While Graph Neural Networks (GNNs) have achieved remarkable success, their design largely relies on empirical intuition rather than theoretical understanding. In this paper, we present a comprehensive analysis of GNN behavior through three fundamental aspects: (1) we establish that \textbf{k-layer} Message Passing Neural Networks efficiently aggregate \textbf{k-hop} neighborhood information through iterative computation, (2) analyze how different loop structures influence neighborhood computation, and (3) examine behavior across structure-feature hybrid and structure-only tasks. For deeper GNNs, we demonstrate that gradient-related issues, rather than just over-smoothing, can significantly impact performance in sparse graphs. We also analyze how different normalization schemes affect model performance and how GNNs make predictions with uniform node features, providing a theoretical framework that bridges the gap between empirical success and theoretical understanding.
@article{arxiv.2502.00140,
title = {Demystifying MPNNs: Message Passing as Merely Efficient Matrix Multiplication},
author = {Qin Jiang and Chengjia Wang and Michael Lones and Wei Pang},
journal= {arXiv preprint arXiv:2502.00140},
year = {2025}
}