# Neighborhood Homophily-based Graph Convolutional Network

arXiv: https://arxiv.org/abs/2301.09851 · HTML: https://mlsanity.com/paper/2301.09851/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 33 references that are in the map.
- First posted on arXiv 24 Jan 2023.

## Builds on (most cited first, 21 of 21)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Simple and Deep Graph Convolutional Networks](https://mlsanity.com/paper/2007.02133/) (2020)
- [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)
- [MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixing](https://mlsanity.com/paper/1905.00067/) (2019)
- [Diffusion Improves Graph Learning](https://mlsanity.com/paper/1911.05485/) (2019)
- [Beyond Low-frequency Information in Graph Convolutional Networks](https://mlsanity.com/paper/2101.00797/) (2021)
- [Graph Neural Networks with Heterophily](https://mlsanity.com/paper/2009.13566/) (2020)
- [BernNet: Learning Arbitrary Graph Spectral Filters via Bernstein Approximation](https://mlsanity.com/paper/2106.10994/) (2021)
- [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)
- [Revisiting Heterophily For Graph Neural Networks](https://mlsanity.com/paper/2210.07606/) (2022)
- [Breaking the Limit of Graph Neural Networks by Improving the Assortativity of Graphs with Local Mixing Patterns](https://mlsanity.com/paper/2106.06586/) (2021)
- [Non-Local Graph Neural Networks](https://mlsanity.com/paper/2005.14612/) (2020)
- [GBK-GNN: Gated Bi-Kernel Graph Neural Networks for Modeling Both Homophily and Heterophily](https://mlsanity.com/paper/2110.15777/) (2021)
- [Break the Ceiling: Stronger Multi-scale Deep Graph Convolutional Networks](https://mlsanity.com/paper/1906.02174/) (2019)
- [Model Degradation Hinders Deep Graph Neural Networks](https://mlsanity.com/paper/2206.04361/) (2022)

## Built on by (most cited first, 7 of 7)

- [A Comprehensive Survey on Graph Reduction: Sparsification, Coarsening, and Condensation](https://mlsanity.com/paper/2402.03358/) (2024)
- [A Survey on Learning from Graphs with Heterophily: Recent Advances and Future Directions](https://mlsanity.com/paper/2401.09769/) (2024)
- [What Is Missing In Homophily? Disentangling Graph Homophily For Graph Neural Networks](https://mlsanity.com/paper/2406.18854/) (2024)
- [Scalable Graph Condensation with Evolving Capabilities](https://mlsanity.com/paper/2502.17614/) (2025)
- [Enhancing Ethereum Fraud Detection via Generative and Contrastive Self-supervision](https://mlsanity.com/paper/2408.00641/) (2024)
- [A Federated Parameter Aggregation Method for Node Classification Tasks with Different Graph Network Structures](https://mlsanity.com/paper/2403.16004/) (2024)
- [It Takes a Graph to Know a Graph: Rewiring for Homophily with a Reference Graph](https://mlsanity.com/paper/2505.12411/) (2025)

## Abstract (arXiv)

Graph neural networks (GNNs) have been proved powerful in graph-oriented tasks. However, many real-world graphs are heterophilous, challenging the homophily assumption of classical GNNs. To solve the universality problem, many studies deepen networks or concatenate intermediate representations, which does not inherently change neighbor aggregation and introduces noise. Recent studies propose new metrics to characterize the homophily, but rarely consider the correlation of the proposed metrics and models. In this paper, we first design a new metric, Neighborhood Homophily (textitNH), to measure the label complexity or purity in node neighborhoods. Furthermore, we incorporate the metric into the classical graph convolutional network (GCN) architecture and propose Neighborhood Homophily-based Graph Convolutional Network (NHGCN). In this framework, neighbors are grouped by estimated textitNH values and aggregated from different channels, and the resulting node predictions are then used in turn to estimate and update textitNH values. The two processes of metric estimation and model inference are alternately optimized to achieve better node classification. NHGCN achieves top overall performance on both homophilous and heterophilous benchmarks, with an improvement of up to 7.4% compared to the current SOTA methods.