Graph Embedding VAE: A Permutation Invariant Model of Graph Structure

TL;DR

This paper introduces a permutation invariant graph generative model using embeddings, which is scalable to large graphs and maintains permutation invariance unlike previous models like GraphRNN.

Contribution

The paper proposes a novel permutation invariant graph embedding VAE that scales efficiently to large graphs and preserves graph structure without losing invariance.

Findings

Model is scalable to large graphs with $O(|V| + |E|)$ complexity.

Maintains permutation invariance in graph generation.

Outperforms existing models in structure preservation.

Abstract

Generative models of graph structure have applications in biology and social sciences. The state of the art is GraphRNN, which decomposes the graph generation process into a series of sequential steps. While effective for modest sizes, it loses its permutation invariance for larger graphs. Instead, we present a permutation invariant latent-variable generative model relying on graph embeddings to encode structure. Using tools from the random graph literature, our model is highly scalable to large graphs with likelihood evaluation and generation in $O(|V | + |E|)$.