Spectral Graph Analysis for Predicting QoE Fairness Sensitivity in Wireless Communication Networks

The evaluation of Quality of Experience (QoE) fairness depends not only on its current state but, more critically, on its sensitivity to changes in Service Level Agreement (SLA) parameters. However, the academic community has long lacked a predictive method connecting underlying topology to high-level service fairness. To bridge this gap, this paper analyzes a QoE imbalance index ($I$) through the lens of spectral graph theory.Our core contribution is the proof of a novel exponential spectral upper bound. This bound reveals that the improvement of QoE fairness exhibits an exponential decay behavior only above a performance threshold determined jointly by network size and connectivity. Its core decay rate is dominated by the weaker of two factors: the SLA stringency ($a$) and the network's spectral gap ($cλ_2$). The upper bound unifies the service protocol and the topological bottleneck within a single performance bound formula for the first time.This theoretical relationship also reveals a clear bottleneck effect, where the system's fairness ceiling is determined by the weaker link between service parameters and network structure. This finding provides a bottleneck-driven principle for resource optimization in network design and enables goal-driven reverse engineering. Extensive numerical experiments on various random graph models and real-world network topologies robustly validate the correctness and universality of our analytical framework.