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

arXiv: https://arxiv.org/abs/2605.12699 · HTML: https://mlsanity.com/paper/2605.12699/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 30 of its 46 references that are in the map.
- First posted on arXiv 12 May 2026.

## Builds on (most cited first, 30 of 30)

- [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)
- [Learning deep representations by mutual information estimation and maximization](https://mlsanity.com/paper/1808.06670/) (2018)
- [Adaptive Universal Generalized PageRank Graph Neural Network](https://mlsanity.com/paper/2006.07988/) (2020)
- [Ups and Downs: Modeling the Visual Evolution of Fashion Trends with One-Class Collaborative Filtering](https://mlsanity.com/paper/1602.01585/) (2016)
- [MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixing](https://mlsanity.com/paper/1905.00067/) (2019)
- [Large Scale Learning on Non-Homophilous Graphs: New Benchmarks and Strong Simple Methods](https://mlsanity.com/paper/2110.14446/) (2021)
- [Graph Neural Networks with Heterophily](https://mlsanity.com/paper/2009.13566/) (2020)
- [Graph Neural Networks for Graphs with Heterophily: A Survey](https://mlsanity.com/paper/2202.07082/) (2022)
- [How Powerful are Spectral Graph Neural Networks](https://mlsanity.com/paper/2205.11172/) (2022)
- [Revisiting Heterophily For Graph Neural Networks](https://mlsanity.com/paper/2210.07606/) (2022)
- [Unsupervised Attributed Multiplex Network Embedding](https://mlsanity.com/paper/1911.06750/) (2019)
- [Representation Learning for Attributed Multiplex Heterogeneous Network](https://mlsanity.com/paper/1905.01669/) (2019)
- [Convolutional Neural Networks on Graphs with Chebyshev Approximation, Revisited](https://mlsanity.com/paper/2202.03580/) (2022)
- [HDMI: High-order Deep Multiplex Infomax](https://mlsanity.com/paper/2102.07810/) (2021)
- [Beyond Smoothing: Unsupervised Graph Representation Learning with Edge Heterophily Discriminating](https://mlsanity.com/paper/2211.14065/) (2022)
- [Rethinking Graph Auto-Encoder Models for Attributed Graph Clustering](https://mlsanity.com/paper/2107.08562/) (2021)
- [Beyond Homophily: Reconstructing Structure for Graph-agnostic Clustering](https://mlsanity.com/paper/2305.02931/) (2023)
- [Multi-Graph Convolution Collaborative Filtering](https://mlsanity.com/paper/2001.00267/) (2020)
- [X-GOAL: Multiplex Heterogeneous Graph Prototypical Contrastive Learning](https://mlsanity.com/paper/2109.03560/) (2021)
- [Breaking the Entanglement of Homophily and Heterophily in Semi-supervised Node Classification](https://mlsanity.com/paper/2312.04111/) (2023)
- [Multi-dimensional Graph Convolutional Networks](https://mlsanity.com/paper/1808.06099/) (2018)
- [Beyond Redundancy: Information-aware Unsupervised Multiplex Graph Structure Learning](https://mlsanity.com/paper/2409.17386/) (2024)
- [MultiVERSE: a multiplex and multiplex-heterogeneous network embedding approach](https://mlsanity.com/paper/2008.10085/) (2020)
- [Unsupervised Network Embedding Beyond Homophily](https://mlsanity.com/paper/2203.10866/) (2022)
- [Semi-Supervised Deep Learning for Multiplex Networks](https://mlsanity.com/paper/2110.02038/) (2021)
- [A Contrastive Variational Graph Auto-Encoder for Node Clustering](https://mlsanity.com/paper/2312.16830/) (2023)
- [The new challenges of multiplex networks: measures and models](https://mlsanity.com/paper/1606.09221/) (2016)
- [Hierarchical Aggregations for High-Dimensional Multiplex Graph Embedding](https://mlsanity.com/paper/2312.16834/) (2023)
- [A Geometric Perspective for High-Dimensional Multiplex Graphs](https://mlsanity.com/paper/2501.17374/) (2025)

## Abstract (arXiv)

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.