  Deep generative models for Natural Language data offer a new angle on the
problem of graph synthesis: by optimizing differentiable models that directly
generate graphs, it is possible to side-step expensive search procedures in the
discrete and vast space of possible graphs. We introduce LIC-GAN, an implicit,
likelihood-free generative model for small graphs that circumvents the need for
expensive graph matching procedures. Our method takes as input a natural
language query and using a combination of language modelling and Generative
Adversarial Networks (GANs) and returns a graph that closely matches the
description of the query. We combine our approach with a reward network to
further enhance the graph generation with desired properties. Our experiments,
show that LIC-GAN does well on metrics such as PropMatch and Closeness getting
scores of 0.36 and 0.48. We also show that LIC-GAN performs as good as ChatGPT,
with ChatGPT getting scores of 0.40 and 0.42. We also conduct a few experiments
to demonstrate the robustness of our method, while also highlighting a few
interesting caveats of the model.
