Title: Statistical Testing on Directed Graphs by Surrogate Data Generation

Abstract

Graph signal processing has recently established itself as a robust analytical framework situated at the convergence of graph theory and signal processing. It offers methodologies for examining signals located on nodes while simultaneously considering the connectivity patterns defined by edges. These techniques have proven effective in diverse contexts, notably in the realm of statistical hypothesis testing. While non-parametric methods relying on surrogate data generation have already been developed for signals on undirected graphs, their application to directed graphs remains an unexplored area.

This study addresses this gap by first re-examining the concept of stationary graph signals within the context of directed graphs. By leveraging the eigendecomposition of the graph shift operator, we introduce a definition for directed graph wide-sense stationary signals. Building on this foundation, we propose a novel framework designed to generate surrogate graph signals that maintain their covariance structure, provided that stationarity assumptions hold. These surrogates allow for the construction of null distributions for test metrics, which then act as a benchmark for comparing against empirical data. To validate our approach, we present illustrative examples and a real-data application. These demonstrations compare the efficacy of our proposed framework against existing methods for undirected graphs and naive permutation techniques, thereby highlighting both the feasibility and the superior performance of our new approach.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC