# MotifNet: a motif-based Graph Convolutional Network for directed graphs

arXiv: https://arxiv.org/abs/1802.01572 · HTML: https://mlsanity.com/paper/1802.01572/

## Key facts

- Cited by 64 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Feb 2018.

## Built on by (most cited first, 30 of 64)

- [Understanding over-squashing and bottlenecks on graphs via curvature](https://mlsanity.com/paper/2111.14522/) (2021)
- [From Stars to Subgraphs: Uplifting Any GNN with Local Structure Awareness](https://mlsanity.com/paper/2110.03753/) (2021)
- [MagNet: A Neural Network for Directed Graphs](https://mlsanity.com/paper/2102.11391/) (2021)
- [Edge Directionality Improves Learning on Heterophilic Graphs](https://mlsanity.com/paper/2305.10498/) (2023)
- [SUGAR: Subgraph Neural Network with Reinforcement Pooling and Self-Supervised Mutual Information Mechanism](https://mlsanity.com/paper/2101.08170/) (2021)
- [Theory of Graph Neural Networks: Representation and Learning](https://mlsanity.com/paper/2204.07697/) (2022)
- [Property-Aware Relation Networks for Few-Shot Molecular Property Prediction](https://mlsanity.com/paper/2107.07994/) (2021)
- [PaSca: a Graph Neural Architecture Search System under the Scalable Paradigm](https://mlsanity.com/paper/2203.00638/) (2022)
- [MSGNN: A Spectral Graph Neural Network Based on a Novel Magnetic Signed Laplacian](https://mlsanity.com/paper/2209.00546/) (2022)
- [Topological Relational Learning on Graphs](https://mlsanity.com/paper/2110.15529/) (2021)
- [TempME: Towards the Explainability of Temporal Graph Neural Networks via Motif Discovery](https://mlsanity.com/paper/2310.19324/) (2023)
- [From Continuous Dynamics to Graph Neural Networks: Neural Diffusion and Beyond](https://mlsanity.com/paper/2310.10121/) (2023)
- [ACE-HGNN: Adaptive Curvature Exploration Hyperbolic Graph Neural Network](https://mlsanity.com/paper/2110.07888/) (2021)
- [Make Heterophily Graphs Better Fit GNN: A Graph Rewiring Approach](https://mlsanity.com/paper/2209.08264/) (2022)
- [Transformers over Directed Acyclic Graphs](https://mlsanity.com/paper/2210.13148/) (2022)
- [Directed Graph Auto-Encoders](https://mlsanity.com/paper/2202.12449/) (2022)
- [Geodesic Graph Neural Network for Efficient Graph Representation Learning](https://mlsanity.com/paper/2210.02636/) (2022)
- [On Structural Expressive Power of Graph Transformers](https://mlsanity.com/paper/2305.13987/) (2023)
- [Hypergraph Convolutional Networks via Equivalency between Hypergraphs and Undirected Graphs](https://mlsanity.com/paper/2203.16939/) (2022)
- [DIGRAC: Digraph Clustering Based on Flow Imbalance](https://mlsanity.com/paper/2106.05194/) (2021)
- [Learning to Count Isomorphisms with Graph Neural Networks](https://mlsanity.com/paper/2302.03266/) (2023)
- [An Explainer for Temporal Graph Neural Networks](https://mlsanity.com/paper/2209.00807/) (2022)
- [NAFS: A Simple yet Tough-to-beat Baseline for Graph Representation Learning](https://mlsanity.com/paper/2206.08583/) (2022)
- [MM-GNN: Mix-Moment Graph Neural Network towards Modeling Neighborhood Feature Distribution](https://mlsanity.com/paper/2208.07012/) (2022)
- [Toward Robust Graph Semi-Supervised Learning against Extreme Data Scarcity](https://mlsanity.com/paper/2208.12422/) (2022)
- [A Magnetic Framelet-Based Convolutional Neural Network for Directed Graphs](https://mlsanity.com/paper/2210.10993/) (2022)
- [MAG-GNN: Reinforcement Learning Boosted Graph Neural Network](https://mlsanity.com/paper/2310.19142/) (2023)
- [Motif Graph Neural Network](https://mlsanity.com/paper/2112.14900/) (2021)
- [Graph Neural Networks in Vision-Language Image Understanding: A Survey](https://mlsanity.com/paper/2303.03761/) (2023)
- [Graph Neural Networks based Log Anomaly Detection and Explanation](https://mlsanity.com/paper/2307.00527/) (2023)

## Abstract (arXiv)

Deep learning on graphs and in particular, graph convolutional neural networks, have recently attracted significant attention in the machine learning community. Many of such techniques explore the analogy between the graph Laplacian eigenvectors and the classical Fourier basis, allowing to formulate the convolution as a multiplication in the spectral domain. One of the key drawback of spectral CNNs is their explicit assumption of an undirected graph, leading to a symmetric Laplacian matrix with orthogonal eigendecomposition. In this work we propose MotifNet, a graph CNN capable of dealing with directed graphs by exploiting local graph motifs. We present experimental evidence showing the advantage of our approach on real data.