Operationalization Matters: When Graph-Aware Learning Adds Value for IC-Based Influence Approximation
Approximating Monte Carlo Independent Cascade (MC-IC) influence rankings with a learned surrogate is only meaningful if the target itself is clearly defined. We study this dependency on the Twitch Gamers graph under two IC operationalizations, keeping the graph, labeled-node sample, split, Monte Carlo budget, and evaluation protocol fixed while using regime-aligned feature policies. Under the structural weighted-cascade regime, binary top-k labels are too unstable for the primary target; in this setting, the best raw-attribute GNN, GCN, remains below degree centrality (ρ = 0.808 vs. 0.826). Under the source-community operationalization, degree centrality becomes uninformative (ρ = −0.006), and raw-attribute GraphSAGE outperforms the pre-specified flat linear-regression (LR) baseline (ρ = 0.915 vs. 0.884). Trained surrogates provide sub-second full-graph inference, whereas MC label generation takes hundreds to about two thousand seconds on the frozen labeled subset. The central finding is conditional: on this graph, neighborhood-aware surrogates add value beyond strong structural, flat, and shallow-embedding alternatives when the target construction moves influence signal away from local degree structure. A supplementary 1-hop neighbor-aggregation diagnostic reaches a Spearman correlation comparable to that of standard Graph-SAGE in the source-community regime, suggesting that part of the observed gain may be attributable to local neighborhood aggregation rather than to learned message passing specifically. The source code and dataset are available at https://github.com/qvinhx89/operationalization-matters-influence.