How to test whether signals on directed networks are statistically real?

Graph signal processing lets you analyze data living on networked nodes while respecting their connections. Testing whether observed patterns are statistically significant is hard—especially on directed networks. This work extends surrogate data methods (which generate fake but realistic alternatives under null assumptions) to directed graphs by preserving the covariance structure of stationary signals. The framework outperforms naive permutation tests and existing undirected techniques on real data.