# 2-hop Neighbor Class Similarity (2NCS): A graph structural metric indicative of graph neural network performance

arXiv: https://arxiv.org/abs/2212.13202 · HTML: https://mlsanity.com/paper/2212.13202/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 17 references that are in the map.
- First posted on arXiv 26 Dec 2022.

## Builds on (most cited first, 9 of 9)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [Multi-scale Attributed Node Embedding](https://mlsanity.com/paper/1909.13021/) (2019)
- [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)
- [Simplifying approach to Node Classification in Graph Neural Networks](https://mlsanity.com/paper/2111.06748/) (2021)

## Built on by (most cited first, 8 of 8)

- [On Performance Discrepancies Across Local Homophily Levels in Graph Neural Networks](https://mlsanity.com/paper/2306.05557/) (2023)
- [What Is Missing In Homophily? Disentangling Graph Homophily For Graph Neural Networks](https://mlsanity.com/paper/2406.18854/) (2024)
- [Clarify Confused Nodes via Separated Learning](https://mlsanity.com/paper/2306.02285/) (2023)
- [Investigating the Interplay between Features and Structures in Graph Learning](https://mlsanity.com/paper/2308.09570/) (2023)
- [GCNH: A Simple Method For Representation Learning On Heterophilous Graphs](https://mlsanity.com/paper/2304.10896/) (2023)
- [Learning Graph Foundation Models on Riemannian Graph-of-Graphs](https://mlsanity.com/paper/2605.09993/) (2026)
- [Lying Graph Convolution: Learning to Lie for Node Classification Tasks](https://mlsanity.com/paper/2405.01247/) (2024)
- [RAwR: Role-Aware Rewiring via Approximate Equitable Partition](https://mlsanity.com/paper/2605.09457/) (2026)

## Abstract (arXiv)

Graph Neural Networks (GNNs) achieve state-of-the-art performance on graph-structured data across numerous domains. Their underlying ability to represent nodes as summaries of their vicinities has proven effective for homophilous graphs in particular, in which same-type nodes tend to connect. On heterophilous graphs, in which different-type nodes are likely connected, GNNs perform less consistently, as neighborhood information might be less representative or even misleading. On the other hand, GNN performance is not inferior on all heterophilous graphs, and there is a lack of understanding of what other graph properties affect GNN performance. In this work, we highlight the limitations of the widely used homophily ratio and the recent Cross-Class Neighborhood Similarity (CCNS) metric in estimating GNN performance. To overcome these limitations, we introduce 2-hop Neighbor Class Similarity (2NCS), a new quantitative graph structural property that correlates with GNN performance more strongly and consistently than alternative metrics. 2NCS considers two-hop neighborhoods as a theoretically derived consequence of the two-step label propagation process governing GCN's training-inference process. Experiments on one synthetic and eight real-world graph datasets confirm consistent improvements over existing metrics in estimating the accuracy of GCN- and GAT-based architectures on the node classification task.