Networks model interactions in complex systems, but traditional features, such as edge counts or centrality, fail to capture their underlying generative processes. While random graph models offer a statistical framework, non-parametric approaches are often needed since the true generative mechanism is unknown. Previous spectral methods, which utilize the eigenvalues of undirected graphs, have enabled tasks such as network comparison and causality detection. However, these methods are limited to undirected graphs, ignoring the directional relationships—such as information flow or regulation—present in many real-world systems. To address this, we extend the spectral analysis to directed graphs by using the full spectrum (both real and imaginary parts) of their asymmetric adjacency matrices. Unlike symmetrizing approaches, our method preserves directional information, enabling more accurate statistical inference in directed networks across various fields, including social science, biology, and communications.