# Understanding the Message Passing in Graph Neural Networks via Power Iteration Clustering

arXiv: https://arxiv.org/abs/2006.00144 · HTML: https://mlsanity.com/paper/2006.00144/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 May 2020.

## Built on by (most cited first, 3 of 3)

- [Does your graph need a confidence boost? Convergent boosted smoothing on graphs with tabular node features](https://mlsanity.com/paper/2110.13413/) (2021)
- [Generating Post-hoc Explanations for Skip-gram-based Node Embeddings by Identifying Important Nodes with Bridgeness](https://mlsanity.com/paper/2304.12036/) (2023)
- [Tired of Over-smoothing? Stress Graph Drawing Is All You Need!](https://mlsanity.com/paper/2211.10579/) (2022)

## Abstract (arXiv)

The mechanism of message passing in graph neural networks (GNNs) is still mysterious. Apart from convolutional neural networks, no theoretical origin for GNNs has been proposed. To our surprise, message passing can be best understood in terms of power iteration. By fully or partly removing activation functions and layer weights of GNNs, we propose subspace power iteration clustering (SPIC) models that iteratively learn with only one aggregator. Experiments show that our models extend GNNs and enhance their capability to process random featured networks. Moreover, we demonstrate the redundancy of some state-of-the-art GNNs in design and define a lower limit for model evaluation by a random aggregator of message passing. Our findings push the boundaries of the theoretical understanding of neural networks.