Deep graph generation models have achieved great successes recently, among which however, are typically unconditioned generative models that have no control over the target graphs given an input graph. In this paper, we propose a novel GraphTranslation-Generative-Adversarial-Networks (GT-GAN) that transforms the input graphs into their target output graphs. GT-GAN consists of a graph translator equipped with innovative graph convolution and deconvolution layers to learn the translation mapping considering both global and local features. A new conditional graph discriminator is proposed to classify the target graphs by conditioning on input graphs while training. Extensive experiments on multiple synthetic and realworld datasets demonstrate that our proposed GT-GAN significantly outperforms other baseline methods in terms of both effectiveness and scalability. For instance, GT-GAN performs at least 10 and 15 time faster than GraphRNN and RandomVAE, respectively, when the size of the graph is around 50.
This paper studies a problem of graph translation, which aims at learning a graph translator to translate an input graph to a target graph. The authors propose an adversarial training framework to learn the graph translator, where a discriminator is trained to discriminate between the true target graph and the translated graph, and the translator is optimized by fooling the discriminator. The authors conduct experiments on both synthetic and real-world datasets. The results prove the effectiveness and the efficiency of the proposed approach over many baselines.
Strengths:
1. The problem is new and well-motivated.
Data translation is an important problem and has been widely studied in many research domains such as computer vision and natural language processing. Despite the importance, the problem has not been thoroughly explored in the graph domain, and most existing studies only focus on standard graph generation problems. In this sense, this paper studies a very new problem, which is quite novel. Moreover, the problem is important, which can have many potential downstream applications on graph data. Overall, the problem is new and well-motivated.
2. The proposed approach is quite intuitive.
The paper proposes an adversarial training approach to the problem, where a graph translator is learned based on a graph discriminator. During training, the graph discriminator aims at discriminating between the true target graph and the translated graph conditioned on an input graph, and the graph translator is trained by fooling the discriminator. The graph translator is built on top of an encoder-decoder framework, where the encoder and decoder are parameterized by graph neural networks. Overall, the proposed method is quite reasonable, which is easy to follow.
3. The results are promising.
The authors conduct extensive experiments on both synthetic and real-world datasets, and compare the proposed approach against many strong baseline methods for graph generation. The results are quite promising, which prove both the effectiveness and the efficiency of the approach.
Weaknesses:
1. The novelty of the proposed approach is limited.
The proposed approach is mainly built on top of the adversarial training framework, where a graph neural network is used to parameterize the graph translator. For adversarial training, although it is very intuitive, such a framework has been widely explored in the data translation problem in other domains, such as image style transfer in CV and text style transfer in NLP. Compared with these works, although the proposed approach studies a new problem, the major idea is the same as the existing studies. For the graph encoder and graph decoder, they are designed based on the idea of graph neural networks, where some propagation layers are designed to propagate information across different nodes. Although the propagation layers are specifically designed for the graph translation problem, I feel like they are not so different from existing studies (e.g, message passing neural network, graph U-net). Therefore, from the model-wise, this paper combines several existing ideas, but does not provide new insights or techniques, so the contribution is quite limited.
2. The writing can be further improved.
The paper is not very well-written. Some parts of the paper are quite hard to follow, and the intuition behind the approach is not well explained. In section 3.2, it is said that "the approach learns global information by looking for more virtual neighbors regarding the latent relations". Here, it is unclear to me what is a virtual neighbor, and what is a latent relation. The authors try to illustrate their idea in figure 2, but the figure is also quite hard to understand. It would be better if the authors could explain the idea of the encoder in a more intuitive way, or give more concrete examples for illustration. Besides, equation (4) (5) and (7) are also hard to understand. The notations in these equations are quite messy, where multiple indices are used (e.g., i, j, k, l, m, n), and the intuition underlying the equations is not well explained, making it hard to understand how the encoder and the decoder work. 
Also, there are many typos in the paper. For example:
In the directed graph, each node have incoming edge(s) and out-going edge(s) -> In the directed graph, each node has incoming edge(s) and out-going edge(s)
in the "node comvolution" layer -> in the "node convolution" layer
First, the “node deconvolution” layer are used to generates -> First, the “node deconvolution” layer is used to generate
The caption of table 1 says that the table shows the node degree distribution distance, but from the main body of texts, only four metrics are about the distribution distance, which is inconsistent to the caption.
Overall, the intuition of the proposed approach is not well explained, and there are many typos to be fixed, so I feel like the writing of the paper should be further improved.