# Statistical Testing on Directed Graphs by Surrogate Data Generation

arXiv: https://arxiv.org/abs/2606.00758 · HTML: https://mlsanity.com/paper/2606.00758/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 47 references that are in the map.
- First posted on arXiv 30 May 2026.

## Builds on (most cited first, 17 of 17)

- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [Diffusion Causal Models for Counterfactual Estimation](https://mlsanity.com/paper/2202.10166/) (2022)
- [Discrete Signal Processing on Graphs: Frequency Analysis](https://mlsanity.com/paper/1307.0468/) (2013)
- [Graph Spectral Image Processing](https://mlsanity.com/paper/1801.04749/) (2018)
- [Stationary Graph Processes and Spectral Estimation](https://mlsanity.com/paper/1603.04667/) (2016)
- [Stationary signal processing on graphs](https://mlsanity.com/paper/1601.02522/) (2016)
- [Signal Processing on Directed Graphs](https://mlsanity.com/paper/2008.00586/) (2020)
- [Forecasting Time Series with VARMA Recursions on Graphs](https://mlsanity.com/paper/1810.08581/) (2018)
- [Graph Learning from Filtered Signals: Graph System and Diffusion Kernel Identification](https://mlsanity.com/paper/1803.02553/) (2018)
- [A Directed Graph Fourier Transform with Spread Frequency Components](https://mlsanity.com/paper/1804.03000/) (2018)
- [A Graph Signal Processing Perspective of Network Multiple Hypothesis Testing with False Discovery Rate Control](https://mlsanity.com/paper/2408.03142/) (2024)
- [BUILD with Precision: Bottom-Up Inference of Linear DAGs](https://mlsanity.com/paper/2512.16111/) (2025)
- [Digraph Signal Processing with Generalized Boundary Conditions](https://mlsanity.com/paper/2005.09762/) (2020)
- [Frequency analysis and filter design for directed graphs with polar decomposition](https://mlsanity.com/paper/2312.11421/) (2023)
- [Causal Link Discovery with Unequal Edge Error Tolerance](https://mlsanity.com/paper/2507.21570/) (2025)
- [Graph Learning from Gaussian and Stationary Graph Signals](https://mlsanity.com/paper/2303.07041/) (2023)
- [Hilbert Transform on Graphs: Let There Be Phase](https://mlsanity.com/paper/2412.18501/) (2024)

## Built on by (most cited first, 1 of 1)

- [TwinS-GCN: Spectral conjugate for Spectral Graph Convolutional Networks](https://mlsanity.com/paper/2609.32940/) (2026)

## Abstract (arXiv)

In recent years, graph signal processing has emerged as a powerful framework at the intersection of signal processing and graph theory, providing tools for the analysis of signals defined on nodes while accounting for their relationships represented by edges. These tools have been successfully applied to various settings, including statistical hypothesis testing. In particular, non-parametric approaches based on surrogate generation have been proposed for signals on undirected graphs. However, they are yet to be extended to directed graphs. In this work, we first revisit the notion of stationary graph signals on directed graphs. Specifically, and through the eigendecomposition of the graph shift operator, we define directed graph wide-sense stationary signals. Then, we propose a new framework to generate surrogate graph signals that preserve covariance structure under stationarity assumptions. Null distributions of the test metric can then be constructed from these surrogates and serve as a reference for the empirical data. Finally, we provide guiding examples and an application on real data, in which we compare the performance of our framework with existing techniques for undirected graphs or based on naive permutation, demonstrating feasibility and superiority of the proposed approach.