  Graph generation with Machine Learning is an open problem with applications
in various research fields. In this work, we propose to cast the generative
process of a graph into a sequential one, relying on a node ordering procedure.
We use this sequential process to design a novel generative model composed of
two recurrent neural networks that learn to predict the edges of graphs: the
first network generates one endpoint of each edge, while the second network
generates the other endpoint conditioned on the state of the first. We test our
approach extensively on five different datasets, comparing with two well-known
baselines coming from graph literature, and two recurrent approaches, one of
which holds state of the art performances. Evaluation is conducted considering
quantitative and qualitative characteristics of the generated samples. Results
show that our approach is able to yield novel, and unique graphs originating
from very different distributions, while retaining structural properties very
similar to those in the training sample. Under the proposed evaluation
framework, our approach is able to reach performances comparable to the current
state of the art on the graph generation task.
