Direction-dependent nodal spectral sensitivity shapes dynamical timescales in complex networks

Directed network dynamics are inherently asymmetric, yet node-level spectral sensitivity often does not explicitly distinguish perturbation direction. Here we formulate an incoming-link-based nodal Fiedler contribution as a direction-aware node-level aggregation of Laplacian spectral sensitivity, measuring the first-order response of the real part of the relevant nonzero directed-Laplacian eigenvalue to a structured perturbation of all incoming links of a node. Building on first-order non-Hermitian perturbation theory, the formulation is defined under explicit assumptions of strong connectivity and spectral simplicity. Across motifs, synthetic ensembles, and empirical directed networks, we show that this incoming-link-based quantity is systematically associated with nodal relaxation and synchronization times, although the strength of the association depends strongly on topology. More importantly, comparison with the corresponding outgoing-link perturbation reveals a pronounced directional asymmetry: the two nodal sensitivities are generally not equivalent and can exhibit qualitatively different relations to nodal timescales. These results support direction-dependent node-level spectral sensitivity as a useful diagnostic feature of directed network dynamics and clarify both its explanatory value and its limitations.