Hierarchical Multi-Resolution Graph Generation Networks

Mahdi Karami, Jun Luo

Keywords: Graph Generative models, GNN, Multinomial distribution

Abstract:

In real world domains, graphs often have natural hierarchies.
However, data-driven graph generation is yet to effectively respect and exploit such structures.
We propose a novel approach that recursively generates community structures at multiple resolutions, with the generated structures conforming to training data distribution at each level of the hierarchy.
While the generation of a community at one level takes place sequentially, lower-level sub-structures of the community can be handled in parallel.
This significantly improves the speed of both generation and learning, resulting in $\mathcal{O}(\log n)$ generative rounds.
Our method is further supported by an expressive probability distribution for intermediate and leaf levels of this hierarchical model.
Our method achieves the state of the art performance in graph generation in both accuracy and efficiency on many datasets.

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