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# Scalable Deep Generative Modeling for Sparse Graphs

*Proceedings of the 37th International Conference on Machine Learning*, PMLR 119:2302-2312, 2020.

#### Abstract

Learning graph generative models is a challenging task for deep learning and has wide applicability to a range of domains like chemistry, biology and social science. However current deep neural methods suffer from limited scalability: for a graph with n nodes and m edges, existing deep neural methods require Omega(n^2) complexity by building up the adjacency matrix. On the other hand, many real world graphs are actually sparse in the sense that m << n^2. Based on this, we develop a novel autoregressive model, named BiGG, that utilizes this sparsity to avoid generating the full adjacency matrix, and importantly reduces the graph generation time complexity to O((n + m) log n). Furthermore, during training this autoregressive model can be parallelized with O(log n) synchronization stages, which makes it much more efficient than other autoregressive models that require Omega(n). Experiments on several benchmarks show that the proposed approach not only scales to orders of magnitude larger graphs than previously possible with deep autoregressive graph generative models, but also yields better graph generation quality.