or improving established methods. Overall, I think the work is novel and interesting. Quality: To the best of my knowledge, the work is technically sound. All claims are well supported by experimental results. Qlarity: The paper is well organized and clearly written. Significance: The methods of improving GVAE to generate graphs of different sizes and using adversarial learning to ensure permutation invariance are important contributions and may have great impacts on future works in graph generation.