Ranking Influential Spreaders Across Transmission Rates: Information Limits of Simulated Supervision and a Transmission-Aware Graph Neural Ranker

Which nodes start the largest outbreaks depends on how transmissible the process is, and the stochastic simulations that define the answer are noisy and expensive. We treat a finite batch of simulations as a noisy channel on the pairwise order of nodes. For any predictor independent of a label batch, the expected Kendall’s τ with that batch then cannot exceed the square root of the agreement between two independent batches. On 24 real networks at 13 transmission levels, one batch of 1000 runs per node misorders 0.9–5.9% of node pairs, and the misordering falls as the inverse square root of the number of runs. The estimated ceiling averages 0.956, and no method exceeds it in any of 304 network–level cells. Rankings at different levels differ by more than this noise in 80% of level pairs. A graph neural ranker that receives the transmission level as an input, trained on synthetic graphs with a pairwise cross-entropy objectiverv:absfilter, reaches a Kendall’s τb of 0.861, 90% of the ceiling. It leads the strongest ofrv:absreimpl three re-implemented learned rankers by 0.026 and propagation entropy, the strongest entropy-based centrality, by 0.030. Reporting accuracy against the noise ceiling separates model error from label noise.