# Signal Processing on Directed Graphs

arXiv: https://arxiv.org/abs/2008.00586 · HTML: https://mlsanity.com/paper/2008.00586/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Aug 2020.

## Built on by (most cited first, 28 of 28)

- [MagNet: A Neural Network for Directed Graphs](https://mlsanity.com/paper/2102.11391/) (2021)
- [Signal Processing on Higher-Order Networks: Livin' on the Edge ... and Beyond](https://mlsanity.com/paper/2101.05510/) (2021)
- [Transformers Meet Directed Graphs](https://mlsanity.com/paper/2302.00049/) (2023)
- [Bridging the Gap between Spatial and Spectral Domains: A Unified Framework for Graph Neural Networks](https://mlsanity.com/paper/2107.10234/) (2021)
- [PyTorch Geometric Signed Directed: A Software Package on Graph Neural Networks for Signed and Directed Graphs](https://mlsanity.com/paper/2202.10793/) (2022)
- [Accelerated Graph Learning from Smooth Signals](https://mlsanity.com/paper/2110.09677/) (2021)
- [Untrained Graph Neural Networks for Denoising](https://mlsanity.com/paper/2109.11700/) (2021)
- [Signal processing on simplicial complexes](https://mlsanity.com/paper/2106.07471/) (2021)
- [Causal Fourier Analysis on Directed Acyclic Graphs and Posets](https://mlsanity.com/paper/2209.07970/) (2022)
- [Graph Convolutions Enrich the Self-Attention in Transformers!](https://mlsanity.com/paper/2312.04234/) (2023)
- [Non-negative Weighted DAG Structure Learning](https://mlsanity.com/paper/2409.07880/) (2024)
- [Convolutional Learning on Directed Acyclic Graphs](https://mlsanity.com/paper/2405.03056/) (2024)
- [Network Topology Inference with Sparsity and Laplacian Constraints](https://mlsanity.com/paper/2309.00960/) (2023)
- [Learning Advanced Self-Attention for Linear Transformers in the Singular Value Domain](https://mlsanity.com/paper/2505.08516/) (2025)
- [Exploiting Non-Negativity in DAG Structure Learning](https://mlsanity.com/paper/2605.19947/) (2026)
- [A Tutorial on the Spectral Theory of Markov Chains](https://mlsanity.com/paper/2207.02296/) (2022)
- [Haar-Laplacian for directed graphs](https://mlsanity.com/paper/2411.15527/) (2024)
- [Directed Acyclic Graph Convolutional Networks](https://mlsanity.com/paper/2506.12218/) (2025)
- [Gauge-Equivariant Graph Networks via Self-Interference Cancellation](https://mlsanity.com/paper/2511.16062/) (2025)
- [Statistical Testing on Directed Graphs by Surrogate Data Generation](https://mlsanity.com/paper/2606.00758/) (2026)
- [Robust Hierarchical Clustering for Directed Networks: An Axiomatic Approach](https://mlsanity.com/paper/2108.07247/) (2021)
- [Lightweight and Interpretable Transformer via Mixed Graph Algorithm Unrolling for Traffic Forecast](https://mlsanity.com/paper/2505.13102/) (2025)
- [Non-negative DAG Learning from Time-Series Data](https://mlsanity.com/paper/2512.07267/) (2025)
- [Topology Identification and Inference over Graphs](https://mlsanity.com/paper/2512.10183/) (2025)
- [A Framework for Directed Hypergraph Signal Processing via tensor t-SVD](https://mlsanity.com/paper/2606.25112/) (2026)
- [Gauge-Invariant, Parameter-Insensitive Regularization for Potential Recovery from Flow on Directed Graphs](https://mlsanity.com/paper/2607.13609/) (2026)
- [TwinS-GCN: Spectral conjugate for Spectral Graph Convolutional Networks](https://mlsanity.com/paper/2609.32940/) (2026)
- [Signal Processing over Product DAGs: Causal Shifts and Filters](https://mlsanity.com/paper/2609.40275/) (2026)

## Abstract (arXiv)

This paper provides an overview of the current landscape of signal processing (SP) on directed graphs (digraphs). Directionality is inherent to many real-world (information, transportation, biological) networks and it should play an integral role in processing and learning from network data. We thus lay out a comprehensive review of recent advances in SP on digraphs, offering insights through comparisons with results available for undirected graphs, discussing emerging directions, establishing links with related areas in machine learning and causal inference in statistics, as well as illustrating their practical relevance to timely applications. To this end, we begin by surveying (orthonormal) signal representations and their graph frequency interpretations based on novel measures of signal variation for digraphs. We then move on to filtering, a central component in deriving a comprehensive theory of SP on digraphs. Indeed, through the lens of filter-based generative signal models, we explore a unified framework to study inverse problems (e.g., sampling and deconvolution on networks), statistical analysis of random signals, and topology inference of digraphs from nodal observations.