# Message Detouring: A Simple Yet Effective Cycle Representation for Expressive Graph Learning

arXiv: https://arxiv.org/abs/2402.08085 · HTML: https://mlsanity.com/paper/2402.08085/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 42 of its 68 references that are in the map.
- First posted on arXiv 12 Feb 2024.

## Builds on (most cited first, 30 of 42)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [Convolutional Networks on Graphs for Learning Molecular Fingerprints](https://mlsanity.com/paper/1509.09292/) (2015)
- [Junction Tree Variational Autoencoder for Molecular Graph Generation](https://mlsanity.com/paper/1802.04364/) (2018)
- [Multi-scale Attributed Node Embedding](https://mlsanity.com/paper/1909.13021/) (2019)
- [Graph Transformer Networks](https://mlsanity.com/paper/1911.06455/) (2019)
- [Provably Powerful Graph Networks](https://mlsanity.com/paper/1905.11136/) (2019)
- [Invariant and Equivariant Graph Networks](https://mlsanity.com/paper/1812.09902/) (2018)
- [Improving Graph Neural Network Expressivity via Subgraph Isomorphism Counting](https://mlsanity.com/paper/2006.09252/) (2020)
- [MAGNN: Metapath Aggregated Graph Neural Network for Heterogeneous Graph Embedding](https://mlsanity.com/paper/2002.01680/) (2020)
- [A Fair Comparison of Graph Neural Networks for Graph Classification](https://mlsanity.com/paper/1912.09893/) (2019)
- [Can Graph Neural Networks Count Substructures?](https://mlsanity.com/paper/2002.04025/) (2020)
- [Weisfeiler and Lehman Go Cellular: CW Networks](https://mlsanity.com/paper/2106.12575/) (2021)
- [The Surprising Power of Graph Neural Networks with Random Node Initialization](https://mlsanity.com/paper/2010.01179/) (2020)
- [Pure Transformers are Powerful Graph Learners](https://mlsanity.com/paper/2207.02505/) (2022)
- [From Stars to Subgraphs: Uplifting Any GNN with Local Structure Awareness](https://mlsanity.com/paper/2110.03753/) (2021)
- [Equivariant Subgraph Aggregation Networks](https://mlsanity.com/paper/2110.02910/) (2021)
- [Graph Inductive Biases in Transformers without Message Passing](https://mlsanity.com/paper/2305.17589/) (2023)
- [On the Universality of Invariant Networks](https://mlsanity.com/paper/1901.09342/) (2019)
- [Weisfeiler and Leman go Machine Learning: The Story so far](https://mlsanity.com/paper/2112.09992/) (2021)
- [Geometric Deep Learning on Molecular Representations](https://mlsanity.com/paper/2107.12375/) (2021)
- [Understanding and Extending Subgraph GNNs by Rethinking Their Symmetries](https://mlsanity.com/paper/2206.11140/) (2022)
- [Not too little, not too much: a theoretical analysis of graph (over)smoothing](https://mlsanity.com/paper/2205.12156/) (2022)
- [Breaking the Limits of Message Passing Graph Neural Networks](https://mlsanity.com/paper/2106.04319/) (2021)
- [Expressive Power of Invariant and Equivariant Graph Neural Networks](https://mlsanity.com/paper/2006.15646/) (2020)
- [Cognitive Graph for Multi-Hop Reading Comprehension at Scale](https://mlsanity.com/paper/1905.05460/) (2019)

## Abstract (arXiv)

Graph learning is crucial in the fields of bioinformatics, social networks, and chemicals. Although high-order graphlets, such as cycles, are critical to achieving an informative graph representation for node classification, edge prediction, and graph recognition, modeling high-order topological characteristics poses significant computational challenges, restricting its widespread applications in machine learning. To address this limitation, we introduce the concept of textitmessage detouring to hierarchically characterize cycle representation throughout the entire graph, which capitalizes on the contrast between the shortest and longest pathways within a range of local topologies associated with each graph node. The topological feature representations derived from our message detouring landscape demonstrate comparable expressive power to high-order textitWeisfeiler-Lehman (WL) tests but much less computational demands. In addition to the integration with graph kernel and message passing neural networks, we present a novel message detouring neural network, which uses Transformer backbone to integrate cycle representations across nodes and edges. Aside from theoretical results, experimental results on expressiveness, graph classification, and node classification show message detouring can significantly outperform current counterpart approaches on various benchmark datasets.