Block-Approximated Exponential Random Graphs
This work addresses the scalability problem for network analysis researchers and practitioners by providing a more direct and interpretable probabilistic model for tasks like link prediction, though it is incremental as it builds on existing ERG and approximation techniques.
The paper tackles the challenge of fitting non-trivial exponential random graphs (ERGs) on large graphs by proposing a block-approximation framework that results in dyadic independent distributions, enabling efficient generation of random networks with properties like degrees and clustering coefficients. Empirical results show competitiveness in speed and accuracy with state-of-the-art methods for link prediction on graphs with millions of nodes.
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.