# Tensor Graph Convolutional Networks for Multi-relational and Robust Learning

arXiv: https://arxiv.org/abs/2003.07729 · HTML: https://mlsanity.com/paper/2003.07729/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Mar 2020.

## Built on by (most cited first, 9 of 9)

- [A Review of Graph Neural Networks and Their Applications in Power Systems](https://mlsanity.com/paper/2101.10025/) (2021)
- [Are Defenses for Graph Neural Networks Robust?](https://mlsanity.com/paper/2301.13694/) (2023)
- [Multiplex Graph Networks for Multimodal Brain Network Analysis](https://mlsanity.com/paper/2108.00158/) (2021)
- [Adapting to Heterophilic Graph Data with Structure-Guided Neighbor Discovery](https://mlsanity.com/paper/2506.08871/) (2025)
- [ScatterSample: Diversified Label Sampling for Data Efficient Graph Neural Network Learning](https://mlsanity.com/paper/2206.04255/) (2022)
- [Understanding the Robustness of Graph Neural Networks against Adversarial Attacks](https://mlsanity.com/paper/2406.13920/) (2024)
- [Explainable Spatio-Temporal GCNNs for Irregular Multivariate Time Series: Architecture and Application to ICU Patient Data](https://mlsanity.com/paper/2411.01070/) (2024)
- [MPXGAT: An Attention based Deep Learning Model for Multiplex Graphs Embedding](https://mlsanity.com/paper/2403.19246/) (2024)
- [Adversarial Graph Neural Network Benchmarks: Towards Practical and Fair Evaluation](https://mlsanity.com/paper/2605.05534/) (2026)

## Abstract (arXiv)

The era of "data deluge" has sparked renewed interest in graph-based learning methods and their widespread applications ranging from sociology and biology to transportation and communications. In this context of graph-aware methods, the present paper introduces a tensor-graph convolutional network (TGCN) for scalable semi-supervised learning (SSL) from data associated with a collection of graphs, that are represented by a tensor. Key aspects of the novel TGCN architecture are the dynamic adaptation to different relations in the tensor graph via learnable weights, and the consideration of graph-based regularizers to promote smoothness and alleviate over-parameterization. The ultimate goal is to design a powerful learning architecture able to: discover complex and highly nonlinear data associations, combine (and select) multiple types of relations, scale gracefully with the graph size, and remain robust to perturbations on the graph edges. The proposed architecture is relevant not only in applications where the nodes are naturally involved in different relations (e.g., a multi-relational graph capturing family, friendship and work relations in a social network), but also in robust learning setups where the graph entails a certain level of uncertainty, and the different tensor slabs correspond to different versions (realizations) of the nominal graph. Numerical tests showcase that the proposed architecture achieves markedly improved performance relative to standard GCNs, copes with state-of-the-art adversarial attacks, and leads to remarkable SSL performance over protein-to-protein interaction networks.