# Enhancing Spectral Graph Neural Networks with LLM-Predicted Homophily

arXiv: https://arxiv.org/abs/2506.14220 · HTML: https://mlsanity.com/paper/2506.14220/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 35 references that are in the map.
- First posted on arXiv 17 Jun 2025.

## Builds on (most cited first, 23 of 23)

- [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)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (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)
- [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)
- [Graph Neural Network for Traffic Forecasting: A Survey](https://mlsanity.com/paper/2101.11174/) (2021)
- [BernNet: Learning Arbitrary Graph Spectral Filters via Bernstein Approximation](https://mlsanity.com/paper/2106.10994/) (2021)
- [Large Language Models on Graphs: A Comprehensive Survey](https://mlsanity.com/paper/2312.02783/) (2023)
- [Specformer: Spectral Graph Neural Networks Meet Transformers](https://mlsanity.com/paper/2303.01028/) (2023)
- [A Survey of Large Language Models for Graphs](https://mlsanity.com/paper/2405.08011/) (2024)
- [A Survey of Graph Neural Networks for Social Recommender Systems](https://mlsanity.com/paper/2212.04481/) (2022)
- [GraphTranslator: Aligning Graph Model to Large Language Model for Open-ended Tasks](https://mlsanity.com/paper/2402.07197/) (2024)
- [GADBench: Revisiting and Benchmarking Supervised Graph Anomaly Detection](https://mlsanity.com/paper/2306.12251/) (2023)
- [Graph-Aware Language Model Pre-Training on a Large Graph Corpus Can Help Multiple Graph Applications](https://mlsanity.com/paper/2306.02592/) (2023)
- [GraphEdit: Large Language Models for Graph Structure Learning](https://mlsanity.com/paper/2402.15183/) (2024)
- [How Universal Polynomial Bases Enhance Spectral Graph Neural Networks: Heterophily, Over-smoothing, and Over-squashing](https://mlsanity.com/paper/2405.12474/) (2024)
- [HP-GMN: Graph Memory Networks for Heterophilous Graphs](https://mlsanity.com/paper/2210.08195/) (2022)
- [SmoothGNN: Smoothing-aware GNN for Unsupervised Node Anomaly Detection](https://mlsanity.com/paper/2405.17525/) (2024)
- [Exploring the Potential of Large Language Models for Heterophilic Graphs](https://mlsanity.com/paper/2408.14134/) (2024)

## Abstract (arXiv)

Spectral Graph Neural Networks (SGNNs) have achieved remarkable performance in tasks such as node classification due to their ability to learn flexible filters. Typically, these filters are learned under the supervision of downstream tasks, enabling SGNNs to adapt to diverse structural patterns. However, in scenarios with limited labeled data, SGNNs often struggle to capture the optimal filter shapes, resulting in degraded performance, especially on graphs with heterophily. Meanwhile, the rapid progress of Large Language Models (LLMs) has opened new possibilities for enhancing graph learning without modifying graph structure or requiring task-specific training. In this work, we propose a novel framework that leverages LLMs to estimate the homophily level of a graph and uses this global structural prior to guide the construction of spectral filters. Specifically, we design a lightweight and plug-and-play pipeline where a small set of labeled node pairs is formatted as natural language prompts for the LLM, which then predicts the graph's homophily ratio. This estimated value informs the spectral filter basis, enabling SGNNs to adapt more effectively to both homophilic and heterophilic structures. Extensive experiments on multiple benchmark datasets demonstrate that our LLM-assisted spectral framework consistently improves performance over strong SGNN baselines. Importantly, this enhancement incurs negligible computational and monetary cost, making it a practical solution for real-world graph applications.