  We present GraphMoE, a novel neural network-based approach to learning
generative models for random graphs. The neural network is trained to match the
distribution of a class of random graphs by way of a moment estimator. The
features used for training are graphlets, subgraph counts of small order. The
neural network accepts random noise as input and outputs vector representations
for nodes in the graph. Random graphs are then realized by applying a kernel to
the representations. Graphs produced this way are demonstrated to be able to
imitate data from chemistry, medicine, and social networks. The produced graphs
are similar enough to the target data to be able to fool discriminator neural
networks otherwise capable of separating classes of random graphs.
