We propose GraphGAN -the first implicit generative model for graphs that enables to mimic real-world networks. We pose the problem of graph generation as learning the distribution of biased random walks over a single input graph. Our model is based on a stochastic neural network that generates discrete output samples, and is trained using the Wasserstein GAN objective. GraphGAN enables us to generate sibling graphs, which have similar properties yet are not exact replicas of the original graph. Moreover, GraphGAN learns a semantic mapping from the latent input space to the generated graph's properties. We discover that sampling from certain regions of the latent space leads to varying properties of the output graphs, with smooth transitions between them. Strong generalization properties of GraphGAN are highlighted by its competitive performance in link prediction as well as promising results on node classification, even though not specifically trained for these tasks.
This paper proposes a WGAN formulation for generating graphs based on random walks. The proposed generator model combines node embeddings, with an LSTM architecture for modeling the sequence of nodes visited in a random walk; the discriminator distinguishes real from fake walks.
The model is learned from a single large input graph (for three real-world networks) and evaluated against one baseline generative graph model: degree-corrected stochastic block models. 
The primary claims of the paper are as follows:
i) The proposed approach is a generative model of graphs, specifically producing "sibling" graphs
ii) The learned latent representation provides an interpretation of generated graph properties
iii) The model generalizes well in terms of link and node classification
The proposed method is novel and the incorporated ideas are quite interesting (e.g., discriminating real from fake random walks, generating random walks from node embeddings and LSTMs). However, from a graph generation perspective, the problem formulation and evaluation do not sufficiently demonstrate the utility of proposed method. 
First, wrt claim (i) the problem of generating "sibling" graphs is ill-posed. Statistical graph models are typically designed to generate a probability distribution over all graphs with N nodes and, as such, are evaluated based on how well they model that distribution. The notion of a "sibling" graph used in this paper is not clearly defined, but it seems to only be useful if the sibling graphs are likely under the distribution. Unfortunately, the likelihood of the sampled graphs is not explicitly evaluated. On the other hand, since many of the edges are shared the "siblings" may be nearly isomorphic to the input graph, which is not useful from a graph modeling perspective. 
For claim (i), the comparison to related work is far from sufficient to demonstrate its utility as a graph generation model. There are many graph models that are superior to DC-SBM, including KPGMs, BETR, ERGMs, hierarchical random graph models and latent space models. Moreover, a very simple baseline to assess the LSTM component of the model, would be to produce a graph by sampling links repeatedly from the latent space of node embeddings. 
Next, the evaluation wrt to claim (ii) is novel and may help developers understand the model characteristics. However, since the properties are measured based on a set of random walks it is still difficult to interpret the impact on the generated graphs (since an arbitrary node in the final graph will have some structure determined from each of the regions). Do the various regions generate different parts of the final graph structure (i.e., focusing on only a subset of the nodes)?   
Lastly, the authors evaluate the learned model on link and node prediction tasks and state that the model's so-so performance supports the claim that the model can generalize. This is the weakest claim of the paper. The learned node embeddings appear to do significantly worse than node2vec, and the full model is worse than DC-SBM. Given that the proposed model is transductive (when there is significant edge overlap) it should do far better than DC-SBM which is inductive. 
Overall, while the paper includes a wide range of experimental evaluation, they are aimed too broadly (and the results are too weak) to support any specific claim of the work. If the goal is to generate transductively (with many similar edges), then it would be better to compare more extensively to alternative node embedding and matrix factorization approaches, and assess the utility of the various modeling choices (e.g., LSTM, in/out embedding). If the goal is to generate inductively, over the full distribution of graphs, then it would be better to (i) assess whether the sampled graphs are isomorphic, and (ii) compare more extensively to alternative graph models (many of which have been published since 2010).