# On Local Aggregation in Heterophilic Graphs

arXiv: https://arxiv.org/abs/2106.03213 · HTML: https://mlsanity.com/paper/2106.03213/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 31 references that are in the map.
- First posted on arXiv 6 Jun 2021.

## Builds on (most cited first, 25 of 25)

- [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)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Link Prediction Based on Graph Neural Networks](https://mlsanity.com/paper/1802.09691/) (2018)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [MINE: Mutual Information Neural Estimation](https://mlsanity.com/paper/1801.04062/) (2018)
- [Measuring and Relieving the Over-smoothing Problem for Graph Neural Networks from the Topological View](https://mlsanity.com/paper/1909.03211/) (2019)
- [Masked Label Prediction: Unified Message Passing Model for Semi-Supervised Classification](https://mlsanity.com/paper/2009.03509/) (2020)
- [Principal Neighbourhood Aggregation for Graph Nets](https://mlsanity.com/paper/2004.05718/) (2020)
- [MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixing](https://mlsanity.com/paper/1905.00067/) (2019)
- [On Mutual Information Maximization for Representation Learning](https://mlsanity.com/paper/1907.13625/) (2019)
- [Dynamic Edge-Conditioned Filters in Convolutional Neural Networks on Graphs](https://mlsanity.com/paper/1704.02901/) (2017)
- [DeeperGCN: All You Need to Train Deeper GCNs](https://mlsanity.com/paper/2006.07739/) (2020)
- [Graph Matching Networks for Learning the Similarity of Graph Structured Objects](https://mlsanity.com/paper/1904.12787/) (2019)
- [Non-Local Graph Neural Networks](https://mlsanity.com/paper/2005.14612/) (2020)
- [Estimating Mixture Entropy with Pairwise Distances](https://mlsanity.com/paper/1706.02419/) (2017)
- [Permutohedral-GCN: Graph Convolutional Networks with Global Attention](https://mlsanity.com/paper/2003.00635/) (2020)
- [Visibility of minorities in social networks](https://mlsanity.com/paper/1702.00150/) (2017)

## Built on by (most cited first, 3 of 3)

- [Taxonomy of Benchmarks in Graph Representation Learning](https://mlsanity.com/paper/2206.07729/) (2022)
- [Heterophilic Graph Neural Networks Optimization with Causal Message-passing](https://mlsanity.com/paper/2411.13821/) (2024)
- [Towards a Taxonomy of Graph Learning Datasets](https://mlsanity.com/paper/2110.14809/) (2021)

## Abstract (arXiv)

Many recent works have studied the performance of Graph Neural Networks (GNNs) in the context of graph homophily - a label-dependent measure of connectivity. Traditional GNNs generate node embeddings by aggregating information from a node's neighbors in the graph. Recent results in node classification tasks show that this local aggregation approach performs poorly in graphs with low homophily (heterophilic graphs). Several mechanisms have been proposed to improve the accuracy of GNNs on such graphs by increasing the aggregation range of a GNN layer, either through multi-hop aggregation, or through long-range aggregation from distant nodes. In this paper, we show that properly tuned classical GNNs and multi-layer perceptrons match or exceed the accuracy of recent long-range aggregation methods on heterophilic graphs. Thus, our results highlight the need for alternative datasets to benchmark long-range GNN aggregation mechanisms. We also show that homophily is a poor measure of the information in a node's local neighborhood and propose the Neighborhood Information Content(NIC) metric, which is a novel information-theoretic graph metric. We argue that NIC is more relevant for local aggregation methods as used by GNNs. We show that, empirically, it correlates better with GNN accuracy in node classification tasks than homophily.