On the Power of Edge Independent Graph Models

Sudhanshu Chanpuriya, Cameron N Musco, Konstantinos Sotiropoulos, Charalampos Tsourakakis

Keywords: graph generative models, random graphs, edge independent models, node embeddings, triangle density

TL;DR: We show that "edge-independent" graph generative models face an inherent tradeoff between memorization and the ability to generate realistic triangle dense graphs.

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 Erdos-Renyi 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.

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Code: https://github.com/konsotirop/edge_independent_models

Community Implementations: [ 1 code implementation](https://www.catalyzex.com/paper/arxiv:2111.00048/code)