  While a wide range of interpretable generative procedures for graphs exist,
matching observed graph topologies with such procedures and choices for its
parameters remains an open problem. Devising generative models that closely
reproduce real-world graphs requires domain knowledge and time-consuming
simulation. While existing deep learning approaches rely on less manual
modelling, they offer little interpretability. This work approaches graph
generation (decoding) as the inverse of graph compression (encoding). We show
that in a disentanglement-focused deep autoencoding framework, specifically
Beta-Variational Autoencoders (Beta-VAE), choices of generative procedures and
their parameters arise naturally in the latent space. Our model is capable of
learning disentangled, interpretable latent variables that represent the
generative parameters of procedurally generated random graphs and real-world
graphs. The degree of disentanglement is quantitatively measured using the
Mutual Information Gap (MIG). When training our Beta-VAE model on ER random
graphs, its latent variables have a near one-to-one mapping to the ER random
graph parameters n and p. We deploy the model to analyse the correlation
between graph topology and node attributes measuring their mutual dependence
without handpicking topological properties.
