On the Power of Edge Independent Graph Models

TL;DR

This paper investigates the limitations of edge independent graph models, showing they cannot produce high triangle densities typical of real-world networks, and proposes a simple balanced model as an alternative.

Contribution

The paper proves inherent limitations of edge independent models in generating dense local structures and introduces a simple model balancing overlap and accuracy.

Findings

Edge independent models cannot generate high triangle densities.

High triangle densities are common in real-world social networks.

A simple balanced model performs comparably to complex models.

Abstract

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 Erd\"{o}s-R\'{e}nyi 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.