I've work with GNNs. I have not explicitly looked into this, but in general, the dynamics of GNNs are really interesting and there are many different lenses in which one can study the behavior of GNNs and find interesting takeaways.

- Explicit Message Passing: https://arxiv.org/abs/2202.11097

- Algorithmic Reasoning: https://arxiv.org/abs/2203.15544

- Diffusion: https://proceedings.mlr.press/v139/chamberlain21a.html

- Spectral: https://arxiv.org/abs/2010.02863

- Sparsity: https://arxiv.org/abs/2211.15335

- Training Tricks: https://arxiv.org/abs/2108.10521

- Interaction Networks / Physical Models: https://arxiv.org/pdf/1612.00222.pdf

- Expressive Power: https://arxiv.org/abs/2308.08235

- "Over-Squashing": https://arxiv.org/abs/2111.14522