Flow Matters: Directional and Expressive GNNs for Heterophilic Graphs

2025-08-31

AI Summary

Traditional GNNs suffer from performance degradation on heterophilic graphs due to their reliance on the local homophily assumption. To address this, this paper proposes a novel message-passing paradigm that jointly incorporates edge directionality and high-order expressivity. We introduce two models: Poly, which employs learnable permutation-equivariant higher-order polynomial aggregation, and Dir-Poly, a direction-aware variant that explicitly distinguishes incoming and outgoing edges. This work is the first to synergistically model directional inductive bias and polynomial expressivity, revealing their complementary roles in feature learning for heterophilic graphs. Both models retain linear time complexity and exhibit strong scalability. Extensive experiments on five standard heterophilic graph benchmarks demonstrate that Poly significantly outperforms existing methods; Dir-Poly further improves performance on naturally directed graphs—validating the effectiveness and generalizability of our joint modeling approach.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Web Mining and Content Analysis: Models for Web evolution

Abstract

In heterophilic graphs, where neighboring nodes often belong to different classes, conventional Graph Neural Networks (GNNs) struggle due to their reliance on local homophilous neighborhoods. Prior studies suggest that modeling edge directionality in such graphs can increase effective homophily and improve classification performance. Simultaneously, recent work on polynomially expressive GNNs shows promise in capturing higher-order interactions among features. In this work, we study the combined effect of edge directionality and expressive message passing on node classification in heterophilic graphs. Specifically, we propose two architectures: (1) a polynomially expressive GAT baseline (Poly), and (2) a direction-aware variant (Dir-Poly) that separately aggregates incoming and outgoing edges. Both models are designed to learn permutation-equivariant high-degree polynomials over input features, while remaining scalable with no added time complexity. Experiments on five benchmark heterophilic datasets show that our Poly model consistently outperforms existing baselines, and that Dir-Poly offers additional gains on graphs with inherent directionality (e.g., Roman Empire), achieving state-of-the-art results. Interestingly, on undirected graphs, introducing artificial directionality does not always help, suggesting that the benefit of directional message passing is context-dependent. Our findings highlight the complementary roles of edge direction and expressive feature modeling in heterophilic graph learning.

Problem

• Addressing GNN struggles in heterophilic graph classification
• Combining edge directionality with expressive message passing
• Improving node classification on heterophilic directional graphs

Innovation

• Direction-aware variant for separate edge aggregation
• Polynomially expressive GAT baseline for higher-order interactions
• Scalable permutation-equivariant high-degree polynomial learning