# Graph in Graph Neural Network

arXiv: https://arxiv.org/abs/2407.00696 · HTML: https://mlsanity.com/paper/2407.00696/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 68 of its 107 references that are in the map.
- First posted on arXiv 30 Jun 2024.

## Builds on (most cited first, 30 of 68)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [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)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Spatial Temporal Graph Convolutional Networks for Skeleton-Based Action Recognition](https://mlsanity.com/paper/1801.07455/) (2018)
- [LightGCN: Simplifying and Powering Graph Convolution Network for Recommendation](https://mlsanity.com/paper/2002.02126/) (2020)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks](https://mlsanity.com/paper/1810.02244/) (2018)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [How Attentive are Graph Attention Networks?](https://mlsanity.com/paper/2105.14491/) (2021)
- [Graph WaveNet for Deep Spatial-Temporal Graph Modeling](https://mlsanity.com/paper/1906.00121/) (2019)
- [Heterogeneous Graph Attention Network](https://mlsanity.com/paper/1903.07293/) (2019)
- [Recipe for a General, Powerful, Scalable Graph Transformer](https://mlsanity.com/paper/2205.12454/) (2022)
- [Benchmarking Graph Neural Networks](https://mlsanity.com/paper/2003.00982/) (2020)
- [Interaction Networks for Learning about Objects, Relations and Physics](https://mlsanity.com/paper/1612.00222/) (2016)
- [Principal Neighbourhood Aggregation for Graph Nets](https://mlsanity.com/paper/2004.05718/) (2020)
- [EvolveGCN: Evolving Graph Convolutional Networks for Dynamic Graphs](https://mlsanity.com/paper/1902.10191/) (2019)
- [Analyzing Learned Molecular Representations for Property Prediction](https://mlsanity.com/paper/1904.01561/) (2019)
- [Learning Multiagent Communication with Backpropagation](https://mlsanity.com/paper/1605.07736/) (2016)
- [Residual Gated Graph ConvNets](https://mlsanity.com/paper/1711.07553/) (2017)
- [Disentangling and Unifying Graph Convolutions for Skeleton-Based Action Recognition](https://mlsanity.com/paper/2003.14111/) (2020)
- [Channel-wise Topology Refinement Graph Convolution for Skeleton-Based Action Recognition](https://mlsanity.com/paper/2107.12213/) (2021)
- [Do Transformers Really Perform Bad for Graph Representation?](https://mlsanity.com/paper/2106.05234/) (2021)

## Abstract (arXiv)

Existing Graph Neural Networks (GNNs) are limited to process graphs each of whose vertices is represented by a vector or a single value, limited their representing capability to describe complex objects. In this paper, we propose the first GNN (called Graph in Graph Neural (GIG) Network) which can process graph-style data (called GIG sample) whose vertices are further represented by graphs. Given a set of graphs or a data sample whose components can be represented by a set of graphs (called multi-graph data sample), our GIG network starts with a GIG sample generation (GSG) module which encodes the input as a GIG sample, where each GIG vertex includes a graph. Then, a set of GIG hidden layers are stacked, with each consisting of: (1) a GIG vertex-level updating (GVU) module that individually updates the graph in every GIG vertex based on its internal information; and (2) a global-level GIG sample updating (GGU) module that updates graphs in all GIG vertices based on their relationships, making the updated GIG vertices become global context-aware. This way, both internal cues within the graph contained in each GIG vertex and the relationships among GIG vertices could be utilized for down-stream tasks. Experimental results demonstrate that our GIG network generalizes well for not only various generic graph analysis tasks but also real-world multi-graph data analysis (e.g., human skeleton video-based action recognition), which achieved the new state-of-the-art results on 13 out of 14 evaluated datasets. Our code is publicly available at https://github.com/wangjs96/Graph-in-Graph-Neural-Network.