Directed Homophily-Aware Graph Neural Network

TL;DR

DHGNN tackles the challenges of heterophily and directionality in graphs by employing two independently trained encoders for forward and backward directions, a resettable homophily-aware gating mechanism, and a structure-aware noise-tolerant fusion that adaptively integrates directional embeddings. The model introduces auxiliary losses to maintain balance and disentanglement between branches, enabling robust learning across varying hop-level homophily. Empirical results on five datasets show DHGNN achieving state-of-the-art performance for node classification and link prediction, with interpretable gating behavior that reveals directional homophily gaps and non-monotonic layer-wise dynamics. The work advances directed-graph learning by effectively harnessing long-range and direction-specific signals, with potential for broader domain applicability and scalable deployment.

Abstract

Graph Neural Networks (GNNs) have achieved significant success in various learning tasks on graph-structured data. Nevertheless, most GNNs struggle to generalize to heterophilic neighborhoods. Additionally, many GNNs ignore the directional nature of real-world graphs, resulting in suboptimal performance on directed graphs with asymmetric structures. In this work, we propose Directed Homophily-aware Graph Neural Network (DHGNN), a novel framework that addresses these limitations by incorporating homophily-aware and direction-sensitive components. DHGNN employs a resettable gating mechanism to adaptively modulate message contributions based on homophily levels and informativeness, and a structure-aware noise-tolerant fusion module to effectively integrate node representations from the original and reverse directions. Extensive experiments on both homophilic and heterophilic directed graph datasets demonstrate that DHGNN outperforms state-of-the-art methods in node classification and link prediction. In particular, DHGNN improves over the best baseline by up to 15.07\% in link prediction. Our analysis further shows that the gating mechanism captures directional homophily gaps and fluctuating homophily across layers, providing deeper insights into message-passing behavior on complex graph structures.

Figures (8)

• Figure 1: The average node-wise homophily ratio in different hops. Forward denotes the direction in which the graph is constructed while backward denotes the reverse direction. The line chart reveals (a) the homophily ratio does not consistently decrease with increasing distance, and (b) the homophily levels of forward and backward neighbors can be different. We further explore this phenomenon with an example in \ref{['app:homoanalysis']}.
• Figure 2: Class connection matrices of the directed and undirected versions of the same graph. The matrices tend to be asymmetric for heterophilic graphs, such as Chameleon. Converting this graph from directed to undirected could eliminate the asymmetry between the edge ratios from class 1 to class 0 and from class 0 to class 1, while the two ratios differ significantly in the original directed graph.
• Figure 3: The framework of DHGNN. "SA Gates" is short for the structure-aware noise-tolerant gates. The model consists of two message-passing modules (one for each edge direction) and a fusion module. Node representations are learned independently for the forward and backward directions, and subsequently fused into a unified representation.
• Figure 4: The gating values of the first five layers on heterophilic and homophilic datasets. The dots on line charts are the mean value over both nodes and chunks, while the box-plots present the distribution of mean gating values over chunks.
• Figure 5: The node classification accuracy and behavior of gating values at deeper layers.

Theorems & Definitions (4)

• Lemma 1: Expected neighbor average
• Theorem 1: Gate Non-Monotonicity
• proof
• Lemma 2: Reset Gate Bounds