Hierarchical knowledge distillation framework for efficient node influence prediction in large-scale complex networks

Node influence prediction is fundamental to epidemic control, viral marketing, and infrastructure resilience, yet traditional susceptible-infected-recovered (SIR) simulations require [Formula: see text] computational operations, rendering real-time applications infeasible for large-scale networks. This paper presents HKD-NIP, a hierarchical knowledge distillation framework that achieves simulation-level accuracy while reducing computational time by 89% and required SIR simulations by 90% through strategic use of only 5-10% labeled nodes. Our dual-teacher architecture employs a general teacher trained on 36 diverse synthetic networks spanning Barabási-Albert, Erdős-Rényi, and Watts-Strogatz topologies to capture transferable structural patterns, while a domain-specific teacher fine-tunes this knowledge using stratified sampling. A lightweight LightGCN-based student model distills knowledge through soft label supervision and contrastive representation alignment, enabling sub-second inference. The hierarchical two-stage distillation is theoretically motivated: the general-to-domain teacher cascade reduces the structural domain gap incrementally, enabling the student to exploit both universal and network-specific propagation patterns-a property that single-stage distillation cannot achieve. Experiments across eight real-world datasets demonstrate Kendall's τ of 0.921 (15.4% improvement over state-of-the-art AGNN) and MSE of 0.0085 (46% improvement over baselines). Statistical validation reports large effect sizes (Cohen's [Formula: see text] versus all baselines). Scalability analysis on synthetic networks up to 500,000 nodes confirms practical execution times while traditional SIR simulation becomes prohibitively expensive. The framework successfully bridges the gap between computational efficiency and prediction accuracy for real-time deployment.