  An important challenge in the field of exponential random graphs (ERGs) is
the fitting of non-trivial ERGs on large graphs. By utilizing fast matrix
block-approximation techniques, we propose an approximative framework to such
non-trivial ERGs that result in dyadic independence (i.e., edge independent)
distributions, while being able to meaningfully model both local information of
the graph (e.g., degrees) as well as global information (e.g., clustering
coefficient, assortativity, etc.) if desired. This allows one to efficiently
generate random networks with similar properties as an observed network, and
the models can be used for several downstream tasks such as link prediction.
Our methods are scalable to sparse graphs consisting of millions of nodes.
Empirical evaluation demonstrates competitiveness in terms of both speed and
accuracy with state-of-the-art methods -- which are typically based on
embedding the graph into some low-dimensional space -- for link prediction,
showcasing the potential of a more direct and interpretable probabalistic model
for this task.
