# Convolutional Learning on Multigraphs

arXiv: https://arxiv.org/abs/2209.11354 · HTML: https://mlsanity.com/paper/2209.11354/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 77 references that are in the map.
- First posted on arXiv 23 Sep 2022.

## Builds on (most cited first, 24 of 24)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [MAGNN: Metapath Aggregated Graph Neural Network for Heterogeneous Graph Embedding](https://mlsanity.com/paper/2002.01680/) (2020)
- [A Note on Over-Smoothing for Graph Neural Networks](https://mlsanity.com/paper/2006.13318/) (2020)
- [Stability Properties of Graph Neural Networks](https://mlsanity.com/paper/1905.04497/) (2019)
- [Convolutional Neural Network Architectures for Signals Supported on Graphs](https://mlsanity.com/paper/1805.00165/) (2018)
- [Representation Learning for Attributed Multiplex Heterogeneous Network](https://mlsanity.com/paper/1905.01669/) (2019)
- [Optimal Wireless Resource Allocation with Random Edge Graph Neural Networks](https://mlsanity.com/paper/1909.01865/) (2019)
- [Towards Optimal Power Control via Ensembling Deep Neural Networks](https://mlsanity.com/paper/1807.10025/) (2018)
- [Graphon Signal Processing](https://mlsanity.com/paper/2003.05030/) (2020)
- [Abstract Diagrammatic Reasoning with Multiplex Graph Networks](https://mlsanity.com/paper/2006.11197/) (2020)
- [Discrete Signal Processing on Graphs: Sampling Theory](https://mlsanity.com/paper/1503.05432/) (2015)
- [An Attention-based Collaboration Framework for Multi-View Network Representation Learning](https://mlsanity.com/paper/1709.06636/) (2017)
- [Multiplex Heterogeneous Graph Convolutional Network](https://mlsanity.com/paper/2208.06129/) (2022)
- [Algebraic Neural Networks: Stability to Deformations](https://mlsanity.com/paper/2009.01433/) (2020)
- [Hate is the New Infodemic: A Topic-aware Modeling of Hate Speech Diffusion on Twitter](https://mlsanity.com/paper/2010.04377/) (2020)
- [Joint predictions of multi-modal ride-hailing demands: a deep multi-task multigraph learning-based approach](https://mlsanity.com/paper/2011.05602/) (2020)
- [Convolutional Filtering and Neural Networks with Non Commutative Algebras](https://mlsanity.com/paper/2108.09923/) (2021)
- [Eigenvector centrality of nodes in multiplex networks](https://mlsanity.com/paper/1305.7445/) (2013)
- [Retweet communities reveal the main sources of hate speech](https://mlsanity.com/paper/2105.14898/) (2021)
- [Multiplex PageRank](https://mlsanity.com/paper/1306.3576/) (2013)
- [Parallel Multi-Graph Convolution Network For Metro Passenger Volume Prediction](https://mlsanity.com/paper/2109.00924/) (2021)
- [Extracting the multimodal fingerprint of urban transportation networks](https://mlsanity.com/paper/2006.03435/) (2020)

## Built on by (most cited first, 10 of 10)

- [Learning with Multigraph Convolutional Filters](https://mlsanity.com/paper/2210.16272/) (2022)
- [PowerFlowMultiNet: Multigraph Neural Networks for Unbalanced Three-Phase Distribution Systems](https://mlsanity.com/paper/2403.00892/) (2024)
- [Convolutional Filtering with RKHS Algebras](https://mlsanity.com/paper/2411.01341/) (2024)
- [What Can We Learn From MIMO Graph Convolutions?](https://mlsanity.com/paper/2505.11346/) (2025)
- [Modality as Heterogeneity: Node Splitting and Graph Rewiring for Multimodal Graph Learning](https://mlsanity.com/paper/2602.00067/) (2026)
- [RKHS Representation of Algebraic Convolutional Filters with Integral Operators](https://mlsanity.com/paper/2602.19094/) (2026)
- [Non Commutative Convolutional Signal Models in Neural Networks: Stability to Small Deformations](https://mlsanity.com/paper/2310.03879/) (2023)
- [HSG-12M: A Large-Scale Benchmark of Spatial Multigraphs from the Energy Spectra of Non-Hermitian Crystals](https://mlsanity.com/paper/2506.08618/) (2025)
- [Multi-view diffusion geometry using intertwined diffusion trajectories](https://mlsanity.com/paper/2512.01484/) (2025)
- [Fundamental Limits of Transferability and Equivariance in Algebraic Signal Models I: Finite Dimensions](https://mlsanity.com/paper/2609.36106/) (2026)

## Abstract (arXiv)

Graph convolutional learning has led to many exciting discoveries in diverse areas. However, in some applications, traditional graphs are insufficient to capture the structure and intricacies of the data. In such scenarios, multigraphs arise naturally as discrete structures in which complex dynamics can be embedded. In this paper, we develop convolutional information processing on multigraphs and introduce convolutional multigraph neural networks (MGNNs). To capture the complex dynamics of information diffusion within and across each of the multigraph's classes of edges, we formalize a convolutional signal processing model, defining the notions of signals, filtering, and frequency representations on multigraphs. Leveraging this model, we develop a multigraph learning architecture, including a sampling procedure to reduce computational complexity. The introduced architecture is applied towards optimal wireless resource allocation and a hate speech localization task, offering improved performance over traditional graph neural networks.