Network Monitoring Using Spectrum-Reduced Laplacian Energy Bounds

Monitoring structural changes in large-scale networks is important in many applications, including communication, social, collaboration, and transportation systems. In this paper, we apply the optimized parametric spectrum-reduced bounds for Laplacian energy developed in our previous theoretical work to the problem of structural network monitoring. The proposed framework evaluates optimized lower and upper bounds together with spectral variance, the third central spectral moment, and algebraic connectivity using only a reduced set of spectral quantities and graph invariants. A voting-based decision mechanism is employed to classify the structural state of a network during its evolution. The framework is evaluated on six benchmark datasets representing different classes of real-world networks under four structural modification scenarios: line addition, line removal, targeted hub failure and rewiring. The experimental results show that gradual edge modifications produce relatively small changes in the monitoring indicators, whereas targeted hub failures lead to larger variations in the optimized bounds and the optimization gap. The study demonstrates the practical use of the proposed spectrum-reduced framework for monitoring structural changes without repeated computation of the complete Laplacian spectrum.