  Most real-world graphs exhibit a hierarchical structure, which is often
overlooked by existing graph generation methods. To address this limitation, we
propose a novel graph generative network that captures the hierarchical nature
of graphs and successively generates the graph sub-structures in a
coarse-to-fine fashion. At each level of hierarchy, this model generates
communities in parallel, followed by the prediction of cross-edges between
communities using separate neural networks. This modular approach enables
scalable graph generation for large and complex graphs. Moreover, we model the
output distribution of edges in the hierarchical graph with a multinomial
distribution and derive a recursive factorization for this distribution. This
enables us to generate community graphs with integer-valued edge weights in an
autoregressive manner. Empirical studies demonstrate the effectiveness and
scalability of our proposed generative model, achieving state-of-the-art
performance in terms of graph quality across various benchmark datasets. The
code is available at https://github.com/Karami-m/HiGen_main.
