# Understanding GNNs and Homophily in Dynamic Node Classification

arXiv: https://arxiv.org/abs/2504.20421 · HTML: https://mlsanity.com/paper/2504.20421/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 56 references that are in the map.
- First posted on arXiv 29 Apr 2025.

## Builds on (most cited first, 30 of 31)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [Adaptive Universal Generalized PageRank Graph Neural Network](https://mlsanity.com/paper/2006.07988/) (2020)
- [Predicting Dynamic Embedding Trajectory in Temporal Interaction Networks](https://mlsanity.com/paper/1908.01207/) (2019)
- [EvolveGCN: Evolving Graph Convolutional Networks for Dynamic Graphs](https://mlsanity.com/paper/1902.10191/) (2019)
- [Beyond Low-frequency Information in Graph Convolutional Networks](https://mlsanity.com/paper/2101.00797/) (2021)
- [Large Scale Learning on Non-Homophilous Graphs: New Benchmarks and Strong Simple Methods](https://mlsanity.com/paper/2110.14446/) (2021)
- [Structured Sequence Modeling with Graph Convolutional Recurrent Networks](https://mlsanity.com/paper/1612.07659/) (2016)
- [Neural Sheaf Diffusion: A Topological Perspective on Heterophily and Oversmoothing in GNNs](https://mlsanity.com/paper/2202.04579/) (2022)
- [Graph Neural Networks with Heterophily](https://mlsanity.com/paper/2009.13566/) (2020)
- [Two Sides of the Same Coin: Heterophily and Oversmoothing in Graph Convolutional Neural Networks](https://mlsanity.com/paper/2102.06462/) (2021)
- [Is Homophily a Necessity for Graph Neural Networks?](https://mlsanity.com/paper/2106.06134/) (2021)
- [Temporal Graph Benchmark for Machine Learning on Temporal Graphs](https://mlsanity.com/paper/2307.01026/) (2023)
- [Motifs in Temporal Networks](https://mlsanity.com/paper/1612.09259/) (2016)
- [Dynamic Graph Convolutional Networks](https://mlsanity.com/paper/1704.06199/) (2017)
- [Characterizing Graph Datasets for Node Classification: Homophily-Heterophily Dichotomy and Beyond](https://mlsanity.com/paper/2209.06177/) (2022)
- [GC-LSTM: Graph Convolution Embedded LSTM for Dynamic Link Prediction](https://mlsanity.com/paper/1812.04206/) (2018)
- [The Anatomy of a Scientific Rumor](https://mlsanity.com/paper/1301.2952/) (2013)
- [DPPIN: A Biological Repository of Dynamic Protein-Protein Interaction Network Data](https://mlsanity.com/paper/2107.02168/) (2021)
- [On Performance Discrepancies Across Local Homophily Levels in Graph Neural Networks](https://mlsanity.com/paper/2306.05557/) (2023)
- [TouchUp-G: Improving Feature Representation through Graph-Centric Finetuning](https://mlsanity.com/paper/2309.13885/) (2023)
- [On the Impact of Feature Heterophily on Link Prediction with Graph Neural Networks](https://mlsanity.com/paper/2409.17475/) (2024)
- [Modeling Information Propagation with Survival Theory](https://mlsanity.com/paper/1305.3616/) (2013)
- [Unveiling the Impact of Local Homophily on GNN Fairness: In-Depth Analysis and New Benchmarks](https://mlsanity.com/paper/2410.04287/) (2024)

## Built on by (most cited first, 2 of 2)

- [Random Search Neural Networks for Efficient and Expressive Graph Learning](https://mlsanity.com/paper/2510.22520/) (2025)
- [When GNNs Fail: Quantifying and Overcoming Temporal Correlation Volatility in Time Series](https://mlsanity.com/paper/2608.07333/) (2026)

## Abstract (arXiv)

Homophily, as a measure, has been critical to increasing our understanding of graph neural networks (GNNs). However, to date this measure has only been analyzed in the context of static graphs. In our work, we explore homophily in dynamic settings. Focusing on graph convolutional networks (GCNs), we demonstrate theoretically that in dynamic settings, current GCN discriminative performance is characterized by the probability that a node's future label is the same as its neighbors' current labels. Based on this insight, we propose dynamic homophily, a new measure of homophily that applies in the dynamic setting. This new measure correlates with GNN discriminative performance and sheds light on how to potentially design more powerful GNNs for dynamic graphs. Leveraging a variety of dynamic node classification datasets, we demonstrate that popular GNNs are not robust to low dynamic homophily. Going forward, our work represents an important step towards understanding homophily and GNN performance in dynamic node classification.