# Robust Graph Neural Networks using Weighted Graph Laplacian

arXiv: https://arxiv.org/abs/2208.01853 · HTML: https://mlsanity.com/paper/2208.01853/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 36 references that are in the map.
- First posted on arXiv 3 Aug 2022.

## Builds on (most cited first, 26 of 26)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [GraphSAINT: Graph Sampling Based Inductive Learning Method](https://mlsanity.com/paper/1907.04931/) (2019)
- [Adversarial Attacks on Neural Networks for Graph Data](https://mlsanity.com/paper/1805.07984/) (2018)
- [Deep Learning on Graphs: A Survey](https://mlsanity.com/paper/1812.04202/) (2018)
- [Graph Structure Learning for Robust Graph Neural Networks](https://mlsanity.com/paper/2005.10203/) (2020)
- [Adversarial Attack on Graph Structured Data](https://mlsanity.com/paper/1806.02371/) (2018)
- [Adversarial Attacks on Graph Neural Networks via Meta Learning](https://mlsanity.com/paper/1902.08412/) (2019)
- [GNNGuard: Defending Graph Neural Networks against Adversarial Attacks](https://mlsanity.com/paper/2006.08149/) (2020)
- [Robustness of Graph Neural Networks at Scale](https://mlsanity.com/paper/2110.14038/) (2021)
- [Graph Adversarial Training: Dynamically Regularizing Based on Graph Structure](https://mlsanity.com/paper/1902.08226/) (2019)
- [DeepRobust: A PyTorch Library for Adversarial Attacks and Defenses](https://mlsanity.com/paper/2005.06149/) (2020)
- [Adversarial Attacks Against Medical Deep Learning Systems](https://mlsanity.com/paper/1804.05296/) (2018)
- [Transferring Robustness for Graph Neural Network Against Poisoning Attacks](https://mlsanity.com/paper/1908.07558/) (2019)
- [A Unified Framework for Structured Graph Learning via Spectral Constraints](https://mlsanity.com/paper/1904.09792/) (2019)
- [Graph Embedding on Biomedical Networks: Methods, Applications, and Evaluations](https://mlsanity.com/paper/1906.05017/) (2019)
- [Adversarial Attacks on Deep Models for Financial Transaction Records](https://mlsanity.com/paper/2106.08361/) (2021)
- [Estimation of positive definite M-matrices and structure learning for attractive Gaussian Markov Random fields](https://mlsanity.com/paper/1404.6640/) (2014)
- [GraphSAC: Detecting anomalies in large-scale graphs](https://mlsanity.com/paper/1910.09589/) (2019)
- [DefenseVGAE: Defending against Adversarial Attacks on Graph Data via a Variational Graph Autoencoder](https://mlsanity.com/paper/2006.08900/) (2020)
- [Adversarial Examples on Graph Data: Deep Insights into Attack and Defense](https://mlsanity.com/paper/1903.01610/) (2019)

## Built on by (most cited first, 4 of 4)

- [Adversarial Robustness in Graph Neural Networks: A Hamiltonian Approach](https://mlsanity.com/paper/2310.06396/) (2023)
- [A Unified Framework for Optimization-Based Graph Coarsening](https://mlsanity.com/paper/2210.00437/) (2022)
- [Heat Kernel Goes Topological](https://mlsanity.com/paper/2507.12380/) (2025)
- [DEGNN: Dual Experts Graph Neural Network Handling Both Edge and Node Feature Noise](https://mlsanity.com/paper/2404.09207/) (2024)

## Abstract (arXiv)

Graph neural network (GNN) is achieving remarkable performances in a variety of application domains. However, GNN is vulnerable to noise and adversarial attacks in input data. Making GNN robust against noises and adversarial attacks is an important problem. The existing defense methods for GNNs are computationally demanding and are not scalable. In this paper, we propose a generic framework for robustifying GNN known as Weighted Laplacian GNN (RWL-GNN). The method combines Weighted Graph Laplacian learning with the GNN implementation. The proposed method benefits from the positive semi-definiteness property of Laplacian matrix, feature smoothness, and latent features via formulating a unified optimization framework, which ensures the adversarial/noisy edges are discarded and connections in the graph are appropriately weighted. For demonstration, the experiments are conducted with Graph convolutional neural network(GCNN) architecture, however, the proposed framework is easily amenable to any existing GNN architecture. The simulation results with benchmark dataset establish the efficacy of the proposed method, both in accuracy and computational efficiency. Code can be accessed at https://github.com/Bharat-Runwal/RWL-GNN.