# D-HYPR: Harnessing Neighborhood Modeling and Asymmetry Preservation for Digraph Representation Learning

arXiv: https://arxiv.org/abs/2112.11734 · HTML: https://mlsanity.com/paper/2112.11734/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 45 of its 68 references that are in the map.
- First posted on arXiv 22 Dec 2021.

## Builds on (most cited first, 30 of 45)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [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)
- [Deep Graph Infomax](https://mlsanity.com/paper/1809.10341/) (2018)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Hyperbolic Neural Networks](https://mlsanity.com/paper/1805.09112/) (2018)
- [Hyperbolic Graph Convolutional Neural Networks](https://mlsanity.com/paper/1910.12933/) (2019)
- [Do Transformers Really Perform Bad for Graph Representation?](https://mlsanity.com/paper/2106.05234/) (2021)
- [SIGN: Scalable Inception Graph Neural Networks](https://mlsanity.com/paper/2004.11198/) (2020)
- [Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometry](https://mlsanity.com/paper/1806.03417/) (2018)
- [A Comprehensive Survey of Graph Embedding: Problems, Techniques and Applications](https://mlsanity.com/paper/1709.07604/) (2017)
- [Hyperbolic Graph Neural Networks](https://mlsanity.com/paper/1910.12892/) (2019)
- [Representation Tradeoffs for Hyperbolic Embeddings](https://mlsanity.com/paper/1804.03329/) (2018)
- [Low-Dimensional Hyperbolic Knowledge Graph Embeddings](https://mlsanity.com/paper/2005.00545/) (2020)
- [Hyperbolic Entailment Cones for Learning Hierarchical Embeddings](https://mlsanity.com/paper/1804.01882/) (2018)
- [A Survey on Graph Kernels](https://mlsanity.com/paper/1903.11835/) (2019)
- [Directional Graph Networks](https://mlsanity.com/paper/2010.02863/) (2020)
- [Constant Curvature Graph Convolutional Networks](https://mlsanity.com/paper/1911.05076/) (2019)

## Built on by (most cited first, 8 of 8)

- [DUPLEX: Dual GAT for Complex Embedding of Directed Graphs](https://mlsanity.com/paper/2406.05391/) (2024)
- [DiRW: Path-Aware Digraph Learning for Heterophily](https://mlsanity.com/paper/2410.10320/) (2024)
- [Towards Data-centric Machine Learning on Directed Graphs: a Survey](https://mlsanity.com/paper/2412.01849/) (2024)
- [Toward Effective Digraph Representation Learning: A Magnetic Adaptive Propagation based Approach](https://mlsanity.com/paper/2501.11817/) (2025)
- [Toward General Digraph Contrastive Learning: A Dual Spatial Perspective](https://mlsanity.com/paper/2510.16311/) (2025)
- [Rethinking Link Prediction for Directed Graphs](https://mlsanity.com/paper/2502.05724/) (2025)
- [Toward Data-centric Directed Graph Learning: An Entropy-driven Approach](https://mlsanity.com/paper/2505.00983/) (2025)
- [State Space Models over Directed Graphs](https://mlsanity.com/paper/2509.13735/) (2025)

## Abstract (arXiv)

Digraph Representation Learning (DRL) aims to learn representations for directed homogeneous graphs (digraphs). Prior work in DRL is largely constrained (e.g., limited to directed acyclic graphs), or has poor generalizability across tasks (e.g., evaluated solely on one task). Most Graph Neural Networks (GNNs) exhibit poor performance on digraphs due to the neglect of modeling neighborhoods and preserving asymmetry. In this paper, we address these notable challenges by leveraging hyperbolic collaborative learning from multi-ordered and partitioned neighborhoods, and regularizers inspired by socio-psychological factors. Our resulting formalism, Digraph Hyperbolic Networks (D-HYPR) - albeit conceptually simple - generalizes to digraphs where cycles and non-transitive relations are common, and is applicable to multiple downstream tasks including node classification, link presence prediction, and link property prediction. In order to assess the effectiveness of D-HYPR, extensive evaluations were performed across 8 real-world digraph datasets involving 21 prior techniques. D-HYPR statistically significantly outperforms the current state of the art. We release our code at https://github.com/hongluzhou/dhypr