Spectral Efficiency Centrality: An Efficient Spectral Approach for Influential Node Identification in Temporal Networks

Abstract

Centrality measures play a vital role in identifying influential nodes in evolving networks. While existing temporal centrality measures primarily rely on local structural properties or temporal paths, spectral node-removal approaches have been largely limited to static networks. To bridge this gap, we propose Spectral Efficiency Centrality (SEC), a temporal spectral centrality framework that quantifies node importance by evaluating the change in spectral radius caused by node removal across temporal snapshots. By capturing the global structural influence of nodes throughout network evolution, SEC identifies nodes that are critical for preserving the structural connectivity and efficiency of temporal networks. To improve computational scalability, we further develop an efficient approximation, ASEC, based on Perron-Frobenius theory and first-order eigenvalue perturbation. ASEC requires only the leading eigenpair and avoids repeated eigendecomposition, making it suitable for large temporal networks. Extensive experiments on multiple real-world temporal datasets demonstrate that SEC and ASEC outperform existing baseline centrality measures in identifying influential nodes under SI, SIS, and IC diffusion models. Statistical significance and robustness analyses further confirm their effectiveness, while ASEC offers a computationally efficient solution for large-scale temporal networks.