Modeling Heterophily in Multiplex Graphs: An Adaptive Approach for Node Classification

2026-05-12

AI Summary

This work addresses the limitations of existing complex graph neural networks for node classification, which often assume homophily and struggle to model the coexistence of homogeneous and heterogeneous relationships across different edge types. To overcome this, we propose an adaptive complex graph neural network that dynamically captures dimension-specific homophily and heterophily through learnable compatibility matrices combined with adaptive low-pass and high-pass graph filters. Our approach leverages Chebyshev polynomial approximation for efficient spectral filtering and employs proximal gradient optimization for training. Extensive experiments on both synthetic and real-world complex graphs demonstrate that the proposed model significantly outperforms state-of-the-art methods, achieving superior node classification performance by effectively modeling the intricate coupling of diverse relational patterns.

Abstract

Existing multiplex graph models often assume homophily, where connected nodes tend to belong to the same class or share similar attributes. Consequently, these models may struggle with graphs exhibiting heterophily, where connected nodes typically belong to different classes and have dissimilar attributes. While recent methods have been developed to learn reliable node representations from unidimensional graphs with heterophily, they do not fully address the complexities of multiplex graphs. In a multiplex graph, nodes are linked through multiple types of edges (referred to as dimensions), which can simultaneously exhibit homophilic and heterophilic interactions. To address this gap, we propose \methodname, a novel method for node classification in multiplex graphs that adapts to both homophilic and heterophilic dimensions. \methodname introduces dimension-specific compatibility matrices to model varying degrees of homophily and heterophily across dimensions. A key innovation is its use of a product of trainable low-pass and high-pass filters, approximated via Chebyshev polynomials, to capture both smooth and abrupt changes in the graph signal. By composing these filters and optimizing label predictions using a proximal-gradient method, \methodname dynamically adjusts to the heterophilic characteristics of each dimension. Extensive experiments on synthetic and real-world datasets provide evidence that \methodname captures the complex interplay of homophilic and heterophilic interactions in multiplex graphs, and tends to yield improved node classification performance compared to state-of-the-art methods.

Problem

• heterophily
• multiplex graphs
• node classification
• homophily
• graph representation

Innovation

• multiplex graphs
• heterophily
• adaptive filtering
• Chebyshev polynomials
• node classification