On the Power of Edge Independent Graph Models
This work addresses a fundamental limitation in graph generative modeling for applications like social network analysis, though it is incremental as it builds on existing edge independent models.
The paper tackles the problem of why many neural-network-based graph generative models fail to reproduce high triangle densities common in real-world networks, proving that edge independent models are inherently limited in generating such high subgraph densities under a bounded overlap condition.
Why do many modern neural-network-based graph generative models fail to reproduce typical real-world network characteristics, such as high triangle density? In this work we study the limitations of edge independent random graph models, in which each edge is added to the graph independently with some probability. Such models include both the classic Erdös-Rényi and stochastic block models, as well as modern generative models such as NetGAN, variational graph autoencoders, and CELL. We prove that subject to a bounded overlap condition, which ensures that the model does not simply memorize a single graph, edge independent models are inherently limited in their ability to generate graphs with high triangle and other subgraph densities. Notably, such high densities are known to appear in real-world social networks and other graphs. We complement our negative results with a simple generative model that balances overlap and accuracy, performing comparably to more complex models in reconstructing many graph statistics.