# Motif Graph Neural Network

arXiv: https://arxiv.org/abs/2112.14900 · HTML: https://mlsanity.com/paper/2112.14900/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 106 references that are in the map.
- First posted on arXiv 30 Dec 2021.

## Builds on (most cited first, 30 of 40)

- [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)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Graph Contrastive Learning with Augmentations](https://mlsanity.com/paper/2010.13902/) (2020)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks](https://mlsanity.com/paper/1810.02244/) (2018)
- [Gated Graph Sequence Neural Networks](https://mlsanity.com/paper/1511.05493/) (2015)
- [Hierarchical Graph Representation Learning with Differentiable Pooling](https://mlsanity.com/paper/1806.08804/) (2018)
- [Graph Neural Networks for Social Recommendation](https://mlsanity.com/paper/1902.07243/) (2019)
- [FastGCN: Fast Learning with Graph Convolutional Networks via Importance Sampling](https://mlsanity.com/paper/1801.10247/) (2018)
- [Graph U-Nets](https://mlsanity.com/paper/1905.05178/) (2019)
- [MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixing](https://mlsanity.com/paper/1905.00067/) (2019)
- [Diffusion Improves Graph Learning](https://mlsanity.com/paper/1911.05485/) (2019)
- [Provably Powerful Graph Networks](https://mlsanity.com/paper/1905.11136/) (2019)
- [Order Matters: Sequence to sequence for sets](https://mlsanity.com/paper/1511.06391/) (2015)
- [graph2vec: Learning Distributed Representations of Graphs](https://mlsanity.com/paper/1707.05005/) (2017)
- [ASAP: Adaptive Structure Aware Pooling for Learning Hierarchical Graph Representations](https://mlsanity.com/paper/1911.07979/) (2019)
- [Characteristic Functions on Graphs: Birds of a Feather, from Statistical Descriptors to Parametric Models](https://mlsanity.com/paper/2005.07959/) (2020)
- [Higher-order organization of complex networks](https://mlsanity.com/paper/1612.08447/) (2016)
- [MotifNet: a motif-based Graph Convolutional Network for directed graphs](https://mlsanity.com/paper/1802.01572/) (2018)
- [NetLSD: Hearing the Shape of a Graph](https://mlsanity.com/paper/1805.10712/) (2018)
- [Boost then Convolve: Gradient Boosting Meets Graph Neural Networks](https://mlsanity.com/paper/2101.08543/) (2021)
- [Bilinear Graph Networks for Visual Question Answering](https://mlsanity.com/paper/1907.09815/) (2019)

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

- [Gegenbauer Graph Neural Networks for Time-varying Signal Reconstruction](https://mlsanity.com/paper/2403.19800/) (2024)
- [ATM-GAD: Adaptive Temporal Motif Graph Anomaly Detection for Financial Transaction Networks](https://mlsanity.com/paper/2508.20829/) (2025)
- [MotifDisco: Motif Causal Discovery For Time Series Motifs](https://mlsanity.com/paper/2409.15219/) (2024)
- [Interpretable High-order Knowledge Graph Neural Network for Predicting Synthetic Lethality in Human Cancers](https://mlsanity.com/paper/2503.06052/) (2025)
- [Disentangled Graph Representation Based on Substructure-Aware Graph Optimal Matching Kernel Convolutional Networks](https://mlsanity.com/paper/2504.16360/) (2025)
- [Node Classification via Simplicial Interaction with Augmented Maximal Clique Selection](https://mlsanity.com/paper/2509.23568/) (2025)
- [Adaptive Node Feature Selection For Graph Neural Networks](https://mlsanity.com/paper/2510.03096/) (2025)
- [Temporal Motif Signatures for Temporal Graph Neural Networks](https://mlsanity.com/paper/2606.01176/) (2026)
- [Motif-Mamba: network motif improved mamba for long-range sequence modeling](https://mlsanity.com/paper/2608.00027/) (2026)
- [Polarity-Asymmetric Structural Calibration for Link Sign Prediction](https://mlsanity.com/paper/2609.05896/) (2026)

## Abstract (arXiv)

Graphs can model complicated interactions between entities, which naturally emerge in many important applications. These applications can often be cast into standard graph learning tasks, in which a crucial step is to learn low-dimensional graph representations. Graph neural networks (GNNs) are currently the most popular model in graph embedding approaches. However, standard GNNs in the neighborhood aggregation paradigm suffer from limited discriminative power in distinguishing high-order graph structures as opposed to low-order structures. To capture high-order structures, researchers have resorted to motifs and developed motif-based GNNs. However, existing motif-based GNNs still often suffer from less discriminative power on high-order structures. To overcome the above limitations, we propose Motif Graph Neural Network (MGNN), a novel framework to better capture high-order structures, hinging on our proposed motif redundancy minimization operator and injective motif combination. First, MGNN produces a set of node representations w.r.t. each motif. The next phase is our proposed redundancy minimization among motifs which compares the motifs with each other and distills the features unique to each motif. Finally, MGNN performs the updating of node representations by combining multiple representations from different motifs. In particular, to enhance the discriminative power, MGNN utilizes an injective function to combine the representations w.r.t. different motifs. We further show that our proposed architecture increases the expressive power of GNNs with a theoretical analysis. We demonstrate that MGNN outperforms state-of-the-art methods on seven public benchmarks on both node classification and graph classification tasks.