[Paper Review] RAW-GNN: RAndom Walk Aggregation based Graph Neural Network

Di Jin, Rui Wang+5 more|arXiv (Cornell University)|Jun 28, 2022

Advanced Graph Neural Networks8 citations

TL;DR

This paper proposes RAW-GNN, a novel Graph Neural Network that uses breadth-first and depth-first random walks to create path-based neighborhoods, replacing traditional neighborhood aggregation. By employing an RNN-based aggregator and attention mechanism to combine homophily (BFS) and heterophily (DFS) signals, RAW-GNN achieves state-of-the-art performance on both homophily and heterophily graphs, outperforming existing methods by up to 10.35% on heterophily datasets.

ABSTRACT

Graph-Convolution-based methods have been successfully applied to representation learning on homophily graphs where nodes with the same label or similar attributes tend to connect with one another. Due to the homophily assumption of Graph Convolutional Networks (GCNs) that these methods use, they are not suitable for heterophily graphs where nodes with different labels or dissimilar attributes tend to be adjacent. Several methods have attempted to address this heterophily problem, but they do not change the fundamental aggregation mechanism of GCNs because they rely on summation operators to aggregate information from neighboring nodes, which is implicitly subject to the homophily assumption. Here, we introduce a novel aggregation mechanism and develop a RAndom Walk Aggregation-based Graph Neural Network (called RAW-GNN) method. The proposed approach integrates the random walk strategy with graph neural networks. The new method utilizes breadth-first random walk search to capture homophily information and depth-first search to collect heterophily information. It replaces the conventional neighborhoods with path-based neighborhoods and introduces a new path-based aggregator based on Recurrent Neural Networks. These designs make RAW-GNN suitable for both homophily and heterophily graphs. Extensive experimental results showed that the new method achieved state-of-the-art performance on a variety of homophily and heterophily graphs.

Motivation & Objective

• To address the limitation of GCNs in heterophily graphs, where nodes with different labels are connected.
• To overcome the implicit homophily bias in standard GCN aggregation mechanisms based on summation operators.
• To develop a unified GNN framework that effectively captures both homophily and heterophily patterns in a single model.
• To improve node classification performance on diverse real-world graphs, including those with low or no homophily.

Proposed method

• The method introduces path-based neighborhoods generated via breadth-first search (BFS) for homophily and depth-first search (DFS) for heterophily.
• It replaces standard neighborhood aggregation with an RNN-based sequential encoder to model ordered neighbor features along random walk paths.
• The model uses an attention mechanism to fuse embeddings from BFS and DFS channels, enabling adaptive trade-off between homophily and heterophily signals.
• Node representations are formed by concatenating strategy-specific embeddings, preventing information mixing and preserving distinct structural patterns.
• The framework is trained end-to-end using cross-entropy loss for node classification tasks.

Experimental results

Research questions

• RQ1 Can a GNN framework effectively handle both homophily and heterophily graphs without relying on label-guided or distance-based aggregation?
• RQ2 Does using random walk-based path neighborhoods improve representation learning on heterophily-dominant graphs?
• RQ3 Can an RNN-based aggregator better model sequential neighbor features than standard summation or attention-based aggregators?
• RQ4 How does the attention-based fusion of BFS and DFS channels affect model performance across different graph types?

Key findings

• RAW-GNN achieves state-of-the-art performance on five out of seven real-world datasets, including all four heterophily-dominant networks: Texas, Wisconsin, Cornell, and Actor.
• On the Actor dataset, RAW-GNN improves accuracy by 10.35% over the second-best method, demonstrating strong superiority in heterophily settings.
• On the Cora dataset, RAW-GNN achieves the highest accuracy (84.86%) among all baselines, outperforming GCN and GraphSAGE by 1.32% and 0.87% respectively.
• Visualization on Cora shows that RAW-GNN produces the clearest class boundaries in t-SNE projections, with minimal class mixing.
• For datasets with low feature homophily ratio (F.H.R < 0.2), the optimal path length is longer, indicating that larger receptive fields are needed to capture hidden neighborhood structures in heterophily graphs.